id	sid	tid	token	lemma	pos
ejpam-1234	1	1	6_matsumura.dvi	6_matsumura.dvi	NUM
ejpam-1234	1	2	european	european	ADJ
ejpam-1234	1	3	journal	journal	NOUN
ejpam-1234	1	4	of	of	ADP
ejpam-1234	1	5	pure	pure	ADJ
ejpam-1234	1	6	and	and	CCONJ
ejpam-1234	1	7	applied	apply	VERB
ejpam-1234	1	8	mathematics	mathematic	NOUN
ejpam-1234	1	9	vol	vol	NOUN
ejpam-1234	1	10	.	.	PROPN
ejpam-1234	1	11	5	5	NUM
ejpam-1234	1	12	,	,	PUNCT
ejpam-1234	1	13	no	no	INTJ
ejpam-1234	1	14	.	.	NOUN
ejpam-1234	1	15	4	4	NUM
ejpam-1234	1	16	,	,	PUNCT
ejpam-1234	1	17	2012	2012	NUM
ejpam-1234	1	18	,	,	PUNCT
ejpam-1234	1	19	492	492	NUM
ejpam-1234	1	20	-	-	SYM
ejpam-1234	1	21	510	510	NUM
ejpam-1234	1	22	issn	issn	PROPN
ejpam-1234	1	23	1307	1307	NUM
ejpam-1234	1	24	-	-	SYM
ejpam-1234	1	25	5543	5543	NUM
ejpam-1234	1	26	–	–	PUNCT
ejpam-1234	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1234	1	28	stringy	stringy	ADJ
ejpam-1234	1	29	and	and	CCONJ
ejpam-1234	1	30	orbiforld	orbiforld	NOUN
ejpam-1234	1	31	cohomology	cohomology	NOUN
ejpam-1234	1	32	of	of	ADP
ejpam-1234	1	33	wreath	wreath	NOUN
ejpam-1234	1	34	product	product	NOUN
ejpam-1234	1	35	orbifolds	orbifolds	AUX
ejpam-1234	1	36	tomoo	tomoo	VERB
ejpam-1234	1	37	matsumura	matsumura	ADJ
ejpam-1234	1	38	department	department	PROPN
ejpam-1234	1	39	of	of	ADP
ejpam-1234	1	40	mathematical	mathematical	ADJ
ejpam-1234	1	41	sciences	sciences	PROPN
ejpam-1234	1	42	,	,	PUNCT
ejpam-1234	1	43	asarc	asarc	NOUN
ejpam-1234	1	44	,	,	PUNCT
ejpam-1234	1	45	kaist	kaist	ADJ
ejpam-1234	1	46	,	,	PUNCT
ejpam-1234	1	47	291	291	NUM
ejpam-1234	1	48	daehak	daehak	NOUN
ejpam-1234	1	49	-	-	PUNCT
ejpam-1234	1	50	ro	ro	NOUN
ejpam-1234	1	51	yuseong	yuseong	PROPN
ejpam-1234	1	52	-	-	PUNCT
ejpam-1234	1	53	gu	gu	NOUN
ejpam-1234	1	54	,	,	PUNCT
ejpam-1234	1	55	daejeon	daejeon	VERB
ejpam-1234	1	56	305	305	NUM
ejpam-1234	1	57	-	-	SYM
ejpam-1234	1	58	701	701	NUM
ejpam-1234	1	59	,	,	PUNCT
ejpam-1234	1	60	south	south	PROPN
ejpam-1234	1	61	korea	korea	PROPN
ejpam-1234	1	62	abstract	abstract	NOUN
ejpam-1234	1	63	.	.	PUNCT
ejpam-1234	2	1	let	let	VERB
ejpam-1234	2	2	[	[	X
ejpam-1234	2	3	x	x	X
ejpam-1234	2	4	/	/	SYM
ejpam-1234	2	5	g	g	NOUN
ejpam-1234	2	6	]	]	PUNCT
ejpam-1234	2	7	be	be	AUX
ejpam-1234	2	8	an	an	DET
ejpam-1234	2	9	orbifold	orbifold	NOUN
ejpam-1234	2	10	which	which	PRON
ejpam-1234	2	11	is	be	AUX
ejpam-1234	2	12	a	a	DET
ejpam-1234	2	13	global	global	ADJ
ejpam-1234	2	14	quotient	quotient	NOUN
ejpam-1234	2	15	of	of	ADP
ejpam-1234	2	16	a	a	DET
ejpam-1234	2	17	compact	compact	ADJ
ejpam-1234	2	18	almost	almost	ADV
ejpam-1234	2	19	complex	complex	ADJ
ejpam-1234	2	20	manifold	manifold	ADJ
ejpam-1234	2	21	x	x	PUNCT
ejpam-1234	2	22	by	by	SCONJ
ejpam-1234	2	23	a	a	DET
ejpam-1234	2	24	finite	finite	ADJ
ejpam-1234	2	25	group	group	NOUN
ejpam-1234	2	26	g.	g.	PROPN
ejpam-1234	2	27	let	let	VERB
ejpam-1234	2	28	σn	σn	NOUN
ejpam-1234	2	29	be	be	AUX
ejpam-1234	2	30	the	the	DET
ejpam-1234	2	31	symmetric	symmetric	ADJ
ejpam-1234	2	32	group	group	NOUN
ejpam-1234	2	33	on	on	ADP
ejpam-1234	2	34	n	n	DET
ejpam-1234	2	35	letters	letter	NOUN
ejpam-1234	2	36	.	.	PUNCT
ejpam-1234	3	1	their	their	PRON
ejpam-1234	3	2	semidirect	semidirect	NOUN
ejpam-1234	3	3	product	product	NOUN
ejpam-1234	3	4	gn	gn	PROPN
ejpam-1234	3	5	⋊σn	⋊σn	PROPN
ejpam-1234	3	6	is	be	AUX
ejpam-1234	3	7	called	call	VERB
ejpam-1234	3	8	the	the	DET
ejpam-1234	3	9	wreath	wreath	NOUN
ejpam-1234	3	10	product	product	NOUN
ejpam-1234	3	11	of	of	ADP
ejpam-1234	3	12	g	g	PROPN
ejpam-1234	3	13	and	and	CCONJ
ejpam-1234	3	14	it	it	PRON
ejpam-1234	3	15	naturally	naturally	ADV
ejpam-1234	3	16	acts	act	VERB
ejpam-1234	3	17	on	on	ADP
ejpam-1234	3	18	the	the	DET
ejpam-1234	3	19	n	n	ADV
ejpam-1234	3	20	-	-	ADJ
ejpam-1234	3	21	fold	fold	ADJ
ejpam-1234	3	22	product	product	NOUN
ejpam-1234	3	23	x	x	PUNCT
ejpam-1234	3	24	n	n	CCONJ
ejpam-1234	3	25	,	,	PUNCT
ejpam-1234	3	26	yielding	yield	VERB
ejpam-1234	3	27	the	the	DET
ejpam-1234	3	28	orbifold	orbifold	NOUN
ejpam-1234	3	29	[	[	X
ejpam-1234	3	30	x	x	X
ejpam-1234	3	31	n/(gn⋊σn	n/(gn⋊σn	NOUN
ejpam-1234	3	32	)	)	PUNCT
ejpam-1234	3	33	]	]	PUNCT
ejpam-1234	3	34	.	.	PUNCT
ejpam-1234	4	1	let	let	VERB
ejpam-1234	4	2	h	h	NOUN
ejpam-1234	4	3	(	(	PUNCT
ejpam-1234	4	4	x	x	NOUN
ejpam-1234	4	5	n	n	CCONJ
ejpam-1234	4	6	,	,	PUNCT
ejpam-1234	4	7	gn⋊σn	gn⋊σn	PROPN
ejpam-1234	4	8	)	)	PUNCT
ejpam-1234	4	9	be	be	AUX
ejpam-1234	4	10	the	the	DET
ejpam-1234	4	11	stringy	stringy	ADJ
ejpam-1234	4	12	cohomology	cohomology	NOUN
ejpam-1234	5	1	[	[	X
ejpam-1234	5	2	7	7	NUM
ejpam-1234	5	3	,	,	PUNCT
ejpam-1234	5	4	10	10	NUM
ejpam-1234	5	5	]	]	PUNCT
ejpam-1234	5	6	of	of	ADP
ejpam-1234	5	7	the	the	DET
ejpam-1234	5	8	(	(	PUNCT
ejpam-1234	5	9	gn⋊σn)-space	gn⋊σn)-space	NOUN
ejpam-1234	5	10	x	x	SYM
ejpam-1234	5	11	n.	n.	NOUN
ejpam-1234	5	12	we	we	PRON
ejpam-1234	5	13	prove	prove	VERB
ejpam-1234	5	14	that	that	SCONJ
ejpam-1234	5	15	the	the	DET
ejpam-1234	5	16	space	space	NOUN
ejpam-1234	5	17	gn	gn	NOUN
ejpam-1234	5	18	-	-	PUNCT
ejpam-1234	5	19	invariants	invariant	NOUN
ejpam-1234	5	20	of	of	ADP
ejpam-1234	5	21	h	h	PROPN
ejpam-1234	5	22	(	(	PUNCT
ejpam-1234	5	23	x	x	SYM
ejpam-1234	5	24	n	n	CCONJ
ejpam-1234	5	25	,	,	PUNCT
ejpam-1234	5	26	gn	gn	PROPN
ejpam-1234	5	27	⋊σn	⋊σn	PROPN
ejpam-1234	5	28	)	)	PUNCT
ejpam-1234	5	29	is	be	AUX
ejpam-1234	5	30	isomorphic	isomorphic	ADJ
ejpam-1234	5	31	to	to	ADP
ejpam-1234	5	32	the	the	DET
ejpam-1234	5	33	algebra	algebra	PROPN
ejpam-1234	5	34	hor	hor	PROPN
ejpam-1234	5	35	b([x	b([x	ADJ
ejpam-1234	5	36	/	/	SYM
ejpam-1234	5	37	g]){σn	g]){σn	NOUN
ejpam-1234	5	38	}	}	PUNCT
ejpam-1234	5	39	introduced	introduce	VERB
ejpam-1234	5	40	by	by	ADP
ejpam-1234	5	41	lehn	lehn	NOUN
ejpam-1234	5	42	and	and	CCONJ
ejpam-1234	5	43	sorger	sorger	NOUN
ejpam-1234	6	1	[	[	X
ejpam-1234	6	2	14	14	NUM
ejpam-1234	6	3	]	]	PUNCT
ejpam-1234	6	4	,	,	PUNCT
ejpam-1234	6	5	where	where	SCONJ
ejpam-1234	6	6	hor	hor	PROPN
ejpam-1234	6	7	b([x	b([x	PROPN
ejpam-1234	6	8	/	/	SYM
ejpam-1234	6	9	g	g	NOUN
ejpam-1234	6	10	]	]	PUNCT
ejpam-1234	6	11	)	)	PUNCT
ejpam-1234	6	12	is	be	AUX
ejpam-1234	6	13	the	the	DET
ejpam-1234	6	14	chen	chen	PROPN
ejpam-1234	6	15	-	-	PUNCT
ejpam-1234	6	16	ruan	ruan	PROPN
ejpam-1234	6	17	orbifold	orbifold	NOUN
ejpam-1234	6	18	cohomology	cohomology	NOUN
ejpam-1234	6	19	of	of	ADP
ejpam-1234	6	20	[	[	X
ejpam-1234	6	21	x	x	X
ejpam-1234	6	22	/	/	SYM
ejpam-1234	6	23	g	g	NOUN
ejpam-1234	6	24	]	]	PUNCT
ejpam-1234	6	25	.	.	PUNCT
ejpam-1234	7	1	we	we	PRON
ejpam-1234	7	2	also	also	ADV
ejpam-1234	7	3	prove	prove	VERB
ejpam-1234	7	4	that	that	SCONJ
ejpam-1234	7	5	,	,	PUNCT
ejpam-1234	7	6	if	if	SCONJ
ejpam-1234	7	7	x	x	PRON
ejpam-1234	7	8	is	be	AUX
ejpam-1234	7	9	a	a	DET
ejpam-1234	7	10	projective	projective	ADJ
ejpam-1234	7	11	surface	surface	NOUN
ejpam-1234	7	12	with	with	ADP
ejpam-1234	7	13	trivial	trivial	ADJ
ejpam-1234	7	14	canonical	canonical	ADJ
ejpam-1234	7	15	class	class	NOUN
ejpam-1234	7	16	and	and	CCONJ
ejpam-1234	7	17	y	y	PROPN
ejpam-1234	7	18	is	be	AUX
ejpam-1234	7	19	a	a	DET
ejpam-1234	7	20	crepant	crepant	ADJ
ejpam-1234	7	21	resolution	resolution	NOUN
ejpam-1234	7	22	of	of	ADP
ejpam-1234	7	23	x	x	PROPN
ejpam-1234	7	24	/	/	SYM
ejpam-1234	7	25	g	g	NOUN
ejpam-1234	7	26	,	,	PUNCT
ejpam-1234	7	27	then	then	ADV
ejpam-1234	7	28	the	the	DET
ejpam-1234	7	29	hilbert	hilbert	PROPN
ejpam-1234	7	30	scheme	scheme	NOUN
ejpam-1234	7	31	of	of	ADP
ejpam-1234	7	32	n	n	NUM
ejpam-1234	7	33	points	point	NOUN
ejpam-1234	7	34	on	on	ADP
ejpam-1234	7	35	y	y	PROPN
ejpam-1234	7	36	,	,	PUNCT
ejpam-1234	7	37	denoted	denote	VERB
ejpam-1234	7	38	by	by	ADP
ejpam-1234	7	39	y	y	PROPN
ejpam-1234	7	40	[	[	X
ejpam-1234	7	41	n	n	X
ejpam-1234	7	42	]	]	PUNCT
ejpam-1234	7	43	,	,	PUNCT
ejpam-1234	7	44	is	be	AUX
ejpam-1234	7	45	a	a	DET
ejpam-1234	7	46	crepant	crepant	ADJ
ejpam-1234	7	47	resolution	resolution	NOUN
ejpam-1234	7	48	of	of	ADP
ejpam-1234	7	49	x	x	PUNCT
ejpam-1234	7	50	n/(gn	n/(gn	PROPN
ejpam-1234	7	51	⋊	⋊	NUM
ejpam-1234	7	52	σn	σn	NOUN
ejpam-1234	7	53	)	)	PUNCT
ejpam-1234	7	54	.	.	PUNCT
ejpam-1234	8	1	furthermore	furthermore	ADV
ejpam-1234	8	2	,	,	PUNCT
ejpam-1234	8	3	if	if	SCONJ
ejpam-1234	8	4	h∗(y	h∗(y	PROPN
ejpam-1234	8	5	)	)	PUNCT
ejpam-1234	8	6	is	be	AUX
ejpam-1234	8	7	isomorphic	isomorphic	ADJ
ejpam-1234	8	8	to	to	ADP
ejpam-1234	8	9	hor	hor	PROPN
ejpam-1234	8	10	b([x	b([x	PROPN
ejpam-1234	8	11	/	/	SYM
ejpam-1234	8	12	g	g	NOUN
ejpam-1234	8	13	]	]	PUNCT
ejpam-1234	8	14	)	)	PUNCT
ejpam-1234	8	15	as	as	ADP
ejpam-1234	8	16	frobenius	frobenius	ADJ
ejpam-1234	8	17	algebras	algebra	NOUN
ejpam-1234	8	18	,	,	PUNCT
ejpam-1234	8	19	then	then	ADV
ejpam-1234	8	20	h∗(y	h∗(y	PROPN
ejpam-1234	8	21	[	[	X
ejpam-1234	8	22	n	n	X
ejpam-1234	8	23	]	]	PUNCT
ejpam-1234	8	24	)	)	PUNCT
ejpam-1234	8	25	is	be	AUX
ejpam-1234	8	26	isomorphic	isomorphic	ADJ
ejpam-1234	8	27	to	to	ADP
ejpam-1234	8	28	h∗	h∗	PROPN
ejpam-1234	8	29	or	or	CCONJ
ejpam-1234	8	30	b	b	PROPN
ejpam-1234	8	31	(	(	PUNCT
ejpam-1234	8	32	[	[	X
ejpam-1234	8	33	x	x	X
ejpam-1234	8	34	n/(gn	n/(gn	PROPN
ejpam-1234	8	35	⋊	⋊	NUM
ejpam-1234	8	36	σn	σn	NOUN
ejpam-1234	8	37	)	)	PUNCT
ejpam-1234	8	38	]	]	PUNCT
ejpam-1234	8	39	)	)	PUNCT
ejpam-1234	8	40	as	as	ADP
ejpam-1234	8	41	rings	ring	NOUN
ejpam-1234	8	42	.	.	PUNCT
ejpam-1234	9	1	thus	thus	ADV
ejpam-1234	9	2	we	we	PRON
ejpam-1234	9	3	verify	verify	VERB
ejpam-1234	9	4	a	a	DET
ejpam-1234	9	5	special	special	ADJ
ejpam-1234	9	6	case	case	NOUN
ejpam-1234	9	7	of	of	ADP
ejpam-1234	9	8	the	the	DET
ejpam-1234	9	9	cohomological	cohomological	ADJ
ejpam-1234	9	10	hyper	hyper	ADJ
ejpam-1234	9	11	-	-	ADJ
ejpam-1234	9	12	kähler	kähler	NOUN
ejpam-1234	9	13	resolution	resolution	NOUN
ejpam-1234	9	14	conjecture	conjecture	NOUN
ejpam-1234	9	15	due	due	ADJ
ejpam-1234	9	16	to	to	ADP
ejpam-1234	9	17	ruan	ruan	NOUN
ejpam-1234	9	18	[	[	X
ejpam-1234	9	19	22	22	NUM
ejpam-1234	9	20	]	]	PUNCT
ejpam-1234	9	21	.	.	PUNCT
ejpam-1234	10	1	2010	2010	NUM
ejpam-1234	10	2	mathematics	mathematic	NOUN
ejpam-1234	10	3	subject	subject	NOUN
ejpam-1234	10	4	classifications	classification	NOUN
ejpam-1234	10	5	:	:	PUNCT
ejpam-1234	10	6	14n35	14n35	NUM
ejpam-1234	10	7	14a20	14a20	NUM
ejpam-1234	10	8	14e15	14e15	NUM
ejpam-1234	11	1	14j81	14j81	NUM
ejpam-1234	11	2	14l30	14l30	NUM
ejpam-1234	11	3	key	key	ADJ
ejpam-1234	11	4	words	word	NOUN
ejpam-1234	11	5	and	and	CCONJ
ejpam-1234	11	6	phrases	phrase	NOUN
ejpam-1234	11	7	:	:	PUNCT
ejpam-1234	11	8	orbifold	orbifold	ADJ
ejpam-1234	11	9	,	,	PUNCT
ejpam-1234	11	10	gromov	gromov	NOUN
ejpam-1234	11	11	-	-	PUNCT
ejpam-1234	11	12	witten	witten	PROPN
ejpam-1234	11	13	theory	theory	NOUN
ejpam-1234	11	14	,	,	PUNCT
ejpam-1234	11	15	frobenius	frobenius	ADJ
ejpam-1234	11	16	algebra	algebra	NOUN
ejpam-1234	11	17	,	,	PUNCT
ejpam-1234	11	18	symmetric	symmetric	ADJ
ejpam-1234	11	19	product	product	NOUN
ejpam-1234	11	20	,	,	PUNCT
ejpam-1234	11	21	wreath	wreath	NOUN
ejpam-1234	11	22	product	product	NOUN
ejpam-1234	11	23	1	1	NUM
ejpam-1234	11	24	.	.	PUNCT
ejpam-1234	11	25	introduction	introduction	NOUN
ejpam-1234	11	26	the	the	DET
ejpam-1234	11	27	stringy	stringy	ADJ
ejpam-1234	11	28	cohomology	cohomology	NOUN
ejpam-1234	11	29	h	h	NOUN
ejpam-1234	11	30	(	(	PUNCT
ejpam-1234	11	31	x	x	INTJ
ejpam-1234	11	32	,	,	PUNCT
ejpam-1234	11	33	g	g	NOUN
ejpam-1234	11	34	)	)	PUNCT
ejpam-1234	11	35	of	of	ADP
ejpam-1234	11	36	an	an	DET
ejpam-1234	11	37	almost	almost	ADV
ejpam-1234	11	38	complex	complex	ADJ
ejpam-1234	11	39	manifold	manifold	ADJ
ejpam-1234	11	40	x	x	PUNCT
ejpam-1234	11	41	with	with	ADP
ejpam-1234	11	42	an	an	DET
ejpam-1234	11	43	action	action	NOUN
ejpam-1234	11	44	of	of	ADP
ejpam-1234	11	45	a	a	DET
ejpam-1234	11	46	finite	finite	ADJ
ejpam-1234	11	47	group	group	NOUN
ejpam-1234	11	48	g	g	PROPN
ejpam-1234	11	49	was	be	AUX
ejpam-1234	11	50	first	first	ADV
ejpam-1234	11	51	introduced	introduce	VERB
ejpam-1234	11	52	by	by	ADP
ejpam-1234	11	53	fantechi	fantechi	NOUN
ejpam-1234	11	54	-	-	PUNCT
ejpam-1234	11	55	göttsche	göttsche	NOUN
ejpam-1234	12	1	[	[	X
ejpam-1234	12	2	7	7	NUM
ejpam-1234	12	3	]	]	PUNCT
ejpam-1234	12	4	and	and	CCONJ
ejpam-1234	12	5	studied	study	VERB
ejpam-1234	12	6	further	far	ADV
ejpam-1234	12	7	by	by	ADP
ejpam-1234	12	8	jarviskaufmann	jarviskaufmann	NOUN
ejpam-1234	12	9	-	-	PUNCT
ejpam-1234	12	10	kimura	kimura	NOUN
ejpam-1234	12	11	[	[	X
ejpam-1234	12	12	10	10	NUM
ejpam-1234	12	13	,	,	PUNCT
ejpam-1234	12	14	11	11	NUM
ejpam-1234	12	15	]	]	PUNCT
ejpam-1234	12	16	.	.	PUNCT
ejpam-1234	13	1	it	it	PRON
ejpam-1234	13	2	is	be	AUX
ejpam-1234	13	3	a	a	DET
ejpam-1234	13	4	g	g	NOUN
ejpam-1234	13	5	-	-	PUNCT
ejpam-1234	13	6	frobenius	frobenius	NOUN
ejpam-1234	13	7	algebra	algebra	NOUN
ejpam-1234	13	8	[	[	X
ejpam-1234	13	9	23	23	NUM
ejpam-1234	13	10	,	,	PUNCT
ejpam-1234	13	11	12	12	NUM
ejpam-1234	13	12	]	]	PUNCT
ejpam-1234	13	13	which	which	PRON
ejpam-1234	13	14	is	be	AUX
ejpam-1234	13	15	a	a	DET
ejpam-1234	13	16	g	g	NOUN
ejpam-1234	13	17	-	-	PUNCT
ejpam-1234	13	18	equivariant	equivariant	ADJ
ejpam-1234	13	19	generalization	generalization	NOUN
ejpam-1234	13	20	of	of	ADP
ejpam-1234	13	21	frobenius	frobenius	NOUN
ejpam-1234	13	22	algebras	algebra	NOUN
ejpam-1234	13	23	and	and	CCONJ
ejpam-1234	13	24	the	the	DET
ejpam-1234	13	25	space	space	NOUN
ejpam-1234	13	26	of	of	ADP
ejpam-1234	13	27	its	its	PRON
ejpam-1234	13	28	g	g	NOUN
ejpam-1234	13	29	-	-	PUNCT
ejpam-1234	13	30	invariants	invariant	NOUN
ejpam-1234	13	31	is	be	AUX
ejpam-1234	13	32	the	the	DET
ejpam-1234	13	33	chen	chen	PROPN
ejpam-1234	13	34	-	-	PUNCT
ejpam-1234	13	35	ruan	ruan	PROPN
ejpam-1234	13	36	orbifold	orbifold	PROPN
ejpam-1234	13	37	cohomology	cohomology	PROPN
ejpam-1234	13	38	h∗	h∗	PROPN
ejpam-1234	13	39	or	or	CCONJ
ejpam-1234	13	40	b	b	PROPN
ejpam-1234	13	41	(	(	PUNCT
ejpam-1234	13	42	[	[	X
ejpam-1234	13	43	x	x	X
ejpam-1234	13	44	/	/	SYM
ejpam-1234	13	45	g	g	NOUN
ejpam-1234	13	46	]	]	PUNCT
ejpam-1234	13	47	)	)	PUNCT
ejpam-1234	13	48	introduced	introduce	VERB
ejpam-1234	13	49	in	in	ADP
ejpam-1234	13	50	[	[	X
ejpam-1234	13	51	4	4	NUM
ejpam-1234	13	52	]	]	PUNCT
ejpam-1234	13	53	.	.	PUNCT
ejpam-1234	14	1	let	let	VERB
ejpam-1234	14	2	w	w	NOUN
ejpam-1234	14	3	be	be	AUX
ejpam-1234	14	4	an	an	DET
ejpam-1234	14	5	orbifold	orbifold	NOUN
ejpam-1234	14	6	and	and	CCONJ
ejpam-1234	14	7	π	π	NOUN
ejpam-1234	14	8	:	:	PUNCT
ejpam-1234	14	9	y	y	PROPN
ejpam-1234	14	10	→	→	PUNCT
ejpam-1234	14	11	w	w	AUX
ejpam-1234	14	12	be	be	AUX
ejpam-1234	14	13	a	a	DET
ejpam-1234	14	14	hyper	hyper	ADJ
ejpam-1234	14	15	-	-	ADJ
ejpam-1234	14	16	kähler	kähler	ADJ
ejpam-1234	14	17	resolution	resolution	NOUN
ejpam-1234	14	18	of	of	ADP
ejpam-1234	14	19	the	the	DET
ejpam-1234	14	20	coarse	coarse	ADJ
ejpam-1234	14	21	moduli	moduli	PROPN
ejpam-1234	14	22	space	space	PROPN
ejpam-1234	14	23	w	w	PROPN
ejpam-1234	14	24	of	of	ADP
ejpam-1234	14	25	w	w	PROPN
ejpam-1234	14	26	.	.	PUNCT
ejpam-1234	15	1	ruan	ruan	PROPN
ejpam-1234	15	2	’s	’s	PART
ejpam-1234	15	3	cohomological	cohomological	ADJ
ejpam-1234	15	4	hyper	hyper	ADJ
ejpam-1234	15	5	-	-	ADJ
ejpam-1234	15	6	kähler	kähler	NOUN
ejpam-1234	15	7	resolution	resolution	NOUN
ejpam-1234	15	8	conjecture	conjecture	NOUN
ejpam-1234	16	1	[	[	X
ejpam-1234	16	2	22	22	NUM
ejpam-1234	16	3	]	]	PUNCT
ejpam-1234	16	4	predicts	predict	VERB
ejpam-1234	16	5	that	that	SCONJ
ejpam-1234	16	6	the	the	DET
ejpam-1234	16	7	ordinary	ordinary	ADJ
ejpam-1234	16	8	cohomology	cohomology	NOUN
ejpam-1234	16	9	ring	ring	NOUN
ejpam-1234	16	10	of	of	ADP
ejpam-1234	16	11	y	y	PROPN
ejpam-1234	16	12	is	be	AUX
ejpam-1234	16	13	isomorphic	isomorphic	ADJ
ejpam-1234	16	14	to	to	ADP
ejpam-1234	16	15	the	the	DET
ejpam-1234	16	16	orbifold	orbifold	ADJ
ejpam-1234	16	17	cohomology	cohomology	NOUN
ejpam-1234	16	18	ring	ring	NOUN
ejpam-1234	16	19	of	of	ADP
ejpam-1234	16	20	w	w	PROPN
ejpam-1234	16	21	over	over	ADP
ejpam-1234	16	22	c	c	NOUN
ejpam-1234	16	23	-	-	PUNCT
ejpam-1234	16	24	coefficients	coefficient	NOUN
ejpam-1234	16	25	.	.	PUNCT
ejpam-1234	17	1	this	this	PRON
ejpam-1234	17	2	is	be	AUX
ejpam-1234	17	3	a	a	DET
ejpam-1234	17	4	special	special	ADJ
ejpam-1234	17	5	case	case	NOUN
ejpam-1234	17	6	of	of	ADP
ejpam-1234	17	7	the	the	DET
ejpam-1234	17	8	crepant	crepant	ADJ
ejpam-1234	17	9	resolution	resolution	NOUN
ejpam-1234	17	10	conjecture	conjecture	NOUN
ejpam-1234	17	11	of	of	ADP
ejpam-1234	17	12	ruan	ruan	NOUN
ejpam-1234	18	1	[	[	X
ejpam-1234	18	2	22	22	NUM
ejpam-1234	18	3	]	]	PUNCT
ejpam-1234	18	4	and	and	CCONJ
ejpam-1234	18	5	bryan	bryan	PROPN
ejpam-1234	18	6	-	-	PUNCT
ejpam-1234	18	7	graber	graber	PROPN
ejpam-1234	19	1	[	[	X
ejpam-1234	19	2	3	3	NUM
ejpam-1234	19	3	]	]	PUNCT
ejpam-1234	19	4	.	.	PUNCT
ejpam-1234	20	1	email	email	NOUN
ejpam-1234	20	2	address	address	PROPN
ejpam-1234	20	3	:	:	PUNCT
ejpam-1234	20	4	tomoomatsumura	tomoomatsumura	PROPN
ejpam-1234	20	5	�	�	PROPN
ejpam-1234	20	6	kaist.a	kaist.a	PROPN
ejpam-1234	20	7	.kr	.kr	PUNCT
ejpam-1234	20	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1234	20	9	492	492	NUM
ejpam-1234	21	1	c	c	X
ejpam-1234	21	2	©	©	PROPN
ejpam-1234	21	3	2012	2012	NUM
ejpam-1234	21	4	ejpam	ejpam	VERB
ejpam-1234	21	5	all	all	DET
ejpam-1234	21	6	rights	right	NOUN
ejpam-1234	21	7	reserved	reserve	VERB
ejpam-1234	21	8	.	.	PUNCT
ejpam-1234	22	1	tomoo	tomoo	VERB
ejpam-1234	22	2	matsumura	matsumura	ADJ
ejpam-1234	22	3	/	/	SYM
ejpam-1234	22	4	eur	eur	PROPN
ejpam-1234	22	5	.	.	PUNCT
ejpam-1234	23	1	j.	j.	PROPN
ejpam-1234	23	2	pure	pure	PROPN
ejpam-1234	23	3	appl	appl	PROPN
ejpam-1234	23	4	.	.	PROPN
ejpam-1234	23	5	math	math	PROPN
ejpam-1234	23	6	,	,	PUNCT
ejpam-1234	23	7	5	5	NUM
ejpam-1234	23	8	(	(	PUNCT
ejpam-1234	23	9	2012	2012	NUM
ejpam-1234	23	10	)	)	PUNCT
ejpam-1234	23	11	,	,	PUNCT
ejpam-1234	23	12	492	492	NUM
ejpam-1234	23	13	-	-	SYM
ejpam-1234	23	14	510	510	NUM
ejpam-1234	23	15	493	493	NUM
ejpam-1234	23	16	among	among	ADP
ejpam-1234	23	17	the	the	DET
ejpam-1234	23	18	examples	example	NOUN
ejpam-1234	23	19	which	which	PRON
ejpam-1234	23	20	support	support	VERB
ejpam-1234	23	21	the	the	DET
ejpam-1234	23	22	cohomological	cohomological	ADJ
ejpam-1234	23	23	hyper	hyper	ADJ
ejpam-1234	23	24	-	-	ADJ
ejpam-1234	23	25	kähler	kähler	NOUN
ejpam-1234	23	26	resolution	resolution	NOUN
ejpam-1234	23	27	conjecture	conjecture	NOUN
ejpam-1234	24	1	,	,	PUNCT
ejpam-1234	24	2	the	the	DET
ejpam-1234	24	3	symmetric	symmetric	ADJ
ejpam-1234	24	4	product	product	NOUN
ejpam-1234	24	5	is	be	AUX
ejpam-1234	24	6	perhaps	perhaps	ADV
ejpam-1234	24	7	the	the	DET
ejpam-1234	24	8	most	most	ADV
ejpam-1234	24	9	fascinating	fascinating	ADJ
ejpam-1234	24	10	.	.	PUNCT
ejpam-1234	25	1	the	the	DET
ejpam-1234	25	2	symmetric	symmetric	ADJ
ejpam-1234	25	3	group	group	NOUN
ejpam-1234	25	4	on	on	ADP
ejpam-1234	25	5	n	n	CCONJ
ejpam-1234	25	6	-	-	PUNCT
ejpam-1234	25	7	letters	letter	NOUN
ejpam-1234	25	8	,	,	PUNCT
ejpam-1234	25	9	σn	σn	NOUN
ejpam-1234	25	10	,	,	PUNCT
ejpam-1234	25	11	naturally	naturally	ADV
ejpam-1234	25	12	acts	act	VERB
ejpam-1234	25	13	on	on	ADP
ejpam-1234	25	14	the	the	DET
ejpam-1234	25	15	n	n	ADV
ejpam-1234	25	16	-	-	ADJ
ejpam-1234	25	17	fold	fold	ADJ
ejpam-1234	25	18	product	product	NOUN
ejpam-1234	25	19	y	y	PROPN
ejpam-1234	25	20	n	n	PROPN
ejpam-1234	25	21	of	of	ADP
ejpam-1234	25	22	a	a	DET
ejpam-1234	25	23	manifold	manifold	ADJ
ejpam-1234	25	24	y	y	NOUN
ejpam-1234	25	25	,	,	PUNCT
ejpam-1234	25	26	yielding	yield	VERB
ejpam-1234	25	27	the	the	DET
ejpam-1234	25	28	symmetric	symmetric	ADJ
ejpam-1234	25	29	product	product	NOUN
ejpam-1234	25	30	orbifold	orbifold	VERB
ejpam-1234	26	1	[	[	X
ejpam-1234	26	2	y	y	NOUN
ejpam-1234	26	3	n	n	CCONJ
ejpam-1234	26	4	/	/	SYM
ejpam-1234	26	5	σn	σn	PROPN
ejpam-1234	26	6	]	]	X
ejpam-1234	26	7	.	.	PUNCT
ejpam-1234	27	1	if	if	SCONJ
ejpam-1234	27	2	y	y	PROPN
ejpam-1234	27	3	is	be	AUX
ejpam-1234	27	4	a	a	DET
ejpam-1234	27	5	projective	projective	ADJ
ejpam-1234	27	6	surface	surface	NOUN
ejpam-1234	27	7	with	with	ADP
ejpam-1234	27	8	trivial	trivial	ADJ
ejpam-1234	27	9	canonical	canonical	ADJ
ejpam-1234	27	10	class	class	NOUN
ejpam-1234	27	11	,	,	PUNCT
ejpam-1234	27	12	then	then	ADV
ejpam-1234	27	13	the	the	DET
ejpam-1234	27	14	hilbert	hilbert	PROPN
ejpam-1234	27	15	scheme	scheme	NOUN
ejpam-1234	27	16	of	of	ADP
ejpam-1234	27	17	n	n	NUM
ejpam-1234	27	18	points	point	NOUN
ejpam-1234	27	19	on	on	ADP
ejpam-1234	27	20	y	y	PROPN
ejpam-1234	27	21	,	,	PUNCT
ejpam-1234	27	22	denoted	denote	VERB
ejpam-1234	27	23	by	by	ADP
ejpam-1234	27	24	y	y	PROPN
ejpam-1234	27	25	[	[	X
ejpam-1234	27	26	n	n	X
ejpam-1234	27	27	]	]	PUNCT
ejpam-1234	27	28	,	,	PUNCT
ejpam-1234	27	29	is	be	AUX
ejpam-1234	27	30	a	a	DET
ejpam-1234	27	31	hyper	hyper	ADJ
ejpam-1234	27	32	-	-	ADJ
ejpam-1234	27	33	kähler	kähler	ADJ
ejpam-1234	27	34	resolution	resolution	NOUN
ejpam-1234	27	35	of	of	ADP
ejpam-1234	27	36	the	the	DET
ejpam-1234	27	37	quotient	quotient	NOUN
ejpam-1234	27	38	space	space	PROPN
ejpam-1234	27	39	y	y	PROPN
ejpam-1234	27	40	n	n	CCONJ
ejpam-1234	27	41	/	/	SYM
ejpam-1234	27	42	σn	σn	X
ejpam-1234	27	43	[	[	X
ejpam-1234	27	44	1	1	NUM
ejpam-1234	27	45	]	]	PUNCT
ejpam-1234	27	46	.	.	PUNCT
ejpam-1234	28	1	fantechi	fantechi	PROPN
ejpam-1234	28	2	and	and	CCONJ
ejpam-1234	28	3	göttsche	göttsche	NOUN
ejpam-1234	29	1	[	[	X
ejpam-1234	29	2	7	7	X
ejpam-1234	29	3	]	]	PUNCT
ejpam-1234	29	4	showed	show	VERB
ejpam-1234	29	5	that	that	SCONJ
ejpam-1234	29	6	the	the	DET
ejpam-1234	29	7	ring	ring	NOUN
ejpam-1234	29	8	of	of	ADP
ejpam-1234	29	9	σn	σn	NOUN
ejpam-1234	29	10	-	-	PUNCT
ejpam-1234	29	11	invariants	invariant	NOUN
ejpam-1234	29	12	of	of	ADP
ejpam-1234	29	13	h	h	PROPN
ejpam-1234	29	14	(	(	PUNCT
ejpam-1234	29	15	y	y	PROPN
ejpam-1234	29	16	n	n	CCONJ
ejpam-1234	29	17	,	,	PUNCT
ejpam-1234	29	18	σn	σn	NOUN
ejpam-1234	29	19	)	)	PUNCT
ejpam-1234	29	20	is	be	AUX
ejpam-1234	29	21	isomorphic	isomorphic	ADJ
ejpam-1234	29	22	to	to	ADP
ejpam-1234	29	23	h∗(y	h∗(y	PROPN
ejpam-1234	29	24	[	[	X
ejpam-1234	29	25	n	n	X
ejpam-1234	29	26	]	]	PUNCT
ejpam-1234	29	27	)	)	PUNCT
ejpam-1234	29	28	over	over	ADP
ejpam-1234	29	29	c.	c.	NOUN
ejpam-1234	29	30	their	their	PRON
ejpam-1234	29	31	proof	proof	NOUN
ejpam-1234	29	32	proceeds	proceed	VERB
ejpam-1234	29	33	by	by	ADP
ejpam-1234	29	34	showing	show	VERB
ejpam-1234	29	35	that	that	SCONJ
ejpam-1234	29	36	h	h	NOUN
ejpam-1234	29	37	(	(	PUNCT
ejpam-1234	29	38	y	y	PROPN
ejpam-1234	29	39	n	n	CCONJ
ejpam-1234	29	40	,	,	PUNCT
ejpam-1234	29	41	σn	σn	NOUN
ejpam-1234	29	42	)	)	PUNCT
ejpam-1234	29	43	is	be	AUX
ejpam-1234	29	44	isomorphic	isomorphic	ADJ
ejpam-1234	29	45	to	to	ADP
ejpam-1234	29	46	the	the	DET
ejpam-1234	29	47	algebra	algebra	NOUN
ejpam-1234	29	48	h∗(x	h∗(x	PROPN
ejpam-1234	29	49	)	)	PUNCT
ejpam-1234	29	50	{	{	PUNCT
ejpam-1234	29	51	sn	sn	NOUN
ejpam-1234	29	52	}	}	PUNCT
ejpam-1234	29	53	defined	define	VERB
ejpam-1234	29	54	by	by	ADP
ejpam-1234	29	55	lehn	lehn	NOUN
ejpam-1234	29	56	and	and	CCONJ
ejpam-1234	29	57	sorger	sorger	NOUN
ejpam-1234	29	58	[	[	X
ejpam-1234	29	59	14	14	NUM
ejpam-1234	29	60	]	]	PUNCT
ejpam-1234	29	61	,	,	PUNCT
ejpam-1234	29	62	i.e.	i.e.	X
ejpam-1234	29	63	h	h	X
ejpam-1234	29	64	(	(	PUNCT
ejpam-1234	29	65	y	y	PROPN
ejpam-1234	29	66	n	n	CCONJ
ejpam-1234	29	67	,	,	PUNCT
ejpam-1234	29	68	σn	σn	NOUN
ejpam-1234	29	69	)	)	PUNCT
ejpam-1234	29	70	∼=	∼=	PROPN
ejpam-1234	29	71	h∗(y	h∗(y	NOUN
ejpam-1234	29	72	)	)	PUNCT
ejpam-1234	29	73	{	{	PUNCT
ejpam-1234	29	74	σn	σn	NOUN
ejpam-1234	29	75	}	}	PUNCT
ejpam-1234	29	76	=	=	NOUN
ejpam-1234	29	77	⇒	⇒	NOUN
ejpam-1234	29	78	h∗or	h∗or	PROPN
ejpam-1234	29	79	b([y	b([y	NOUN
ejpam-1234	29	80	n	n	CCONJ
ejpam-1234	29	81	/	/	SYM
ejpam-1234	29	82	σn	σn	NOUN
ejpam-1234	29	83	]	]	PUNCT
ejpam-1234	29	84	)	)	PUNCT
ejpam-1234	29	85	∼=	∼=	PROPN
ejpam-1234	29	86	h∗(y	h∗(y	NOUN
ejpam-1234	29	87	)	)	PUNCT
ejpam-1234	29	88	{	{	PUNCT
ejpam-1234	29	89	σn	σn	NOUN
ejpam-1234	29	90	}	}	PUNCT
ejpam-1234	29	91	σn	σn	NOUN
ejpam-1234	29	92	∼=	∼=	PROPN
ejpam-1234	29	93	h∗(y	h∗(y	NOUN
ejpam-1234	29	94	[	[	X
ejpam-1234	29	95	n	n	X
ejpam-1234	29	96	]	]	X
ejpam-1234	29	97	)	)	PUNCT
ejpam-1234	29	98	where	where	SCONJ
ejpam-1234	29	99	the	the	DET
ejpam-1234	29	100	last	last	ADJ
ejpam-1234	29	101	isomorphism	isomorphism	NOUN
ejpam-1234	29	102	is	be	AUX
ejpam-1234	29	103	due	due	ADJ
ejpam-1234	29	104	to	to	ADP
ejpam-1234	29	105	[	[	X
ejpam-1234	29	106	14	14	NUM
ejpam-1234	29	107	]	]	PUNCT
ejpam-1234	29	108	(	(	PUNCT
ejpam-1234	29	109	see	see	VERB
ejpam-1234	29	110	also	also	ADV
ejpam-1234	29	111	[	[	X
ejpam-1234	29	112	24	24	NUM
ejpam-1234	29	113	,	,	PUNCT
ejpam-1234	29	114	18	18	NUM
ejpam-1234	29	115	,	,	PUNCT
ejpam-1234	29	116	16	16	NUM
ejpam-1234	29	117	]	]	PUNCT
ejpam-1234	29	118	)	)	PUNCT
ejpam-1234	29	119	.	.	PUNCT
ejpam-1234	30	1	in	in	ADP
ejpam-1234	30	2	this	this	DET
ejpam-1234	30	3	paper	paper	NOUN
ejpam-1234	30	4	,	,	PUNCT
ejpam-1234	30	5	we	we	PRON
ejpam-1234	30	6	consider	consider	VERB
ejpam-1234	30	7	a	a	DET
ejpam-1234	30	8	generalization	generalization	NOUN
ejpam-1234	30	9	of	of	ADP
ejpam-1234	30	10	the	the	DET
ejpam-1234	30	11	algebra	algebra	NOUN
ejpam-1234	30	12	isomorphism	isomorphism	NOUN
ejpam-1234	30	13	on	on	ADP
ejpam-1234	30	14	the	the	DET
ejpam-1234	30	15	left	left	ADJ
ejpam-1234	30	16	-	-	PUNCT
ejpam-1234	30	17	hand	hand	NOUN
ejpam-1234	30	18	side	side	NOUN
ejpam-1234	30	19	of	of	ADP
ejpam-1234	30	20	the	the	DET
ejpam-1234	30	21	arrow	arrow	NOUN
ejpam-1234	30	22	above	above	ADV
ejpam-1234	30	23	,	,	PUNCT
ejpam-1234	30	24	namely	namely	ADV
ejpam-1234	30	25	,	,	PUNCT
ejpam-1234	30	26	replace	replace	VERB
ejpam-1234	30	27	y	y	NOUN
ejpam-1234	30	28	by	by	ADP
ejpam-1234	30	29	an	an	DET
ejpam-1234	30	30	orbifold	orbifold	NOUN
ejpam-1234	30	31	[	[	X
ejpam-1234	30	32	x	x	X
ejpam-1234	30	33	/	/	SYM
ejpam-1234	30	34	g	g	NOUN
ejpam-1234	30	35	]	]	PUNCT
ejpam-1234	30	36	and	and	CCONJ
ejpam-1234	30	37	h∗(y	h∗(y	PROPN
ejpam-1234	30	38	)	)	PUNCT
ejpam-1234	30	39	by	by	ADP
ejpam-1234	30	40	h∗	h∗	PROPN
ejpam-1234	30	41	or	or	CCONJ
ejpam-1234	30	42	b	b	PROPN
ejpam-1234	30	43	(	(	PUNCT
ejpam-1234	30	44	[	[	X
ejpam-1234	30	45	x	x	X
ejpam-1234	30	46	/	/	SYM
ejpam-1234	30	47	g	g	NOUN
ejpam-1234	30	48	]	]	PUNCT
ejpam-1234	30	49	)	)	PUNCT
ejpam-1234	30	50	.	.	PUNCT
ejpam-1234	31	1	the	the	DET
ejpam-1234	31	2	symmetric	symmetric	ADJ
ejpam-1234	31	3	group	group	NOUN
ejpam-1234	31	4	σn	σn	NOUN
ejpam-1234	31	5	naturally	naturally	ADV
ejpam-1234	31	6	acts	act	VERB
ejpam-1234	31	7	on	on	ADP
ejpam-1234	31	8	the	the	DET
ejpam-1234	31	9	n	n	ADV
ejpam-1234	31	10	-	-	ADJ
ejpam-1234	31	11	fold	fold	ADJ
ejpam-1234	31	12	product	product	NOUN
ejpam-1234	31	13	gn	gn	PROPN
ejpam-1234	31	14	and	and	CCONJ
ejpam-1234	31	15	their	their	PRON
ejpam-1234	31	16	semidirect	semidirect	NOUN
ejpam-1234	31	17	product	product	NOUN
ejpam-1234	31	18	gn	gn	PROPN
ejpam-1234	31	19	⋊σn	⋊σn	PROPN
ejpam-1234	31	20	is	be	AUX
ejpam-1234	31	21	called	call	VERB
ejpam-1234	31	22	the	the	DET
ejpam-1234	31	23	wreath	wreath	NOUN
ejpam-1234	31	24	product	product	NOUN
ejpam-1234	31	25	of	of	ADP
ejpam-1234	31	26	g.	g.	PROPN
ejpam-1234	31	27	it	it	PRON
ejpam-1234	31	28	naturally	naturally	ADV
ejpam-1234	31	29	acts	act	VERB
ejpam-1234	31	30	on	on	ADP
ejpam-1234	31	31	the	the	DET
ejpam-1234	31	32	n	n	ADV
ejpam-1234	31	33	-	-	ADJ
ejpam-1234	31	34	fold	fold	ADJ
ejpam-1234	31	35	product	product	NOUN
ejpam-1234	31	36	x	x	PUNCT
ejpam-1234	31	37	n	n	CCONJ
ejpam-1234	31	38	,	,	PUNCT
ejpam-1234	31	39	yielding	yield	VERB
ejpam-1234	31	40	the	the	DET
ejpam-1234	31	41	orbifold	orbifold	NOUN
ejpam-1234	31	42	[	[	X
ejpam-1234	31	43	x	x	X
ejpam-1234	31	44	n/(gn⋊σn	n/(gn⋊σn	NOUN
ejpam-1234	31	45	)	)	PUNCT
ejpam-1234	31	46	]	]	PUNCT
ejpam-1234	31	47	.	.	PUNCT
ejpam-1234	32	1	this	this	DET
ejpam-1234	32	2	orbifold	orbifold	NOUN
ejpam-1234	32	3	is	be	AUX
ejpam-1234	32	4	called	call	VERB
ejpam-1234	32	5	the	the	DET
ejpam-1234	32	6	wreath	wreath	NOUN
ejpam-1234	32	7	product	product	NOUN
ejpam-1234	32	8	orbifold	orbifold	NOUN
ejpam-1234	32	9	of	of	ADP
ejpam-1234	32	10	a	a	DET
ejpam-1234	32	11	g	g	NOUN
ejpam-1234	32	12	-	-	PUNCT
ejpam-1234	32	13	space	space	NOUN
ejpam-1234	32	14	x	x	NOUN
ejpam-1234	32	15	.	.	PUNCT
ejpam-1234	33	1	the	the	DET
ejpam-1234	33	2	linear	linear	ADJ
ejpam-1234	33	3	structure	structure	NOUN
ejpam-1234	33	4	of	of	ADP
ejpam-1234	33	5	the	the	DET
ejpam-1234	33	6	orbifold	orbifold	ADJ
ejpam-1234	33	7	cohomology	cohomology	NOUN
ejpam-1234	33	8	of	of	ADP
ejpam-1234	33	9	a	a	DET
ejpam-1234	33	10	wreath	wreath	NOUN
ejpam-1234	33	11	product	product	NOUN
ejpam-1234	33	12	orbifold	orbifold	NOUN
ejpam-1234	33	13	has	have	AUX
ejpam-1234	33	14	been	be	AUX
ejpam-1234	33	15	studied	study	VERB
ejpam-1234	33	16	in	in	ADP
ejpam-1234	33	17	a	a	DET
ejpam-1234	33	18	sequence	sequence	NOUN
ejpam-1234	33	19	of	of	ADP
ejpam-1234	33	20	papers	paper	NOUN
ejpam-1234	33	21	by	by	ADP
ejpam-1234	33	22	qin	qin	PROPN
ejpam-1234	33	23	,	,	PUNCT
ejpam-1234	33	24	wang	wang	PROPN
ejpam-1234	33	25	and	and	CCONJ
ejpam-1234	33	26	zhou	zhou	PROPN
ejpam-1234	33	27	,	,	PUNCT
ejpam-1234	33	28	cf	cf	INTJ
ejpam-1234	33	29	.	.	PUNCT
ejpam-1234	34	1	[	[	X
ejpam-1234	34	2	18	18	NUM
ejpam-1234	34	3	,	,	PUNCT
ejpam-1234	34	4	25	25	NUM
ejpam-1234	34	5	,	,	PUNCT
ejpam-1234	34	6	26	26	NUM
ejpam-1234	34	7	]	]	PUNCT
ejpam-1234	34	8	through	through	ADP
ejpam-1234	34	9	a	a	DET
ejpam-1234	34	10	careful	careful	ADJ
ejpam-1234	34	11	analysis	analysis	NOUN
ejpam-1234	34	12	of	of	ADP
ejpam-1234	34	13	the	the	DET
ejpam-1234	34	14	fixed	fix	VERB
ejpam-1234	34	15	point	point	NOUN
ejpam-1234	34	16	loci	locus	NOUN
ejpam-1234	34	17	.	.	PUNCT
ejpam-1234	35	1	however	however	ADV
ejpam-1234	35	2	,	,	PUNCT
ejpam-1234	35	3	one	one	NUM
ejpam-1234	35	4	of	of	ADP
ejpam-1234	35	5	the	the	DET
ejpam-1234	35	6	goals	goal	NOUN
ejpam-1234	35	7	of	of	ADP
ejpam-1234	35	8	this	this	DET
ejpam-1234	35	9	paper	paper	NOUN
ejpam-1234	35	10	is	be	AUX
ejpam-1234	35	11	to	to	PART
ejpam-1234	35	12	analyze	analyze	VERB
ejpam-1234	35	13	the	the	DET
ejpam-1234	35	14	multiplication	multiplication	NOUN
ejpam-1234	35	15	in	in	ADP
ejpam-1234	35	16	stringy	stringy	ADJ
ejpam-1234	35	17	cohomology	cohomology	NOUN
ejpam-1234	35	18	and	and	CCONJ
ejpam-1234	35	19	in	in	ADP
ejpam-1234	35	20	chen	chen	PROPN
ejpam-1234	35	21	-	-	PUNCT
ejpam-1234	35	22	ruan	ruan	PROPN
ejpam-1234	35	23	orbifold	orbifold	NOUN
ejpam-1234	35	24	cohomology	cohomology	NOUN
ejpam-1234	35	25	of	of	ADP
ejpam-1234	35	26	a	a	DET
ejpam-1234	35	27	wreath	wreath	NOUN
ejpam-1234	35	28	product	product	NOUN
ejpam-1234	35	29	orbifold	orbifold	VERB
ejpam-1234	35	30	.	.	PUNCT
ejpam-1234	36	1	the	the	DET
ejpam-1234	36	2	multiplication	multiplication	NOUN
ejpam-1234	36	3	in	in	ADP
ejpam-1234	36	4	the	the	DET
ejpam-1234	36	5	special	special	ADJ
ejpam-1234	36	6	case	case	NOUN
ejpam-1234	36	7	when	when	SCONJ
ejpam-1234	36	8	x	x	PROPN
ejpam-1234	36	9	=	=	SYM
ejpam-1234	36	10	c2	c2	PROPN
ejpam-1234	36	11	and	and	CCONJ
ejpam-1234	36	12	g	g	PROPN
ejpam-1234	36	13	is	be	AUX
ejpam-1234	36	14	a	a	DET
ejpam-1234	36	15	finite	finite	ADJ
ejpam-1234	36	16	subgroup	subgroup	NOUN
ejpam-1234	36	17	of	of	ADP
ejpam-1234	36	18	sl2(c	sl2(c	PROPN
ejpam-1234	36	19	)	)	PUNCT
ejpam-1234	36	20	has	have	AUX
ejpam-1234	36	21	been	be	AUX
ejpam-1234	36	22	studied	study	VERB
ejpam-1234	36	23	in	in	ADP
ejpam-1234	36	24	[	[	X
ejpam-1234	36	25	6	6	NUM
ejpam-1234	36	26	,	,	PUNCT
ejpam-1234	36	27	19	19	NUM
ejpam-1234	36	28	]	]	PUNCT
ejpam-1234	36	29	.	.	PUNCT
ejpam-1234	37	1	the	the	DET
ejpam-1234	37	2	main	main	ADJ
ejpam-1234	37	3	result	result	NOUN
ejpam-1234	37	4	of	of	ADP
ejpam-1234	37	5	this	this	DET
ejpam-1234	37	6	paper	paper	NOUN
ejpam-1234	37	7	is	be	AUX
ejpam-1234	37	8	theorem	theorem	VERB
ejpam-1234	37	9	4	4	NUM
ejpam-1234	37	10	which	which	PRON
ejpam-1234	37	11	proves	prove	VERB
ejpam-1234	37	12	that	that	SCONJ
ejpam-1234	37	13	,	,	PUNCT
ejpam-1234	37	14	when	when	SCONJ
ejpam-1234	37	15	x	x	PRON
ejpam-1234	37	16	is	be	AUX
ejpam-1234	37	17	compact	compact	ADJ
ejpam-1234	37	18	,	,	PUNCT
ejpam-1234	37	19	there	there	PRON
ejpam-1234	37	20	is	be	VERB
ejpam-1234	37	21	a	a	DET
ejpam-1234	37	22	canonical	canonical	ADJ
ejpam-1234	37	23	σn	σn	NOUN
ejpam-1234	37	24	-	-	PUNCT
ejpam-1234	37	25	frobenius	frobenius	NOUN
ejpam-1234	37	26	algebra	algebra	NOUN
ejpam-1234	37	27	isomorphism	isomorphism	NOUN
ejpam-1234	37	28	h	h	NOUN
ejpam-1234	37	29	(	(	PUNCT
ejpam-1234	37	30	x	x	SYM
ejpam-1234	37	31	n	n	CCONJ
ejpam-1234	37	32	,	,	PUNCT
ejpam-1234	37	33	gn	gn	PROPN
ejpam-1234	37	34	⋊σn	⋊σn	PROPN
ejpam-1234	37	35	)	)	PUNCT
ejpam-1234	37	36	gn	gn	PROPN
ejpam-1234	38	1	∼=	∼=	PROPN
ejpam-1234	38	2	h∗or	h∗or	NUM
ejpam-1234	38	3	b([x	b([x	NOUN
ejpam-1234	38	4	/	/	SYM
ejpam-1234	38	5	g]){σn	g]){σn	NOUN
ejpam-1234	38	6	}	}	PUNCT
ejpam-1234	38	7	.	.	PUNCT
ejpam-1234	39	1	when	when	SCONJ
ejpam-1234	39	2	g	g	PROPN
ejpam-1234	39	3	is	be	AUX
ejpam-1234	39	4	a	a	DET
ejpam-1234	39	5	trivial	trivial	ADJ
ejpam-1234	39	6	group	group	NOUN
ejpam-1234	39	7	,	,	PUNCT
ejpam-1234	39	8	this	this	DET
ejpam-1234	39	9	isomorphism	isomorphism	NOUN
ejpam-1234	39	10	reduces	reduce	VERB
ejpam-1234	39	11	to	to	ADP
ejpam-1234	39	12	the	the	DET
ejpam-1234	39	13	isomorphism	isomorphism	NOUN
ejpam-1234	39	14	defined	define	VERB
ejpam-1234	39	15	by	by	ADP
ejpam-1234	39	16	fantechi	fantechi	PROPN
ejpam-1234	39	17	and	and	CCONJ
ejpam-1234	39	18	göttsche	göttsche	NOUN
ejpam-1234	39	19	[	[	X
ejpam-1234	39	20	7	7	NUM
ejpam-1234	39	21	]	]	PUNCT
ejpam-1234	39	22	.	.	PUNCT
ejpam-1234	40	1	this	this	DET
ejpam-1234	40	2	result	result	NOUN
ejpam-1234	40	3	means	mean	VERB
ejpam-1234	40	4	that	that	SCONJ
ejpam-1234	40	5	h	h	NOUN
ejpam-1234	40	6	(	(	PUNCT
ejpam-1234	40	7	x	x	SYM
ejpam-1234	40	8	n	n	CCONJ
ejpam-1234	40	9	,	,	PUNCT
ejpam-1234	40	10	gn	gn	PROPN
ejpam-1234	40	11	⋊	⋊	NUM
ejpam-1234	40	12	σn	σn	NOUN
ejpam-1234	40	13	)	)	PUNCT
ejpam-1234	40	14	gn	gn	PROPN
ejpam-1234	40	15	gives	give	VERB
ejpam-1234	40	16	a	a	DET
ejpam-1234	40	17	geometric	geometric	ADJ
ejpam-1234	40	18	construction	construction	NOUN
ejpam-1234	40	19	of	of	ADP
ejpam-1234	40	20	the	the	DET
ejpam-1234	40	21	second	second	ADJ
ejpam-1234	40	22	quantization	quantization	NOUN
ejpam-1234	40	23	[	[	X
ejpam-1234	40	24	definition	definition	NOUN
ejpam-1234	40	25	8.16	8.16	NUM
ejpam-1234	40	26	,	,	PUNCT
ejpam-1234	40	27	13	13	NUM
ejpam-1234	40	28	]	]	PUNCT
ejpam-1234	40	29	of	of	ADP
ejpam-1234	40	30	an	an	DET
ejpam-1234	40	31	orbifold	orbifold	NOUN
ejpam-1234	41	1	[	[	X
ejpam-1234	41	2	x	x	X
ejpam-1234	41	3	/	/	SYM
ejpam-1234	41	4	g	g	NOUN
ejpam-1234	41	5	]	]	PUNCT
ejpam-1234	41	6	.	.	PUNCT
ejpam-1234	42	1	there	there	PRON
ejpam-1234	42	2	are	be	VERB
ejpam-1234	42	3	two	two	NUM
ejpam-1234	42	4	results	result	NOUN
ejpam-1234	42	5	that	that	PRON
ejpam-1234	42	6	play	play	VERB
ejpam-1234	42	7	key	key	ADJ
ejpam-1234	42	8	roles	role	NOUN
ejpam-1234	42	9	in	in	ADP
ejpam-1234	42	10	our	our	PRON
ejpam-1234	42	11	proof	proof	NOUN
ejpam-1234	42	12	of	of	ADP
ejpam-1234	42	13	the	the	DET
ejpam-1234	42	14	main	main	ADJ
ejpam-1234	42	15	theorem	theorem	NOUN
ejpam-1234	42	16	.	.	PUNCT
ejpam-1234	43	1	one	one	NUM
ejpam-1234	43	2	is	be	AUX
ejpam-1234	43	3	the	the	DET
ejpam-1234	43	4	formula	formula	NOUN
ejpam-1234	43	5	(	(	PUNCT
ejpam-1234	43	6	1	1	X
ejpam-1234	43	7	)	)	PUNCT
ejpam-1234	43	8	proved	prove	VERB
ejpam-1234	43	9	in	in	ADP
ejpam-1234	43	10	[	[	X
ejpam-1234	43	11	11	11	NUM
ejpam-1234	43	12	]	]	PUNCT
ejpam-1234	43	13	for	for	ADP
ejpam-1234	43	14	the	the	DET
ejpam-1234	43	15	obstruction	obstruction	NOUN
ejpam-1234	43	16	bundle	bundle	NOUN
ejpam-1234	43	17	of	of	ADP
ejpam-1234	43	18	the	the	DET
ejpam-1234	43	19	stringy	stringy	ADJ
ejpam-1234	43	20	cohomology	cohomology	NOUN
ejpam-1234	43	21	.	.	PUNCT
ejpam-1234	44	1	since	since	SCONJ
ejpam-1234	44	2	their	their	PRON
ejpam-1234	44	3	definition	definition	NOUN
ejpam-1234	44	4	avoids	avoid	VERB
ejpam-1234	44	5	any	any	DET
ejpam-1234	44	6	construction	construction	NOUN
ejpam-1234	44	7	of	of	ADP
ejpam-1234	44	8	complex	complex	ADJ
ejpam-1234	44	9	curves	curve	NOUN
ejpam-1234	44	10	,	,	PUNCT
ejpam-1234	44	11	admissible	admissible	ADJ
ejpam-1234	44	12	covers	cover	NOUN
ejpam-1234	44	13	,	,	PUNCT
ejpam-1234	44	14	or	or	CCONJ
ejpam-1234	44	15	moduli	moduli	NOUN
ejpam-1234	44	16	spaces	space	NOUN
ejpam-1234	44	17	,	,	PUNCT
ejpam-1234	44	18	it	it	PRON
ejpam-1234	44	19	greatly	greatly	ADV
ejpam-1234	44	20	simplifies	simplify	VERB
ejpam-1234	44	21	the	the	DET
ejpam-1234	44	22	analysis	analysis	NOUN
ejpam-1234	44	23	of	of	ADP
ejpam-1234	44	24	the	the	DET
ejpam-1234	44	25	obstruction	obstruction	NOUN
ejpam-1234	44	26	bundle	bundle	NOUN
ejpam-1234	44	27	and	and	CCONJ
ejpam-1234	44	28	allows	allow	VERB
ejpam-1234	44	29	us	we	PRON
ejpam-1234	44	30	to	to	PART
ejpam-1234	44	31	write	write	VERB
ejpam-1234	44	32	the	the	DET
ejpam-1234	44	33	obstruction	obstruction	NOUN
ejpam-1234	44	34	bundle	bundle	NOUN
ejpam-1234	44	35	of	of	ADP
ejpam-1234	44	36	[	[	X
ejpam-1234	44	37	x	x	X
ejpam-1234	44	38	n/(gn	n/(gn	PROPN
ejpam-1234	44	39	⋊	⋊	NUM
ejpam-1234	44	40	σn	σn	NOUN
ejpam-1234	44	41	)	)	PUNCT
ejpam-1234	44	42	]	]	PUNCT
ejpam-1234	44	43	in	in	ADP
ejpam-1234	44	44	terms	term	NOUN
ejpam-1234	44	45	of	of	ADP
ejpam-1234	44	46	the	the	DET
ejpam-1234	44	47	ones	one	NOUN
ejpam-1234	44	48	of	of	ADP
ejpam-1234	44	49	[	[	X
ejpam-1234	44	50	x	x	X
ejpam-1234	44	51	/	/	SYM
ejpam-1234	44	52	g	g	NOUN
ejpam-1234	44	53	]	]	PUNCT
ejpam-1234	44	54	and	and	CCONJ
ejpam-1234	44	55	[	[	X
ejpam-1234	44	56	x	x	X
ejpam-1234	44	57	n	n	CCONJ
ejpam-1234	44	58	/	/	SYM
ejpam-1234	44	59	σn	σn	NOUN
ejpam-1234	44	60	]	]	X
ejpam-1234	44	61	.	.	PUNCT
ejpam-1234	45	1	the	the	DET
ejpam-1234	45	2	other	other	ADJ
ejpam-1234	45	3	result	result	NOUN
ejpam-1234	45	4	is	be	AUX
ejpam-1234	45	5	theorem	theorem	VERB
ejpam-1234	45	6	6.5	6.5	NUM
ejpam-1234	45	7	of	of	ADP
ejpam-1234	45	8	[	[	X
ejpam-1234	45	9	13	13	NUM
ejpam-1234	45	10	]	]	PUNCT
ejpam-1234	45	11	which	which	PRON
ejpam-1234	45	12	states	state	VERB
ejpam-1234	45	13	that	that	SCONJ
ejpam-1234	45	14	there	there	PRON
ejpam-1234	45	15	is	be	VERB
ejpam-1234	45	16	a	a	DET
ejpam-1234	45	17	unique	unique	ADJ
ejpam-1234	45	18	product	product	NOUN
ejpam-1234	45	19	structure	structure	NOUN
ejpam-1234	45	20	on	on	ADP
ejpam-1234	45	21	a	a	DET
ejpam-1234	45	22	normalized	normalize	VERB
ejpam-1234	45	23	,	,	PUNCT
ejpam-1234	45	24	special	special	ADJ
ejpam-1234	45	25	σn	σn	NOUN
ejpam-1234	45	26	-	-	PUNCT
ejpam-1234	45	27	frobenius	frobenius	NOUN
ejpam-1234	45	28	algebra	algebra	NOUN
ejpam-1234	45	29	(	(	PUNCT
ejpam-1234	45	30	reviewed	review	VERB
ejpam-1234	45	31	in	in	ADP
ejpam-1234	45	32	appendix	appendix	NOUN
ejpam-1234	45	33	)	)	PUNCT
ejpam-1234	45	34	.	.	PUNCT
ejpam-1234	46	1	lemma	lemma	PROPN
ejpam-1234	46	2	3	3	NUM
ejpam-1234	46	3	which	which	PRON
ejpam-1234	46	4	computes	compute	VERB
ejpam-1234	46	5	the	the	DET
ejpam-1234	46	6	obstruction	obstruction	NOUN
ejpam-1234	46	7	bundle	bundle	NOUN
ejpam-1234	46	8	in	in	ADP
ejpam-1234	46	9	a	a	DET
ejpam-1234	46	10	certain	certain	ADJ
ejpam-1234	46	11	case	case	NOUN
ejpam-1234	46	12	using	use	VERB
ejpam-1234	46	13	the	the	DET
ejpam-1234	46	14	formula	formula	NOUN
ejpam-1234	46	15	(	(	PUNCT
ejpam-1234	46	16	1	1	X
ejpam-1234	46	17	)	)	PUNCT
ejpam-1234	46	18	is	be	AUX
ejpam-1234	46	19	necessary	necessary	ADJ
ejpam-1234	46	20	to	to	PART
ejpam-1234	46	21	apply	apply	VERB
ejpam-1234	46	22	theorem	theorem	ADJ
ejpam-1234	46	23	6.5	6.5	NUM
ejpam-1234	46	24	of	of	ADP
ejpam-1234	46	25	[	[	X
ejpam-1234	46	26	13	13	NUM
ejpam-1234	46	27	]	]	PUNCT
ejpam-1234	46	28	and	and	CCONJ
ejpam-1234	46	29	prove	prove	VERB
ejpam-1234	46	30	our	our	PRON
ejpam-1234	46	31	main	main	ADJ
ejpam-1234	46	32	theorem	theorem	NOUN
ejpam-1234	46	33	.	.	PUNCT
ejpam-1234	47	1	the	the	DET
ejpam-1234	47	2	direct	direct	ADJ
ejpam-1234	47	3	and	and	CCONJ
ejpam-1234	47	4	geometric	geometric	ADJ
ejpam-1234	47	5	proof	proof	NOUN
ejpam-1234	47	6	of	of	ADP
ejpam-1234	47	7	theorem	theorem	NOUN
ejpam-1234	47	8	4	4	NUM
ejpam-1234	47	9	in	in	ADP
ejpam-1234	47	10	the	the	DET
ejpam-1234	47	11	case	case	NOUN
ejpam-1234	47	12	of	of	ADP
ejpam-1234	47	13	an	an	DET
ejpam-1234	47	14	abelian	abelian	ADJ
ejpam-1234	47	15	group	group	NOUN
ejpam-1234	47	16	g	g	PROPN
ejpam-1234	47	17	is	be	AUX
ejpam-1234	47	18	also	also	ADV
ejpam-1234	47	19	available	available	ADJ
ejpam-1234	47	20	in	in	ADP
ejpam-1234	47	21	[	[	X
ejpam-1234	47	22	17	17	NUM
ejpam-1234	47	23	]	]	PUNCT
ejpam-1234	47	24	.	.	PUNCT
ejpam-1234	48	1	in	in	ADP
ejpam-1234	48	2	order	order	NOUN
ejpam-1234	48	3	to	to	PART
ejpam-1234	48	4	relate	relate	VERB
ejpam-1234	48	5	our	our	PRON
ejpam-1234	48	6	result	result	NOUN
ejpam-1234	48	7	to	to	ADP
ejpam-1234	48	8	ruan	ruan	PROPN
ejpam-1234	48	9	’s	’s	PART
ejpam-1234	48	10	conjecture	conjecture	NOUN
ejpam-1234	48	11	,	,	PUNCT
ejpam-1234	48	12	we	we	PRON
ejpam-1234	48	13	prove	prove	VERB
ejpam-1234	48	14	that	that	SCONJ
ejpam-1234	48	15	,	,	PUNCT
ejpam-1234	48	16	if	if	SCONJ
ejpam-1234	48	17	x	x	X
ejpam-1234	48	18	/	/	SYM
ejpam-1234	48	19	g	g	PROPN
ejpam-1234	48	20	is	be	AUX
ejpam-1234	48	21	an	an	DET
ejpam-1234	48	22	even	even	ADV
ejpam-1234	48	23	dimensional	dimensional	ADJ
ejpam-1234	48	24	gorenstein	gorenstein	ADJ
ejpam-1234	48	25	variety	variety	NOUN
ejpam-1234	48	26	and	and	CCONJ
ejpam-1234	48	27	y	y	PROPN
ejpam-1234	48	28	is	be	AUX
ejpam-1234	48	29	a	a	DET
ejpam-1234	48	30	crepant	crepant	ADJ
ejpam-1234	48	31	resolution	resolution	NOUN
ejpam-1234	48	32	of	of	ADP
ejpam-1234	48	33	x	x	PROPN
ejpam-1234	48	34	/	/	SYM
ejpam-1234	48	35	g	g	NOUN
ejpam-1234	48	36	,	,	PUNCT
ejpam-1234	48	37	then	then	ADV
ejpam-1234	48	38	the	the	DET
ejpam-1234	48	39	natural	natural	ADJ
ejpam-1234	48	40	map	map	NOUN
ejpam-1234	48	41	y	y	PROPN
ejpam-1234	48	42	n	n	CCONJ
ejpam-1234	48	43	/	/	SYM
ejpam-1234	48	44	σn	σn	NOUN
ejpam-1234	48	45	−→	−→	NOUN
ejpam-1234	48	46	x	x	X
ejpam-1234	48	47	n/(gn	n/(gn	PROPN
ejpam-1234	48	48	⋊σn	⋊σn	PROPN
ejpam-1234	48	49	)	)	PUNCT
ejpam-1234	48	50	is	be	AUX
ejpam-1234	48	51	crepant	crepant	ADJ
ejpam-1234	48	52	(	(	PUNCT
ejpam-1234	48	53	theorem	theorem	NOUN
ejpam-1234	48	54	5	5	NUM
ejpam-1234	48	55	)	)	PUNCT
ejpam-1234	48	56	.	.	PUNCT
ejpam-1234	49	1	this	this	PRON
ejpam-1234	49	2	implies	imply	VERB
ejpam-1234	49	3	that	that	SCONJ
ejpam-1234	49	4	,	,	PUNCT
ejpam-1234	49	5	if	if	SCONJ
ejpam-1234	49	6	y	y	PROPN
ejpam-1234	49	7	is	be	AUX
ejpam-1234	49	8	a	a	DET
ejpam-1234	49	9	projective	projective	ADJ
ejpam-1234	49	10	surface	surface	NOUN
ejpam-1234	49	11	with	with	ADP
ejpam-1234	49	12	the	the	DET
ejpam-1234	49	13	trivial	trivial	ADJ
ejpam-1234	49	14	canonical	canonical	ADJ
ejpam-1234	49	15	class	class	NOUN
ejpam-1234	49	16	,	,	PUNCT
ejpam-1234	49	17	then	then	ADV
ejpam-1234	49	18	y	y	PROPN
ejpam-1234	50	1	[	[	X
ejpam-1234	50	2	n	n	X
ejpam-1234	50	3	]	]	X
ejpam-1234	50	4	is	be	AUX
ejpam-1234	50	5	a	a	DET
ejpam-1234	50	6	crepant	crepant	ADJ
ejpam-1234	50	7	resolution	resolution	NOUN
ejpam-1234	50	8	of	of	ADP
ejpam-1234	50	9	x	x	PUNCT
ejpam-1234	50	10	n/(gn	n/(gn	PROPN
ejpam-1234	50	11	⋊	⋊	NUM
ejpam-1234	50	12	σn	σn	NOUN
ejpam-1234	50	13	)	)	PUNCT
ejpam-1234	50	14	,	,	PUNCT
ejpam-1234	50	15	i.e.	i.e.	X
ejpam-1234	50	16	tomoo	tomoo	VERB
ejpam-1234	50	17	matsumura	matsumura	ADJ
ejpam-1234	50	18	/	/	SYM
ejpam-1234	50	19	eur	eur	PROPN
ejpam-1234	50	20	.	.	PUNCT
ejpam-1234	51	1	j.	j.	PROPN
ejpam-1234	51	2	pure	pure	PROPN
ejpam-1234	51	3	appl	appl	PROPN
ejpam-1234	51	4	.	.	PROPN
ejpam-1234	51	5	math	math	PROPN
ejpam-1234	51	6	,	,	PUNCT
ejpam-1234	51	7	5	5	NUM
ejpam-1234	51	8	(	(	PUNCT
ejpam-1234	51	9	2012	2012	NUM
ejpam-1234	51	10	)	)	PUNCT
ejpam-1234	51	11	,	,	PUNCT
ejpam-1234	51	12	492	492	NUM
ejpam-1234	51	13	-	-	SYM
ejpam-1234	51	14	510	510	NUM
ejpam-1234	51	15	494	494	NUM
ejpam-1234	51	16	the	the	DET
ejpam-1234	51	17	composition	composition	NOUN
ejpam-1234	51	18	y	y	PROPN
ejpam-1234	52	1	[	[	X
ejpam-1234	52	2	n	n	CCONJ
ejpam-1234	52	3	]	]	X
ejpam-1234	52	4	−→	−→	PROPN
ejpam-1234	52	5	y	y	PROPN
ejpam-1234	52	6	n	n	CCONJ
ejpam-1234	52	7	/	/	SYM
ejpam-1234	52	8	σn	σn	NOUN
ejpam-1234	52	9	−→	−→	NOUN
ejpam-1234	52	10	x	x	SYM
ejpam-1234	52	11	n/(gn	n/(gn	PROPN
ejpam-1234	52	12	⋊	⋊	NUM
ejpam-1234	52	13	σn	σn	NOUN
ejpam-1234	52	14	)	)	PUNCT
ejpam-1234	52	15	is	be	AUX
ejpam-1234	52	16	a	a	DET
ejpam-1234	52	17	crepant	crepant	ADJ
ejpam-1234	52	18	resolution	resolution	NOUN
ejpam-1234	52	19	(	(	PUNCT
ejpam-1234	52	20	conjectured	conjecture	VERB
ejpam-1234	52	21	in	in	ADP
ejpam-1234	52	22	[	[	X
ejpam-1234	52	23	25	25	NUM
ejpam-1234	52	24	,	,	PUNCT
ejpam-1234	52	25	p.20	p.20	X
ejpam-1234	52	26	]	]	X
ejpam-1234	52	27	)	)	PUNCT
ejpam-1234	52	28	.	.	PUNCT
ejpam-1234	53	1	together	together	ADV
ejpam-1234	53	2	with	with	ADP
ejpam-1234	53	3	theorem	theorem	NOUN
ejpam-1234	53	4	4	4	NUM
ejpam-1234	53	5	and	and	CCONJ
ejpam-1234	53	6	the	the	DET
ejpam-1234	53	7	result	result	NOUN
ejpam-1234	53	8	in	in	ADP
ejpam-1234	53	9	[	[	X
ejpam-1234	53	10	14	14	NUM
ejpam-1234	53	11	]	]	PUNCT
ejpam-1234	53	12	,	,	PUNCT
ejpam-1234	53	13	we	we	PRON
ejpam-1234	53	14	obtain	obtain	VERB
ejpam-1234	53	15	a	a	DET
ejpam-1234	53	16	verification	verification	NOUN
ejpam-1234	53	17	of	of	ADP
ejpam-1234	53	18	the	the	DET
ejpam-1234	53	19	cohomological	cohomological	ADJ
ejpam-1234	53	20	hyper	hyper	ADJ
ejpam-1234	53	21	-	-	ADJ
ejpam-1234	53	22	kähler	kähler	NOUN
ejpam-1234	53	23	resolution	resolution	NOUN
ejpam-1234	53	24	conjecture	conjecture	NOUN
ejpam-1234	53	25	in	in	ADP
ejpam-1234	53	26	a	a	DET
ejpam-1234	53	27	special	special	ADJ
ejpam-1234	53	28	case	case	NOUN
ejpam-1234	53	29	:	:	PUNCT
ejpam-1234	53	30	if	if	SCONJ
ejpam-1234	53	31	h∗(y	h∗(y	PROPN
ejpam-1234	53	32	)	)	PUNCT
ejpam-1234	53	33	∼=	∼=	PROPN
ejpam-1234	53	34	h∗	h∗	NOUN
ejpam-1234	53	35	or	or	CCONJ
ejpam-1234	53	36	b	b	PROPN
ejpam-1234	53	37	(	(	PUNCT
ejpam-1234	53	38	[	[	X
ejpam-1234	53	39	x	x	X
ejpam-1234	53	40	/	/	SYM
ejpam-1234	53	41	g	g	NOUN
ejpam-1234	53	42	]	]	PUNCT
ejpam-1234	53	43	)	)	PUNCT
ejpam-1234	53	44	,	,	PUNCT
ejpam-1234	53	45	then	then	ADV
ejpam-1234	53	46	h∗or	h∗or	NUM
ejpam-1234	53	47	b([x	b([x	ADJ
ejpam-1234	53	48	n/(gn⋊σn	n/(gn⋊σn	PROPN
ejpam-1234	53	49	)	)	PUNCT
ejpam-1234	53	50	]	]	PUNCT
ejpam-1234	53	51	)	)	PUNCT
ejpam-1234	53	52	∼=	∼=	PROPN
ejpam-1234	53	53	h∗or	h∗or	NUM
ejpam-1234	53	54	b([x	b([x	ADJ
ejpam-1234	53	55	/	/	SYM
ejpam-1234	53	56	g]){σn	g]){σn	NOUN
ejpam-1234	53	57	}	}	PUNCT
ejpam-1234	53	58	σn	σn	NOUN
ejpam-1234	53	59	∼=	∼=	PROPN
ejpam-1234	53	60	h∗(y	h∗(y	PROPN
ejpam-1234	53	61	)	)	PUNCT
ejpam-1234	53	62	{	{	PUNCT
ejpam-1234	53	63	σn	σn	NOUN
ejpam-1234	53	64	}	}	PUNCT
ejpam-1234	53	65	σn	σn	NOUN
ejpam-1234	53	66	∼=	∼=	PROPN
ejpam-1234	53	67	h∗(y	h∗(y	NOUN
ejpam-1234	53	68	[	[	X
ejpam-1234	53	69	n	n	X
ejpam-1234	53	70	]	]	PUNCT
ejpam-1234	53	71	)	)	PUNCT
ejpam-1234	53	72	.	.	PUNCT
ejpam-1234	54	1	when	when	SCONJ
ejpam-1234	54	2	x	x	PRON
ejpam-1234	54	3	=	=	SYM
ejpam-1234	54	4	c2	c2	PROPN
ejpam-1234	54	5	and	and	CCONJ
ejpam-1234	54	6	g	g	PROPN
ejpam-1234	54	7	is	be	AUX
ejpam-1234	54	8	a	a	DET
ejpam-1234	54	9	finite	finite	ADJ
ejpam-1234	54	10	subgroup	subgroup	NOUN
ejpam-1234	54	11	of	of	ADP
ejpam-1234	54	12	sl2(c	sl2(c	PROPN
ejpam-1234	54	13	)	)	PUNCT
ejpam-1234	54	14	,	,	PUNCT
ejpam-1234	54	15	it	it	PRON
ejpam-1234	54	16	is	be	AUX
ejpam-1234	54	17	proved	prove	VERB
ejpam-1234	54	18	in	in	ADP
ejpam-1234	54	19	a	a	DET
ejpam-1234	54	20	completely	completely	ADV
ejpam-1234	54	21	different	different	ADJ
ejpam-1234	54	22	way	way	NOUN
ejpam-1234	55	1	[	[	X
ejpam-1234	55	2	6	6	NUM
ejpam-1234	55	3	]	]	PUNCT
ejpam-1234	55	4	.	.	PUNCT
ejpam-1234	56	1	the	the	DET
ejpam-1234	56	2	structure	structure	NOUN
ejpam-1234	56	3	of	of	ADP
ejpam-1234	56	4	the	the	DET
ejpam-1234	56	5	rest	rest	NOUN
ejpam-1234	56	6	of	of	ADP
ejpam-1234	56	7	the	the	DET
ejpam-1234	56	8	paper	paper	NOUN
ejpam-1234	56	9	is	be	AUX
ejpam-1234	56	10	as	as	SCONJ
ejpam-1234	56	11	follows	follow	VERB
ejpam-1234	56	12	.	.	PUNCT
ejpam-1234	57	1	in	in	ADP
ejpam-1234	57	2	section	section	NOUN
ejpam-1234	57	3	2	2	NUM
ejpam-1234	57	4	,	,	PUNCT
ejpam-1234	57	5	we	we	PRON
ejpam-1234	57	6	review	review	VERB
ejpam-1234	57	7	the	the	DET
ejpam-1234	57	8	definition	definition	NOUN
ejpam-1234	57	9	of	of	ADP
ejpam-1234	57	10	a	a	DET
ejpam-1234	57	11	g	g	NOUN
ejpam-1234	57	12	-	-	PUNCT
ejpam-1234	57	13	frobenius	frobenius	NOUN
ejpam-1234	57	14	algebra	algebra	NOUN
ejpam-1234	57	15	and	and	CCONJ
ejpam-1234	57	16	show	show	VERB
ejpam-1234	57	17	that	that	SCONJ
ejpam-1234	57	18	,	,	PUNCT
ejpam-1234	57	19	if	if	SCONJ
ejpam-1234	57	20	h	h	NOUN
ejpam-1234	57	21	is	be	AUX
ejpam-1234	57	22	an	an	DET
ejpam-1234	57	23	(	(	PUNCT
ejpam-1234	57	24	k	k	X
ejpam-1234	57	25	⋊	⋊	NUM
ejpam-1234	57	26	l)-frobenius	l)-frobenius	PROPN
ejpam-1234	57	27	algebra	algebra	NOUN
ejpam-1234	57	28	,	,	PUNCT
ejpam-1234	57	29	then	then	ADV
ejpam-1234	57	30	the	the	DET
ejpam-1234	57	31	k	k	NOUN
ejpam-1234	57	32	-	-	PUNCT
ejpam-1234	57	33	invariants	invariant	NOUN
ejpam-1234	57	34	of	of	ADP
ejpam-1234	57	35	h	h	NOUN
ejpam-1234	57	36	form	form	VERB
ejpam-1234	57	37	an	an	DET
ejpam-1234	57	38	l	l	NOUN
ejpam-1234	57	39	-	-	ADJ
ejpam-1234	57	40	frobenius	frobenius	ADJ
ejpam-1234	57	41	algebra	algebra	NOUN
ejpam-1234	57	42	.	.	PUNCT
ejpam-1234	58	1	also	also	ADV
ejpam-1234	58	2	we	we	PRON
ejpam-1234	58	3	review	review	VERB
ejpam-1234	58	4	the	the	DET
ejpam-1234	58	5	construction	construction	NOUN
ejpam-1234	58	6	of	of	ADP
ejpam-1234	58	7	stringy	stringy	ADJ
ejpam-1234	58	8	and	and	CCONJ
ejpam-1234	58	9	orbifold	orbifold	ADJ
ejpam-1234	58	10	cohomology	cohomology	NOUN
ejpam-1234	58	11	following	follow	VERB
ejpam-1234	58	12	[	[	X
ejpam-1234	58	13	11	11	NUM
ejpam-1234	58	14	]	]	PUNCT
ejpam-1234	58	15	.	.	PUNCT
ejpam-1234	59	1	in	in	ADP
ejpam-1234	59	2	section	section	NOUN
ejpam-1234	59	3	3	3	NUM
ejpam-1234	59	4	,	,	PUNCT
ejpam-1234	59	5	we	we	PRON
ejpam-1234	59	6	study	study	VERB
ejpam-1234	59	7	wreath	wreath	NOUN
ejpam-1234	59	8	product	product	NOUN
ejpam-1234	59	9	orbifolds	orbifold	VERB
ejpam-1234	59	10	and	and	CCONJ
ejpam-1234	59	11	compute	compute	VERB
ejpam-1234	59	12	the	the	DET
ejpam-1234	59	13	obstruction	obstruction	NOUN
ejpam-1234	59	14	bundles	bundle	NOUN
ejpam-1234	59	15	for	for	ADP
ejpam-1234	59	16	the	the	DET
ejpam-1234	59	17	cases	case	NOUN
ejpam-1234	59	18	that	that	PRON
ejpam-1234	59	19	we	we	PRON
ejpam-1234	59	20	need	need	VERB
ejpam-1234	59	21	to	to	PART
ejpam-1234	59	22	prove	prove	VERB
ejpam-1234	59	23	the	the	DET
ejpam-1234	59	24	main	main	ADJ
ejpam-1234	59	25	theorem	theorem	NOUN
ejpam-1234	59	26	.	.	PUNCT
ejpam-1234	60	1	in	in	ADP
ejpam-1234	60	2	section	section	NOUN
ejpam-1234	60	3	4	4	NUM
ejpam-1234	60	4	,	,	PUNCT
ejpam-1234	60	5	we	we	PRON
ejpam-1234	60	6	prove	prove	VERB
ejpam-1234	60	7	the	the	DET
ejpam-1234	60	8	main	main	ADJ
ejpam-1234	60	9	theorem	theorem	NOUN
ejpam-1234	60	10	.	.	PUNCT
ejpam-1234	61	1	in	in	ADP
ejpam-1234	61	2	section	section	NOUN
ejpam-1234	61	3	5	5	NUM
ejpam-1234	61	4	,	,	PUNCT
ejpam-1234	61	5	we	we	PRON
ejpam-1234	61	6	prove	prove	VERB
ejpam-1234	61	7	the	the	DET
ejpam-1234	61	8	crepantness	crepantness	NOUN
ejpam-1234	61	9	of	of	ADP
ejpam-1234	61	10	the	the	DET
ejpam-1234	61	11	map	map	NOUN
ejpam-1234	61	12	y	y	PROPN
ejpam-1234	61	13	n	n	CCONJ
ejpam-1234	61	14	/	/	SYM
ejpam-1234	61	15	σn	σn	NOUN
ejpam-1234	61	16	−→	−→	NOUN
ejpam-1234	61	17	x	x	X
ejpam-1234	61	18	n/(gn	n/(gn	PROPN
ejpam-1234	61	19	⋊σn	⋊σn	PROPN
ejpam-1234	61	20	)	)	PUNCT
ejpam-1234	61	21	and	and	CCONJ
ejpam-1234	61	22	apply	apply	VERB
ejpam-1234	61	23	our	our	PRON
ejpam-1234	61	24	main	main	ADJ
ejpam-1234	61	25	theorem	theorem	NOUN
ejpam-1234	61	26	to	to	PART
ejpam-1234	61	27	verify	verify	VERB
ejpam-1234	61	28	the	the	DET
ejpam-1234	61	29	spacial	spacial	ADJ
ejpam-1234	61	30	case	case	NOUN
ejpam-1234	61	31	of	of	ADP
ejpam-1234	61	32	the	the	DET
ejpam-1234	61	33	cohomological	cohomological	ADJ
ejpam-1234	61	34	hyper	hyper	ADJ
ejpam-1234	61	35	-	-	ADJ
ejpam-1234	61	36	kähler	kähler	NOUN
ejpam-1234	61	37	resolution	resolution	NOUN
ejpam-1234	61	38	conjecture	conjecture	NOUN
ejpam-1234	61	39	.	.	PUNCT
ejpam-1234	62	1	in	in	ADP
ejpam-1234	62	2	the	the	DET
ejpam-1234	62	3	appendix	appendix	NOUN
ejpam-1234	62	4	,	,	PUNCT
ejpam-1234	62	5	we	we	PRON
ejpam-1234	62	6	review	review	VERB
ejpam-1234	62	7	the	the	DET
ejpam-1234	62	8	construction	construction	NOUN
ejpam-1234	62	9	of	of	ADP
ejpam-1234	62	10	lehn	lehn	NOUN
ejpam-1234	62	11	-	-	PUNCT
ejpam-1234	62	12	sorger	sorger	NOUN
ejpam-1234	62	13	’s	’s	PART
ejpam-1234	62	14	algebras	algebra	NOUN
ejpam-1234	62	15	and	and	CCONJ
ejpam-1234	62	16	the	the	DET
ejpam-1234	62	17	uniqueness	uniqueness	NOUN
ejpam-1234	62	18	theorem	theorem	NOUN
ejpam-1234	62	19	of	of	ADP
ejpam-1234	62	20	kaufmann	kaufmann	PROPN
ejpam-1234	62	21	.	.	PUNCT
ejpam-1234	63	1	unless	unless	SCONJ
ejpam-1234	63	2	otherwise	otherwise	ADV
ejpam-1234	63	3	specified	specify	VERB
ejpam-1234	63	4	,	,	PUNCT
ejpam-1234	63	5	we	we	PRON
ejpam-1234	63	6	assume	assume	VERB
ejpam-1234	63	7	throughout	throughout	ADP
ejpam-1234	63	8	the	the	DET
ejpam-1234	63	9	paper	paper	NOUN
ejpam-1234	63	10	that	that	PRON
ejpam-1234	63	11	all	all	DET
ejpam-1234	63	12	groups	group	NOUN
ejpam-1234	63	13	are	be	AUX
ejpam-1234	63	14	finite	finite	ADJ
ejpam-1234	63	15	and	and	CCONJ
ejpam-1234	63	16	all	all	DET
ejpam-1234	63	17	group	group	NOUN
ejpam-1234	63	18	actions	action	NOUN
ejpam-1234	63	19	are	be	AUX
ejpam-1234	63	20	left	leave	VERB
ejpam-1234	63	21	actions	action	NOUN
ejpam-1234	63	22	.	.	PUNCT
ejpam-1234	64	1	also	also	ADV
ejpam-1234	64	2	,	,	PUNCT
ejpam-1234	64	3	unless	unless	SCONJ
ejpam-1234	64	4	otherwise	otherwise	ADV
ejpam-1234	64	5	specified	specify	VERB
ejpam-1234	64	6	,	,	PUNCT
ejpam-1234	64	7	all	all	PRON
ejpam-1234	64	8	of	of	ADP
ejpam-1234	64	9	the	the	DET
ejpam-1234	64	10	vector	vector	NOUN
ejpam-1234	64	11	spaces	space	NOUN
ejpam-1234	64	12	are	be	AUX
ejpam-1234	64	13	finite	finite	ADJ
ejpam-1234	64	14	dimensional	dimensional	ADJ
ejpam-1234	64	15	and	and	CCONJ
ejpam-1234	64	16	over	over	ADP
ejpam-1234	64	17	q	q	NOUN
ejpam-1234	64	18	,	,	PUNCT
ejpam-1234	64	19	and	and	CCONJ
ejpam-1234	64	20	all	all	DET
ejpam-1234	64	21	coefficient	coefficient	NOUN
ejpam-1234	64	22	rings	ring	NOUN
ejpam-1234	64	23	for	for	ADP
ejpam-1234	64	24	cohomology	cohomology	NOUN
ejpam-1234	64	25	and	and	CCONJ
ejpam-1234	64	26	k	k	NOUN
ejpam-1234	64	27	-	-	NOUN
ejpam-1234	64	28	theory	theory	NOUN
ejpam-1234	64	29	are	be	AUX
ejpam-1234	64	30	q.	q.	NOUN
ejpam-1234	64	31	2	2	NUM
ejpam-1234	64	32	.	.	PUNCT
ejpam-1234	65	1	g	g	NOUN
ejpam-1234	65	2	-	-	PUNCT
ejpam-1234	65	3	frobenius	frobenius	NOUN
ejpam-1234	65	4	algebras	algebra	NOUN
ejpam-1234	65	5	and	and	CCONJ
ejpam-1234	65	6	semidirect	semidirect	PROPN
ejpam-1234	65	7	products	product	NOUN
ejpam-1234	65	8	recall	recall	VERB
ejpam-1234	65	9	the	the	DET
ejpam-1234	65	10	definition	definition	NOUN
ejpam-1234	65	11	of	of	ADP
ejpam-1234	65	12	a	a	DET
ejpam-1234	65	13	g	g	NOUN
ejpam-1234	65	14	-	-	PUNCT
ejpam-1234	65	15	frobenius	frobenius	NOUN
ejpam-1234	65	16	algebra	algebra	NOUN
ejpam-1234	65	17	for	for	ADP
ejpam-1234	65	18	a	a	DET
ejpam-1234	65	19	group	group	NOUN
ejpam-1234	65	20	g	g	NOUN
ejpam-1234	65	21	from	from	ADP
ejpam-1234	65	22	[	[	X
ejpam-1234	65	23	11	11	NUM
ejpam-1234	65	24	]	]	PUNCT
ejpam-1234	65	25	section	section	NOUN
ejpam-1234	65	26	3	3	NUM
ejpam-1234	65	27	.	.	PUNCT
ejpam-1234	65	28	definition	definition	NOUN
ejpam-1234	65	29	1	1	NUM
ejpam-1234	65	30	.	.	PUNCT
ejpam-1234	66	1	let	let	VERB
ejpam-1234	66	2	g	g	PRON
ejpam-1234	66	3	be	be	AUX
ejpam-1234	66	4	a	a	DET
ejpam-1234	66	5	group	group	NOUN
ejpam-1234	66	6	.	.	PUNCT
ejpam-1234	67	1	a	a	DET
ejpam-1234	67	2	g	g	NOUN
ejpam-1234	67	3	-	-	PUNCT
ejpam-1234	67	4	graded	grade	VERB
ejpam-1234	67	5	g	g	NOUN
ejpam-1234	67	6	-	-	PUNCT
ejpam-1234	67	7	module	module	NOUN
ejpam-1234	67	8	(	(	PUNCT
ejpam-1234	67	9	h	h	NOUN
ejpam-1234	67	10	,	,	PUNCT
ejpam-1234	67	11	ρ	ρ	PROPN
ejpam-1234	67	12	)	)	PUNCT
ejpam-1234	67	13	is	be	AUX
ejpam-1234	67	14	a	a	DET
ejpam-1234	67	15	g	g	NOUN
ejpam-1234	67	16	-	-	PUNCT
ejpam-1234	67	17	graded	grade	VERB
ejpam-1234	67	18	vector	vector	NOUN
ejpam-1234	67	19	space	space	NOUN
ejpam-1234	67	20	h	h	NOUN
ejpam-1234	67	21	:	:	PUNCT
ejpam-1234	67	22	=	=	PROPN
ejpam-1234	67	23	⊕	⊕	PROPN
ejpam-1234	67	24	g∈ghg	g∈ghg	PROPN
ejpam-1234	67	25	with	with	ADP
ejpam-1234	67	26	the	the	DET
ejpam-1234	67	27	structure	structure	NOUN
ejpam-1234	67	28	of	of	ADP
ejpam-1234	67	29	a	a	DET
ejpam-1234	67	30	left	left	ADJ
ejpam-1234	67	31	g	g	NOUN
ejpam-1234	67	32	-	-	PUNCT
ejpam-1234	67	33	module	module	NOUN
ejpam-1234	67	34	by	by	ADP
ejpam-1234	67	35	isomorphisms	isomorphisms	PROPN
ejpam-1234	67	36	ρg	ρg	PROPN
ejpam-1234	67	37	:	:	PUNCT
ejpam-1234	67	38	h	h	PROPN
ejpam-1234	67	39	≃	≃	VERB
ejpam-1234	67	40	−→	−→	NOUN
ejpam-1234	67	41	h	h	NOUN
ejpam-1234	67	42	such	such	ADJ
ejpam-1234	67	43	that	that	SCONJ
ejpam-1234	67	44	ρg	ρg	NOUN
ejpam-1234	67	45	takes	take	VERB
ejpam-1234	67	46	hh	hh	PROPN
ejpam-1234	67	47	to	to	ADP
ejpam-1234	67	48	hghg−1	hghg−1	PROPN
ejpam-1234	67	49	for	for	ADP
ejpam-1234	67	50	all	all	DET
ejpam-1234	67	51	g	g	NOUN
ejpam-1234	67	52	,	,	PUNCT
ejpam-1234	67	53	h	h	NOUN
ejpam-1234	67	54	in	in	ADP
ejpam-1234	67	55	g.	g.	PROPN
ejpam-1234	67	56	we	we	PRON
ejpam-1234	67	57	denote	denote	VERB
ejpam-1234	67	58	a	a	DET
ejpam-1234	67	59	vector	vector	NOUN
ejpam-1234	67	60	in	in	ADP
ejpam-1234	67	61	hg	hg	NOUN
ejpam-1234	67	62	by	by	ADP
ejpam-1234	67	63	vg	vg	NOUN
ejpam-1234	67	64	for	for	ADP
ejpam-1234	67	65	any	any	DET
ejpam-1234	67	66	g	g	PROPN
ejpam-1234	67	67	∈	∈	PROPN
ejpam-1234	67	68	g	g	NOUN
ejpam-1234	67	69	definition	definition	NOUN
ejpam-1234	67	70	2	2	NUM
ejpam-1234	67	71	.	.	PUNCT
ejpam-1234	68	1	a	a	DET
ejpam-1234	68	2	tuple	tuple	NOUN
ejpam-1234	68	3	(	(	PUNCT
ejpam-1234	68	4	h	h	NOUN
ejpam-1234	68	5	,	,	PUNCT
ejpam-1234	68	6	ρ	ρ	PROPN
ejpam-1234	68	7	,	,	PUNCT
ejpam-1234	68	8	·	·	PUNCT
ejpam-1234	68	9	,	,	PUNCT
ejpam-1234	68	10	1,η	1,η	NUM
ejpam-1234	68	11	)	)	PUNCT
ejpam-1234	68	12	is	be	AUX
ejpam-1234	68	13	said	say	VERB
ejpam-1234	68	14	to	to	PART
ejpam-1234	68	15	be	be	AUX
ejpam-1234	68	16	a	a	DET
ejpam-1234	68	17	g-(equivariant	g-(equivariant	NOUN
ejpam-1234	68	18	)	)	PUNCT
ejpam-1234	68	19	frobenius	frobenius	NOUN
ejpam-1234	68	20	algebra	algebra	NOUN
ejpam-1234	68	21	provided	provide	VERB
ejpam-1234	68	22	that	that	SCONJ
ejpam-1234	68	23	the	the	DET
ejpam-1234	68	24	following	follow	VERB
ejpam-1234	68	25	properties	property	NOUN
ejpam-1234	68	26	hold	hold	VERB
ejpam-1234	68	27	:	:	PUNCT
ejpam-1234	68	28	i	i	X
ejpam-1234	68	29	)	)	PUNCT
ejpam-1234	68	30	(	(	PUNCT
ejpam-1234	68	31	g	g	NOUN
ejpam-1234	68	32	-	-	PUNCT
ejpam-1234	68	33	graded	grade	VERB
ejpam-1234	68	34	g	g	NOUN
ejpam-1234	68	35	-	-	PUNCT
ejpam-1234	68	36	module	module	NOUN
ejpam-1234	68	37	)	)	PUNCT
ejpam-1234	68	38	(	(	PUNCT
ejpam-1234	68	39	h	h	NOUN
ejpam-1234	68	40	,	,	PUNCT
ejpam-1234	68	41	ρ	ρ	PROPN
ejpam-1234	68	42	)	)	PUNCT
ejpam-1234	68	43	is	be	AUX
ejpam-1234	68	44	a	a	DET
ejpam-1234	68	45	g	g	NOUN
ejpam-1234	68	46	-	-	PUNCT
ejpam-1234	68	47	graded	grade	VERB
ejpam-1234	68	48	g	g	NOUN
ejpam-1234	68	49	-	-	PUNCT
ejpam-1234	68	50	module	module	NOUN
ejpam-1234	68	51	.	.	PUNCT
ejpam-1234	68	52	ii	ii	PROPN
ejpam-1234	68	53	)	)	PUNCT
ejpam-1234	68	54	(	(	PUNCT
ejpam-1234	68	55	self	self	NOUN
ejpam-1234	68	56	-	-	PUNCT
ejpam-1234	68	57	invariance	invariance	NOUN
ejpam-1234	68	58	)	)	PUNCT
ejpam-1234	68	59	for	for	ADP
ejpam-1234	68	60	all	all	DET
ejpam-1234	68	61	g	g	NOUN
ejpam-1234	68	62	in	in	ADP
ejpam-1234	68	63	g	g	PROPN
ejpam-1234	68	64	,	,	PUNCT
ejpam-1234	68	65	ρg	ρg	PROPN
ejpam-1234	68	66	:	:	PUNCT
ejpam-1234	68	67	hg	hg	NOUN
ejpam-1234	68	68	→hg	→hg	NOUN
ejpam-1234	68	69	is	be	AUX
ejpam-1234	68	70	the	the	DET
ejpam-1234	68	71	identity	identity	NOUN
ejpam-1234	68	72	map	map	NOUN
ejpam-1234	68	73	.	.	PUNCT
ejpam-1234	69	1	iii	iii	X
ejpam-1234	69	2	)	)	PUNCT
ejpam-1234	69	3	(	(	PUNCT
ejpam-1234	69	4	metric	metric	NOUN
ejpam-1234	69	5	)	)	PUNCT
ejpam-1234	69	6	η	η	PROPN
ejpam-1234	69	7	is	be	AUX
ejpam-1234	69	8	a	a	DET
ejpam-1234	69	9	symmetric	symmetric	ADJ
ejpam-1234	69	10	non	non	ADJ
ejpam-1234	69	11	-	-	ADJ
ejpam-1234	69	12	degenerate	degenerate	ADJ
ejpam-1234	69	13	bilinear	bilinear	NOUN
ejpam-1234	69	14	form	form	NOUN
ejpam-1234	69	15	on	on	ADP
ejpam-1234	69	16	h	h	PROPN
ejpam-1234	69	17	s.t	s.t	PROPN
ejpam-1234	69	18	.	.	PUNCT
ejpam-1234	69	19	η(vg	η(vg	PROPN
ejpam-1234	69	20	,	,	PUNCT
ejpam-1234	69	21	vh	vh	PROPN
ejpam-1234	69	22	)	)	PUNCT
ejpam-1234	69	23	=	=	SYM
ejpam-1234	69	24	0	0	PUNCT
ejpam-1234	69	25	unless	unless	SCONJ
ejpam-1234	69	26	gh=	gh=	ADJ
ejpam-1234	69	27	1	1	NUM
ejpam-1234	69	28	.	.	NUM
ejpam-1234	69	29	iv	iv	X
ejpam-1234	69	30	)	)	PUNCT
ejpam-1234	69	31	(	(	PUNCT
ejpam-1234	69	32	associativity	associativity	NOUN
ejpam-1234	69	33	)	)	PUNCT
ejpam-1234	69	34	(	(	PUNCT
ejpam-1234	69	35	h	h	NOUN
ejpam-1234	69	36	,	,	PUNCT
ejpam-1234	69	37	·	·	PUNCT
ejpam-1234	69	38	,	,	PUNCT
ejpam-1234	69	39	1	1	NUM
ejpam-1234	69	40	)	)	PUNCT
ejpam-1234	69	41	is	be	AUX
ejpam-1234	69	42	a	a	DET
ejpam-1234	69	43	unital	unital	ADJ
ejpam-1234	69	44	associative	associative	ADJ
ejpam-1234	69	45	algebra	algebra	NOUN
ejpam-1234	69	46	.	.	PUNCT
ejpam-1234	70	1	v	v	X
ejpam-1234	70	2	)	)	PUNCT
ejpam-1234	70	3	(	(	PUNCT
ejpam-1234	70	4	g	g	NOUN
ejpam-1234	70	5	-	-	PUNCT
ejpam-1234	70	6	graded	grade	VERB
ejpam-1234	70	7	multiplication	multiplication	NOUN
ejpam-1234	70	8	)	)	PUNCT
ejpam-1234	70	9	vg	vg	ADP
ejpam-1234	70	10	·	·	PUNCT
ejpam-1234	70	11	vh	vh	PROPN
ejpam-1234	70	12	∈hgh	∈hgh	PUNCT
ejpam-1234	70	13	for	for	ADP
ejpam-1234	70	14	all	all	DET
ejpam-1234	70	15	g	g	NOUN
ejpam-1234	70	16	,	,	PUNCT
ejpam-1234	70	17	h	h	NOUN
ejpam-1234	70	18	∈	∈	PROPN
ejpam-1234	70	19	g.	g.	PROPN
ejpam-1234	70	20	vi	vi	PROPN
ejpam-1234	70	21	)	)	PUNCT
ejpam-1234	70	22	(	(	PUNCT
ejpam-1234	70	23	braided	braid	VERB
ejpam-1234	70	24	commutativity	commutativity	NOUN
ejpam-1234	70	25	)	)	PUNCT
ejpam-1234	70	26	vg	vg	ADP
ejpam-1234	70	27	·	·	PUNCT
ejpam-1234	70	28	vh	vh	X
ejpam-1234	70	29	=	=	PUNCT
ejpam-1234	70	30	ρg(vh	ρg(vh	PROPN
ejpam-1234	70	31	)	)	PUNCT
ejpam-1234	70	32	·	·	PUNCT
ejpam-1234	71	1	vg	vg	ADP
ejpam-1234	71	2	for	for	ADP
ejpam-1234	71	3	all	all	DET
ejpam-1234	71	4	g	g	NOUN
ejpam-1234	71	5	,	,	PUNCT
ejpam-1234	71	6	h	h	PROPN
ejpam-1234	71	7	∈	∈	PROPN
ejpam-1234	71	8	g.	g.	PROPN
ejpam-1234	71	9	vii	vii	PROPN
ejpam-1234	71	10	)	)	PUNCT
ejpam-1234	71	11	(	(	PUNCT
ejpam-1234	71	12	g	g	NOUN
ejpam-1234	71	13	-	-	PUNCT
ejpam-1234	71	14	equivariance	equivariance	NOUN
ejpam-1234	71	15	of	of	ADP
ejpam-1234	71	16	the	the	DET
ejpam-1234	71	17	multiplication	multiplication	NOUN
ejpam-1234	71	18	)	)	PUNCT
ejpam-1234	71	19	ρg(v	ρg(v	NOUN
ejpam-1234	71	20	)	)	PUNCT
ejpam-1234	71	21	·	·	PUNCT
ejpam-1234	71	22	ρg(w	ρg(w	X
ejpam-1234	71	23	)	)	PUNCT
ejpam-1234	71	24	=	=	SYM
ejpam-1234	71	25	ρg(v	ρg(v	X
ejpam-1234	71	26	·	·	PUNCT
ejpam-1234	71	27	w	w	X
ejpam-1234	71	28	)	)	PUNCT
ejpam-1234	71	29	for	for	ADP
ejpam-1234	71	30	all	all	DET
ejpam-1234	71	31	g	g	NOUN
ejpam-1234	71	32	in	in	ADP
ejpam-1234	71	33	g	g	NOUN
ejpam-1234	71	34	,	,	PUNCT
ejpam-1234	71	35	and	and	CCONJ
ejpam-1234	71	36	all	all	DET
ejpam-1234	71	37	v	v	NOUN
ejpam-1234	71	38	,	,	PUNCT
ejpam-1234	71	39	w	w	NOUN
ejpam-1234	71	40	∈h	∈h	NOUN
ejpam-1234	71	41	.	.	PUNCT
ejpam-1234	72	1	tomoo	tomoo	VERB
ejpam-1234	72	2	matsumura	matsumura	ADJ
ejpam-1234	72	3	/	/	SYM
ejpam-1234	72	4	eur	eur	PROPN
ejpam-1234	72	5	.	.	PUNCT
ejpam-1234	73	1	j.	j.	PROPN
ejpam-1234	73	2	pure	pure	PROPN
ejpam-1234	73	3	appl	appl	PROPN
ejpam-1234	73	4	.	.	PROPN
ejpam-1234	73	5	math	math	PROPN
ejpam-1234	73	6	,	,	PUNCT
ejpam-1234	73	7	5	5	NUM
ejpam-1234	73	8	(	(	PUNCT
ejpam-1234	73	9	2012	2012	NUM
ejpam-1234	73	10	)	)	PUNCT
ejpam-1234	73	11	,	,	PUNCT
ejpam-1234	73	12	492	492	NUM
ejpam-1234	73	13	-	-	SYM
ejpam-1234	73	14	510	510	NUM
ejpam-1234	73	15	495	495	NUM
ejpam-1234	73	16	viii	viii	NOUN
ejpam-1234	73	17	)	)	PUNCT
ejpam-1234	73	18	(	(	PUNCT
ejpam-1234	73	19	g	g	NOUN
ejpam-1234	73	20	-	-	PUNCT
ejpam-1234	73	21	invariance	invariance	NOUN
ejpam-1234	73	22	of	of	ADP
ejpam-1234	73	23	the	the	DET
ejpam-1234	73	24	metric	metric	ADJ
ejpam-1234	73	25	)	)	PUNCT
ejpam-1234	73	26	η(ρg(v),ρg(w	η(ρg(v),ρg(w	NOUN
ejpam-1234	73	27	)	)	PUNCT
ejpam-1234	73	28	)	)	PUNCT
ejpam-1234	74	1	=	=	PUNCT
ejpam-1234	74	2	η(v	η(v	NOUN
ejpam-1234	74	3	,	,	PUNCT
ejpam-1234	74	4	w	w	NOUN
ejpam-1234	74	5	)	)	PUNCT
ejpam-1234	74	6	for	for	ADP
ejpam-1234	74	7	all	all	DET
ejpam-1234	74	8	g	g	NOUN
ejpam-1234	74	9	in	in	ADP
ejpam-1234	74	10	g	g	NOUN
ejpam-1234	74	11	,	,	PUNCT
ejpam-1234	74	12	and	and	CCONJ
ejpam-1234	74	13	all	all	DET
ejpam-1234	74	14	v	v	NOUN
ejpam-1234	74	15	,	,	PUNCT
ejpam-1234	74	16	w	w	NOUN
ejpam-1234	74	17	∈h	∈h	NOUN
ejpam-1234	74	18	.	.	PUNCT
ejpam-1234	75	1	ix	ix	ADV
ejpam-1234	75	2	)	)	PUNCT
ejpam-1234	75	3	(	(	PUNCT
ejpam-1234	75	4	invariance	invariance	NOUN
ejpam-1234	75	5	of	of	ADP
ejpam-1234	75	6	the	the	DET
ejpam-1234	75	7	metric	metric	ADJ
ejpam-1234	75	8	)	)	PUNCT
ejpam-1234	75	9	η(v1	η(v1	X
ejpam-1234	75	10	·	·	PUNCT
ejpam-1234	75	11	v2	v2	PROPN
ejpam-1234	75	12	,	,	PUNCT
ejpam-1234	75	13	v3	v3	PROPN
ejpam-1234	75	14	)	)	PUNCT
ejpam-1234	75	15	=	=	SYM
ejpam-1234	75	16	η(v1	η(v1	NOUN
ejpam-1234	75	17	,	,	PUNCT
ejpam-1234	75	18	v2	v2	PROPN
ejpam-1234	75	19	·	·	SYM
ejpam-1234	75	20	v3	v3	PROPN
ejpam-1234	75	21	)	)	PUNCT
ejpam-1234	75	22	for	for	ADP
ejpam-1234	75	23	all	all	DET
ejpam-1234	75	24	v1	v1	NOUN
ejpam-1234	75	25	,	,	PUNCT
ejpam-1234	75	26	v2	v2	PROPN
ejpam-1234	75	27	,	,	PUNCT
ejpam-1234	75	28	v3	v3	PROPN
ejpam-1234	75	29	∈h	∈h	NOUN
ejpam-1234	75	30	.	.	PUNCT
ejpam-1234	76	1	x	x	X
ejpam-1234	76	2	)	)	PUNCT
ejpam-1234	76	3	g	g	NOUN
ejpam-1234	76	4	-	-	PUNCT
ejpam-1234	76	5	invariant	invariant	ADJ
ejpam-1234	76	6	identity	identity	NOUN
ejpam-1234	76	7	)	)	PUNCT
ejpam-1234	76	8	ρg(1	ρg(1	NOUN
ejpam-1234	76	9	)	)	PUNCT
ejpam-1234	76	10	=	=	SYM
ejpam-1234	76	11	1	1	NUM
ejpam-1234	76	12	for	for	ADP
ejpam-1234	76	13	all	all	DET
ejpam-1234	76	14	g	g	NOUN
ejpam-1234	76	15	in	in	ADP
ejpam-1234	76	16	g.	g.	PROPN
ejpam-1234	76	17	xi	xi	PROPN
ejpam-1234	76	18	)	)	PUNCT
ejpam-1234	76	19	(	(	PUNCT
ejpam-1234	76	20	trace	trace	NOUN
ejpam-1234	76	21	axiom	axiom	NOUN
ejpam-1234	76	22	)	)	PUNCT
ejpam-1234	76	23	for	for	ADP
ejpam-1234	76	24	all	all	DET
ejpam-1234	76	25	a	a	PRON
ejpam-1234	76	26	,	,	PUNCT
ejpam-1234	76	27	b	b	NOUN
ejpam-1234	76	28	in	in	ADP
ejpam-1234	76	29	g	g	PROPN
ejpam-1234	76	30	and	and	CCONJ
ejpam-1234	76	31	v	v	NOUN
ejpam-1234	76	32	in	in	ADP
ejpam-1234	76	33	h[a	h[a	PROPN
ejpam-1234	76	34	,	,	PUNCT
ejpam-1234	76	35	b	b	NOUN
ejpam-1234	76	36	]	]	X
ejpam-1234	76	37	,	,	PUNCT
ejpam-1234	76	38	if	if	SCONJ
ejpam-1234	76	39	lv	lv	PROPN
ejpam-1234	76	40	denotes	denote	VERB
ejpam-1234	76	41	the	the	DET
ejpam-1234	76	42	left	left	ADJ
ejpam-1234	76	43	multiplication	multiplication	NOUN
ejpam-1234	76	44	by	by	ADP
ejpam-1234	76	45	v	v	NOUN
ejpam-1234	76	46	,	,	PUNCT
ejpam-1234	76	47	then	then	ADV
ejpam-1234	76	48	the	the	DET
ejpam-1234	76	49	following	follow	VERB
ejpam-1234	76	50	equation	equation	NOUN
ejpam-1234	76	51	is	be	AUX
ejpam-1234	76	52	satisfied	satisfied	ADJ
ejpam-1234	76	53	:	:	PUNCT
ejpam-1234	76	54	trha	trha	NOUN
ejpam-1234	76	55	(	(	PUNCT
ejpam-1234	76	56	lv	lv	PROPN
ejpam-1234	76	57	◦	◦	NOUN
ejpam-1234	76	58	ρb	ρb	NUM
ejpam-1234	76	59	)	)	PUNCT
ejpam-1234	76	60	=	=	PUNCT
ejpam-1234	77	1	trhb	trhb	NOUN
ejpam-1234	77	2	(	(	PUNCT
ejpam-1234	77	3	ρa−1	ρa−1	PROPN
ejpam-1234	77	4	◦	◦	NOUN
ejpam-1234	77	5	lv	lv	PROPN
ejpam-1234	77	6	)	)	PUNCT
ejpam-1234	77	7	.	.	PUNCT
ejpam-1234	78	1	remark	remark	PROPN
ejpam-1234	78	2	1	1	NUM
ejpam-1234	78	3	.	.	NOUN
ejpam-1234	78	4	1	1	NUM
ejpam-1234	78	5	)	)	PUNCT
ejpam-1234	78	6	the	the	DET
ejpam-1234	78	7	g	g	NOUN
ejpam-1234	78	8	-	-	PUNCT
ejpam-1234	78	9	frobenius	frobenius	NOUN
ejpam-1234	78	10	algebras	algebra	NOUN
ejpam-1234	78	11	are	be	AUX
ejpam-1234	78	12	introduced	introduce	VERB
ejpam-1234	78	13	in	in	ADP
ejpam-1234	78	14	[	[	X
ejpam-1234	78	15	23	23	NUM
ejpam-1234	78	16	,	,	PUNCT
ejpam-1234	78	17	12	12	NUM
ejpam-1234	78	18	]	]	PUNCT
ejpam-1234	78	19	.	.	PUNCT
ejpam-1234	79	1	definition	definition	NOUN
ejpam-1234	79	2	2.1.1	2.1.1	NUM
ejpam-1234	79	3	of	of	ADP
ejpam-1234	79	4	[	[	X
ejpam-1234	79	5	12	12	NUM
ejpam-1234	79	6	]	]	PUNCT
ejpam-1234	79	7	is	be	AUX
ejpam-1234	79	8	slightly	slightly	ADV
ejpam-1234	79	9	more	more	ADV
ejpam-1234	79	10	general	general	ADJ
ejpam-1234	79	11	than	than	ADP
ejpam-1234	79	12	the	the	DET
ejpam-1234	79	13	above	above	ADJ
ejpam-1234	79	14	definition	definition	NOUN
ejpam-1234	79	15	(	(	PUNCT
ejpam-1234	79	16	see	see	VERB
ejpam-1234	79	17	ii	ii	NOUN
ejpam-1234	79	18	)	)	PUNCT
ejpam-1234	79	19	and	and	CCONJ
ejpam-1234	79	20	xi	xi	NOUN
ejpam-1234	79	21	)	)	PUNCT
ejpam-1234	79	22	)	)	PUNCT
ejpam-1234	79	23	.	.	PUNCT
ejpam-1234	80	1	our	our	PRON
ejpam-1234	80	2	definition	definition	NOUN
ejpam-1234	80	3	is	be	AUX
ejpam-1234	80	4	obtained	obtain	VERB
ejpam-1234	80	5	by	by	ADP
ejpam-1234	80	6	setting	set	VERB
ejpam-1234	80	7	χg	χg	NOUN
ejpam-1234	80	8	=	=	SYM
ejpam-1234	80	9	1	1	NUM
ejpam-1234	80	10	for	for	ADP
ejpam-1234	80	11	all	all	PRON
ejpam-1234	80	12	g	g	PROPN
ejpam-1234	80	13	∈	∈	PROPN
ejpam-1234	80	14	g.	g.	NOUN
ejpam-1234	80	15	2	2	NUM
ejpam-1234	80	16	)	)	PUNCT
ejpam-1234	80	17	a	a	DET
ejpam-1234	80	18	g	g	NOUN
ejpam-1234	80	19	-	-	PUNCT
ejpam-1234	80	20	frobenius	frobenius	NOUN
ejpam-1234	80	21	algebra	algebra	NOUN
ejpam-1234	80	22	when	when	SCONJ
ejpam-1234	80	23	g	g	PROPN
ejpam-1234	80	24	=	=	SYM
ejpam-1234	80	25	{	{	PUNCT
ejpam-1234	80	26	1	1	NUM
ejpam-1234	80	27	}	}	PUNCT
ejpam-1234	80	28	is	be	AUX
ejpam-1234	80	29	a	a	DET
ejpam-1234	80	30	frobenius	frobenius	ADJ
ejpam-1234	80	31	algebra	algebra	NOUN
ejpam-1234	80	32	in	in	ADP
ejpam-1234	80	33	the	the	DET
ejpam-1234	80	34	usual	usual	ADJ
ejpam-1234	80	35	sense	sense	NOUN
ejpam-1234	80	36	.	.	PUNCT
ejpam-1234	81	1	3	3	X
ejpam-1234	81	2	)	)	PUNCT
ejpam-1234	81	3	we	we	PRON
ejpam-1234	81	4	can	can	AUX
ejpam-1234	81	5	also	also	ADV
ejpam-1234	81	6	define	define	VERB
ejpam-1234	81	7	a	a	DET
ejpam-1234	81	8	g	g	NOUN
ejpam-1234	81	9	-	-	PUNCT
ejpam-1234	81	10	frobenius	frobenius	NOUN
ejpam-1234	81	11	superalgebra	superalgebra	NOUN
ejpam-1234	81	12	[	[	X
ejpam-1234	81	13	12	12	NUM
ejpam-1234	81	14	]	]	PUNCT
ejpam-1234	81	15	by	by	ADP
ejpam-1234	81	16	introducing	introduce	VERB
ejpam-1234	81	17	z/2z	z/2z	NOUN
ejpam-1234	81	18	-	-	PUNCT
ejpam-1234	81	19	grading	grade	VERB
ejpam-1234	81	20	and	and	CCONJ
ejpam-1234	81	21	by	by	ADP
ejpam-1234	81	22	introducing	introduce	VERB
ejpam-1234	81	23	signs	sign	NOUN
ejpam-1234	81	24	in	in	ADP
ejpam-1234	81	25	the	the	DET
ejpam-1234	81	26	usual	usual	ADJ
ejpam-1234	81	27	manner	manner	NOUN
ejpam-1234	81	28	,	,	PUNCT
ejpam-1234	81	29	c.f	c.f	PROPN
ejpam-1234	81	30	.	.	PROPN
ejpam-1234	81	31	section	section	PROPN
ejpam-1234	81	32	1.2	1.2	NUM
ejpam-1234	81	33	of	of	ADP
ejpam-1234	81	34	[	[	X
ejpam-1234	81	35	13	13	NUM
ejpam-1234	81	36	]	]	PUNCT
ejpam-1234	81	37	.	.	PUNCT
ejpam-1234	82	1	definition	definition	NOUN
ejpam-1234	82	2	3	3	NUM
ejpam-1234	82	3	.	.	PUNCT
ejpam-1234	83	1	a	a	DET
ejpam-1234	83	2	g	g	NOUN
ejpam-1234	83	3	-	-	PUNCT
ejpam-1234	83	4	frobenius	frobenius	NOUN
ejpam-1234	83	5	algebra	algebra	NOUN
ejpam-1234	83	6	h	h	NOUN
ejpam-1234	83	7	is	be	AUX
ejpam-1234	83	8	said	say	VERB
ejpam-1234	83	9	to	to	PART
ejpam-1234	83	10	be	be	AUX
ejpam-1234	83	11	q	q	ADV
ejpam-1234	83	12	-	-	PUNCT
ejpam-1234	83	13	graded	grade	VERB
ejpam-1234	83	14	if	if	SCONJ
ejpam-1234	83	15	each	each	DET
ejpam-1234	83	16	hg	hg	NOUN
ejpam-1234	83	17	comes	come	VERB
ejpam-1234	83	18	with	with	ADP
ejpam-1234	83	19	a	a	DET
ejpam-1234	83	20	qgrading	qgrade	VERB
ejpam-1234	83	21	hg	hg	X
ejpam-1234	83	22	=	=	PROPN
ejpam-1234	83	23	⊕	⊕	PROPN
ejpam-1234	83	24	r∈qhg	r∈qhg	PROPN
ejpam-1234	83	25	,	,	PUNCT
ejpam-1234	83	26	r	r	NOUN
ejpam-1234	83	27	and	and	CCONJ
ejpam-1234	83	28	the	the	DET
ejpam-1234	83	29	g	g	NOUN
ejpam-1234	83	30	-	-	PUNCT
ejpam-1234	83	31	action	action	NOUN
ejpam-1234	83	32	and	and	CCONJ
ejpam-1234	83	33	the	the	DET
ejpam-1234	83	34	multiplication	multiplication	NOUN
ejpam-1234	83	35	respect	respect	VERB
ejpam-1234	83	36	the	the	DET
ejpam-1234	83	37	q	q	NOUN
ejpam-1234	83	38	-	-	PUNCT
ejpam-1234	83	39	grading	grade	VERB
ejpam-1234	83	40	and	and	CCONJ
ejpam-1234	83	41	the	the	DET
ejpam-1234	83	42	metric	metric	PROPN
ejpam-1234	83	43	η	η	PROPN
ejpam-1234	83	44	satisfies	satisfy	VERB
ejpam-1234	83	45	η(v	η(v	NOUN
ejpam-1234	83	46	,	,	PUNCT
ejpam-1234	83	47	w	w	NOUN
ejpam-1234	83	48	)	)	PUNCT
ejpam-1234	83	49	=	=	SYM
ejpam-1234	83	50	0	0	PUNCT
ejpam-1234	84	1	unless	unless	SCONJ
ejpam-1234	84	2	deg	deg	PROPN
ejpam-1234	84	3	a	a	DET
ejpam-1234	84	4	+	+	PROPN
ejpam-1234	84	5	deg	deg	PROPN
ejpam-1234	84	6	b	b	X
ejpam-1234	84	7	=	=	SYM
ejpam-1234	84	8	d	d	PROPN
ejpam-1234	84	9	≥	≥	NUM
ejpam-1234	84	10	0	0	NUM
ejpam-1234	84	11	,	,	PUNCT
ejpam-1234	84	12	i.e.	i.e.	X
ejpam-1234	84	13	h	h	NOUN
ejpam-1234	84	14	has	have	AUX
ejpam-1234	84	15	degree	degree	NOUN
ejpam-1234	84	16	d.	d.	NOUN
ejpam-1234	84	17	in	in	ADP
ejpam-1234	84	18	this	this	DET
ejpam-1234	84	19	paper	paper	NOUN
ejpam-1234	84	20	,	,	PUNCT
ejpam-1234	84	21	we	we	PRON
ejpam-1234	84	22	assume	assume	VERB
ejpam-1234	84	23	that	that	SCONJ
ejpam-1234	84	24	all	all	DET
ejpam-1234	84	25	g	g	NOUN
ejpam-1234	84	26	-	-	PUNCT
ejpam-1234	84	27	frobenius	frobenius	NOUN
ejpam-1234	84	28	algebras	algebra	NOUN
ejpam-1234	84	29	are	be	AUX
ejpam-1234	84	30	q	q	ADJ
ejpam-1234	84	31	-	-	PUNCT
ejpam-1234	84	32	graded	grade	VERB
ejpam-1234	84	33	.	.	PUNCT
ejpam-1234	85	1	2.1	2.1	NUM
ejpam-1234	85	2	.	.	PUNCT
ejpam-1234	86	1	k	k	X
ejpam-1234	86	2	-	-	PUNCT
ejpam-1234	86	3	invariants	invariant	NOUN
ejpam-1234	86	4	of	of	ADP
ejpam-1234	86	5	a	a	DET
ejpam-1234	86	6	k⋊	k⋊	NOUN
ejpam-1234	86	7	l	l	NOUN
ejpam-1234	86	8	-	-	ADJ
ejpam-1234	86	9	frobenius	frobenius	ADJ
ejpam-1234	86	10	algebra	algebra	NOUN
ejpam-1234	86	11	let	let	VERB
ejpam-1234	86	12	k	k	NOUN
ejpam-1234	86	13	and	and	CCONJ
ejpam-1234	86	14	l	l	PROPN
ejpam-1234	86	15	be	be	AUX
ejpam-1234	86	16	groups	group	NOUN
ejpam-1234	86	17	.	.	PUNCT
ejpam-1234	87	1	suppose	suppose	VERB
ejpam-1234	87	2	that	that	SCONJ
ejpam-1234	87	3	l	l	NOUN
ejpam-1234	87	4	acts	act	VERB
ejpam-1234	87	5	on	on	ADP
ejpam-1234	87	6	k	k	PROPN
ejpam-1234	87	7	from	from	ADP
ejpam-1234	87	8	left	leave	VERB
ejpam-1234	87	9	where	where	SCONJ
ejpam-1234	87	10	the	the	DET
ejpam-1234	87	11	action	action	NOUN
ejpam-1234	87	12	of	of	ADP
ejpam-1234	87	13	l	l	PROPN
ejpam-1234	87	14	∈	∈	PROPN
ejpam-1234	87	15	l	l	NOUN
ejpam-1234	87	16	on	on	ADP
ejpam-1234	87	17	k	k	PROPN
ejpam-1234	87	18	∈	∈	PROPN
ejpam-1234	87	19	k	k	PROPN
ejpam-1234	87	20	is	be	AUX
ejpam-1234	87	21	denoted	denote	VERB
ejpam-1234	87	22	by	by	ADP
ejpam-1234	87	23	k	k	PROPN
ejpam-1234	87	24	l	l	PROPN
ejpam-1234	87	25	7→	7→	PROPN
ejpam-1234	87	26	kl−1	kl−1	VERB
ejpam-1234	87	27	.	.	PUNCT
ejpam-1234	88	1	let	let	VERB
ejpam-1234	88	2	k⋊	k⋊	PROPN
ejpam-1234	88	3	l	l	NOUN
ejpam-1234	88	4	be	be	AUX
ejpam-1234	88	5	a	a	DET
ejpam-1234	88	6	semidirect	semidirect	NOUN
ejpam-1234	88	7	of	of	ADP
ejpam-1234	88	8	groups	group	NOUN
ejpam-1234	88	9	k	k	PROPN
ejpam-1234	88	10	and	and	CCONJ
ejpam-1234	88	11	l	l	NOUN
ejpam-1234	88	12	with	with	ADP
ejpam-1234	88	13	respect	respect	NOUN
ejpam-1234	88	14	to	to	ADP
ejpam-1234	88	15	this	this	DET
ejpam-1234	88	16	action	action	NOUN
ejpam-1234	88	17	.	.	PUNCT
ejpam-1234	89	1	we	we	PRON
ejpam-1234	89	2	identify	identify	VERB
ejpam-1234	89	3	k	k	PROPN
ejpam-1234	89	4	with	with	SCONJ
ejpam-1234	89	5	the	the	DET
ejpam-1234	89	6	normal	normal	ADJ
ejpam-1234	89	7	subgroup	subgroup	NOUN
ejpam-1234	89	8	k⋊	k⋊	NOUN
ejpam-1234	89	9	1	1	NUM
ejpam-1234	89	10	and	and	CCONJ
ejpam-1234	89	11	hence	hence	ADV
ejpam-1234	89	12	the	the	DET
ejpam-1234	89	13	left	left	ADJ
ejpam-1234	89	14	adjoint	adjoint	NOUN
ejpam-1234	89	15	action	action	NOUN
ejpam-1234	89	16	of	of	ADP
ejpam-1234	89	17	l	l	NOUN
ejpam-1234	89	18	on	on	ADP
ejpam-1234	89	19	k	k	PROPN
ejpam-1234	89	20	can	can	AUX
ejpam-1234	89	21	be	be	AUX
ejpam-1234	89	22	identified	identify	VERB
ejpam-1234	89	23	with	with	ADP
ejpam-1234	89	24	the	the	DET
ejpam-1234	89	25	given	give	VERB
ejpam-1234	89	26	action	action	NOUN
ejpam-1234	89	27	of	of	ADP
ejpam-1234	89	28	l	l	NOUN
ejpam-1234	89	29	on	on	ADP
ejpam-1234	89	30	k	k	X
ejpam-1234	89	31	,	,	PUNCT
ejpam-1234	89	32	namely	namely	ADV
ejpam-1234	89	33	,	,	PUNCT
ejpam-1234	89	34	we	we	PRON
ejpam-1234	89	35	have	have	VERB
ejpam-1234	89	36	kl−1	kl−1	NOUN
ejpam-1234	89	37	=	=	SYM
ejpam-1234	89	38	lkl−1	lkl−1	NOUN
ejpam-1234	89	39	,	,	PUNCT
ejpam-1234	89	40	i.e.	i.e.	X
ejpam-1234	89	41	lkl	lkl	PROPN
ejpam-1234	89	42	=	=	SYM
ejpam-1234	89	43	kl	kl	NOUN
ejpam-1234	89	44	or	or	CCONJ
ejpam-1234	89	45	lk	lk	PROPN
ejpam-1234	89	46	=	=	PROPN
ejpam-1234	89	47	kl−1	kl−1	PROPN
ejpam-1234	89	48	l.	l.	NOUN
ejpam-1234	89	49	let	let	VERB
ejpam-1234	89	50	(	(	PUNCT
ejpam-1234	89	51	h	h	NOUN
ejpam-1234	89	52	,	,	PUNCT
ejpam-1234	89	53	ρ	ρ	PROPN
ejpam-1234	89	54	,	,	PUNCT
ejpam-1234	89	55	·	·	PUNCT
ejpam-1234	89	56	,	,	PUNCT
ejpam-1234	89	57	1,η	1,η	NUM
ejpam-1234	89	58	)	)	PUNCT
ejpam-1234	89	59	be	be	VERB
ejpam-1234	89	60	a	a	DET
ejpam-1234	89	61	(	(	PUNCT
ejpam-1234	89	62	k⋊l)-frobenius	k⋊l)-frobenius	PROPN
ejpam-1234	89	63	algebra	algebra	PROPN
ejpam-1234	89	64	.	.	PUNCT
ejpam-1234	90	1	let	let	VERB
ejpam-1234	90	2	πk	πk	X
ejpam-1234	90	3	:	:	PUNCT
ejpam-1234	90	4	h	h	NOUN
ejpam-1234	90	5	→h	→h	PUNCT
ejpam-1234	90	6	be	be	AUX
ejpam-1234	90	7	the	the	DET
ejpam-1234	90	8	averaging	averaging	NOUN
ejpam-1234	90	9	map	map	NOUN
ejpam-1234	90	10	over	over	ADP
ejpam-1234	90	11	k	k	NOUN
ejpam-1234	90	12	:	:	PUNCT
ejpam-1234	90	13	πk(v	πk(v	NUM
ejpam-1234	90	14	)	)	PUNCT
ejpam-1234	90	15	:	:	PUNCT
ejpam-1234	90	16	=	=	SYM
ejpam-1234	90	17	1	1	NUM
ejpam-1234	90	18	|k|	|k|	NOUN
ejpam-1234	90	19	∑	∑	ADV
ejpam-1234	90	20	k∈k	k∈k	NOUN
ejpam-1234	90	21	ρk(v	ρk(v	NUM
ejpam-1234	90	22	)	)	PUNCT
ejpam-1234	90	23	.	.	PUNCT
ejpam-1234	91	1	the	the	DET
ejpam-1234	91	2	image	image	NOUN
ejpam-1234	91	3	πk(h	πk(h	AUX
ejpam-1234	91	4	)	)	PUNCT
ejpam-1234	91	5	is	be	AUX
ejpam-1234	91	6	the	the	DET
ejpam-1234	91	7	space	space	NOUN
ejpam-1234	91	8	of	of	ADP
ejpam-1234	91	9	k	k	NOUN
ejpam-1234	91	10	-	-	PUNCT
ejpam-1234	91	11	invariants	invariant	NOUN
ejpam-1234	91	12	of	of	ADP
ejpam-1234	91	13	h	h	NOUN
ejpam-1234	91	14	,	,	PUNCT
ejpam-1234	91	15	which	which	PRON
ejpam-1234	91	16	we	we	PRON
ejpam-1234	91	17	denote	denote	VERB
ejpam-1234	91	18	by	by	ADP
ejpam-1234	91	19	h	h	PROPN
ejpam-1234	91	20	k.	k.	PROPN
ejpam-1234	91	21	the	the	DET
ejpam-1234	91	22	direct	direct	ADJ
ejpam-1234	91	23	sum	sum	NOUN
ejpam-1234	91	24	h[l	h[l	NOUN
ejpam-1234	91	25	]	]	PUNCT
ejpam-1234	91	26	:	:	PUNCT
ejpam-1234	91	27	=	=	SYM
ejpam-1234	91	28	⊕k∈khkl	⊕k∈khkl	NOUN
ejpam-1234	91	29	is	be	AUX
ejpam-1234	91	30	a	a	DET
ejpam-1234	91	31	k	k	NOUN
ejpam-1234	91	32	-	-	NOUN
ejpam-1234	91	33	module	module	NOUN
ejpam-1234	91	34	and	and	CCONJ
ejpam-1234	91	35	so	so	ADV
ejpam-1234	91	36	denote	denote	VERB
ejpam-1234	91	37	its	its	PRON
ejpam-1234	91	38	k	k	NOUN
ejpam-1234	91	39	-	-	PUNCT
ejpam-1234	91	40	invariants	invariant	NOUN
ejpam-1234	91	41	also	also	ADV
ejpam-1234	91	42	by	by	ADP
ejpam-1234	91	43	h	h	PROPN
ejpam-1234	91	44	k	k	PROPN
ejpam-1234	92	1	[	[	X
ejpam-1234	92	2	l	l	X
ejpam-1234	92	3	]	]	X
ejpam-1234	92	4	:	:	PUNCT
ejpam-1234	92	5	=	=	SYM
ejpam-1234	92	6	πk(h[l	πk(h[l	NOUN
ejpam-1234	92	7	]	]	PUNCT
ejpam-1234	92	8	)	)	PUNCT
ejpam-1234	92	9	.	.	PUNCT
ejpam-1234	93	1	the	the	DET
ejpam-1234	93	2	following	follow	VERB
ejpam-1234	93	3	theorem	theorem	NOUN
ejpam-1234	93	4	is	be	AUX
ejpam-1234	93	5	the	the	DET
ejpam-1234	93	6	starting	starting	NOUN
ejpam-1234	93	7	point	point	NOUN
ejpam-1234	93	8	of	of	ADP
ejpam-1234	93	9	this	this	DET
ejpam-1234	93	10	paper	paper	NOUN
ejpam-1234	93	11	.	.	PUNCT
ejpam-1234	94	1	theorem	theorem	NOUN
ejpam-1234	94	2	1	1	NUM
ejpam-1234	94	3	.	.	PUNCT
ejpam-1234	95	1	if	if	SCONJ
ejpam-1234	95	2	h	h	NOUN
ejpam-1234	95	3	is	be	AUX
ejpam-1234	95	4	a	a	DET
ejpam-1234	95	5	(	(	PUNCT
ejpam-1234	95	6	k⋊	k⋊	PROPN
ejpam-1234	95	7	l)-frobenius	l)-frobenius	PROPN
ejpam-1234	95	8	algebra	algebra	PROPN
ejpam-1234	95	9	,	,	PUNCT
ejpam-1234	95	10	then	then	ADV
ejpam-1234	95	11	h	h	PROPN
ejpam-1234	95	12	k	k	PROPN
ejpam-1234	95	13	is	be	AUX
ejpam-1234	95	14	an	an	DET
ejpam-1234	95	15	l	l	ADJ
ejpam-1234	95	16	-	-	ADJ
ejpam-1234	95	17	frobenius	frobenius	ADJ
ejpam-1234	95	18	algebra	algebra	NOUN
ejpam-1234	95	19	.	.	PUNCT
ejpam-1234	96	1	proof	proof	NOUN
ejpam-1234	96	2	.	.	PUNCT
ejpam-1234	97	1	all	all	PRON
ejpam-1234	97	2	of	of	ADP
ejpam-1234	97	3	the	the	DET
ejpam-1234	97	4	properties	property	NOUN
ejpam-1234	97	5	except	except	SCONJ
ejpam-1234	97	6	the	the	DET
ejpam-1234	97	7	self	self	NOUN
ejpam-1234	97	8	-	-	PUNCT
ejpam-1234	97	9	invariance	invariance	NOUN
ejpam-1234	97	10	property	property	NOUN
ejpam-1234	97	11	and	and	CCONJ
ejpam-1234	97	12	the	the	DET
ejpam-1234	97	13	trace	trace	NOUN
ejpam-1234	97	14	axiom	axiom	NOUN
ejpam-1234	97	15	follow	follow	VERB
ejpam-1234	97	16	immediately	immediately	ADV
ejpam-1234	97	17	from	from	ADP
ejpam-1234	97	18	those	those	DET
ejpam-1234	97	19	properties	property	NOUN
ejpam-1234	97	20	of	of	ADP
ejpam-1234	97	21	h	h	NOUN
ejpam-1234	97	22	.	.	PUNCT
ejpam-1234	98	1	the	the	DET
ejpam-1234	98	2	self	self	NOUN
ejpam-1234	98	3	-	-	PUNCT
ejpam-1234	98	4	invariance	invariance	NOUN
ejpam-1234	98	5	property	property	NOUN
ejpam-1234	98	6	of	of	ADP
ejpam-1234	98	7	h	h	NOUN
ejpam-1234	98	8	k	k	PROPN
ejpam-1234	98	9	is	be	AUX
ejpam-1234	98	10	that	that	SCONJ
ejpam-1234	98	11	,	,	PUNCT
ejpam-1234	98	12	for	for	ADP
ejpam-1234	98	13	all	all	DET
ejpam-1234	98	14	l	l	NOUN
ejpam-1234	98	15	∈	∈	PROPN
ejpam-1234	98	16	l	l	NOUN
ejpam-1234	98	17	,	,	PUNCT
ejpam-1234	98	18	ρl	ρl	INTJ
ejpam-1234	98	19	:	:	PUNCT
ejpam-1234	98	20	h	h	PROPN
ejpam-1234	99	1	k	k	X
ejpam-1234	100	1	[	[	X
ejpam-1234	100	2	l	l	X
ejpam-1234	100	3	]	]	X
ejpam-1234	100	4	→h	→h	PUNCT
ejpam-1234	100	5	k	k	X
ejpam-1234	101	1	[	[	X
ejpam-1234	101	2	l	l	X
ejpam-1234	101	3	]	]	X
ejpam-1234	101	4	is	be	AUX
ejpam-1234	101	5	the	the	DET
ejpam-1234	101	6	identity	identity	NOUN
ejpam-1234	101	7	map	map	NOUN
ejpam-1234	101	8	.	.	PUNCT
ejpam-1234	102	1	this	this	PRON
ejpam-1234	102	2	is	be	AUX
ejpam-1234	102	3	true	true	ADJ
ejpam-1234	102	4	because	because	SCONJ
ejpam-1234	102	5	of	of	ADP
ejpam-1234	102	6	the	the	DET
ejpam-1234	102	7	self	self	NOUN
ejpam-1234	102	8	-	-	PUNCT
ejpam-1234	102	9	invariance	invariance	NOUN
ejpam-1234	102	10	property	property	NOUN
ejpam-1234	102	11	tomoo	tomoo	VERB
ejpam-1234	102	12	matsumura	matsumura	ADJ
ejpam-1234	102	13	/	/	SYM
ejpam-1234	102	14	eur	eur	PROPN
ejpam-1234	102	15	.	.	PUNCT
ejpam-1234	103	1	j.	j.	PROPN
ejpam-1234	103	2	pure	pure	PROPN
ejpam-1234	103	3	appl	appl	PROPN
ejpam-1234	103	4	.	.	PROPN
ejpam-1234	103	5	math	math	PROPN
ejpam-1234	103	6	,	,	PUNCT
ejpam-1234	103	7	5	5	NUM
ejpam-1234	103	8	(	(	PUNCT
ejpam-1234	103	9	2012	2012	NUM
ejpam-1234	103	10	)	)	PUNCT
ejpam-1234	103	11	,	,	PUNCT
ejpam-1234	103	12	492	492	NUM
ejpam-1234	103	13	-	-	SYM
ejpam-1234	103	14	510	510	NUM
ejpam-1234	103	15	496	496	NUM
ejpam-1234	103	16	of	of	ADP
ejpam-1234	103	17	h	h	NOUN
ejpam-1234	103	18	.	.	PUNCT
ejpam-1234	104	1	indeed	indeed	ADV
ejpam-1234	104	2	,	,	PUNCT
ejpam-1234	104	3	for	for	ADP
ejpam-1234	104	4	all	all	DET
ejpam-1234	104	5	kl	kl	NOUN
ejpam-1234	104	6	∈	∈	PROPN
ejpam-1234	104	7	k	k	PROPN
ejpam-1234	104	8	⋊	⋊	PROPN
ejpam-1234	104	9	l	l	NOUN
ejpam-1234	104	10	,	,	PUNCT
ejpam-1234	104	11	ρkl	ρkl	NOUN
ejpam-1234	104	12	restricted	restrict	VERB
ejpam-1234	104	13	to	to	ADP
ejpam-1234	104	14	hkl	hkl	NOUN
ejpam-1234	104	15	is	be	AUX
ejpam-1234	104	16	the	the	DET
ejpam-1234	104	17	identity	identity	NOUN
ejpam-1234	104	18	map	map	NOUN
ejpam-1234	104	19	so	so	SCONJ
ejpam-1234	104	20	that	that	SCONJ
ejpam-1234	104	21	ρk	ρk	AUX
ejpam-1234	104	22	=	=	PUNCT
ejpam-1234	104	23	ρl−1	ρl−1	PROPN
ejpam-1234	104	24	on	on	ADP
ejpam-1234	104	25	hkl	hkl	NOUN
ejpam-1234	104	26	.	.	PUNCT
ejpam-1234	105	1	let	let	VERB
ejpam-1234	105	2	v	v	ADP
ejpam-1234	105	3	∈hk0	∈hk0	NOUN
ejpam-1234	105	4	l	l	NOUN
ejpam-1234	105	5	,	,	PUNCT
ejpam-1234	105	6	then	then	ADV
ejpam-1234	105	7	ρlπk(v	ρlπk(v	NUM
ejpam-1234	105	8	)	)	PUNCT
ejpam-1234	105	9	=	=	SYM
ejpam-1234	106	1	1	1	NUM
ejpam-1234	106	2	|k|	|k|	NOUN
ejpam-1234	106	3	∑	∑	PUNCT
ejpam-1234	106	4	k∈k	k∈k	NOUN
ejpam-1234	106	5	ρlρkv	ρlρkv	NOUN
ejpam-1234	106	6	=	=	SYM
ejpam-1234	106	7	1	1	NUM
ejpam-1234	106	8	|k|	|k|	NOUN
ejpam-1234	106	9	∑	∑	PROPN
ejpam-1234	106	10	k′∈k	k′∈k	PROPN
ejpam-1234	106	11	ρk′ρl	ρk′ρl	X
ejpam-1234	106	12	v	v	NOUN
ejpam-1234	106	13	=	=	SYM
ejpam-1234	106	14	1	1	NUM
ejpam-1234	106	15	|k|	|k|	NOUN
ejpam-1234	106	16	∑	∑	PROPN
ejpam-1234	106	17	k′∈k	k′∈k	PROPN
ejpam-1234	106	18	ρk′ρk−1	ρk′ρk−1	PROPN
ejpam-1234	106	19	0	0	NUM
ejpam-1234	106	20	v	v	NOUN
ejpam-1234	106	21	=	=	SYM
ejpam-1234	106	22	1	1	NUM
ejpam-1234	106	23	|k|	|k|	PROPN
ejpam-1234	106	24	∑	∑	PUNCT
ejpam-1234	106	25	k′′∈k	k′′∈k	PROPN
ejpam-1234	106	26	ρk′′v	ρk′′v	PROPN
ejpam-1234	106	27	=	=	PUNCT
ejpam-1234	106	28	πk(v	πk(v	NUM
ejpam-1234	106	29	)	)	PUNCT
ejpam-1234	106	30	for	for	ADP
ejpam-1234	106	31	the	the	DET
ejpam-1234	106	32	trace	trace	NOUN
ejpam-1234	106	33	axiom	axiom	NOUN
ejpam-1234	106	34	for	for	ADP
ejpam-1234	106	35	h	h	PROPN
ejpam-1234	106	36	k	k	PROPN
ejpam-1234	106	37	,	,	PUNCT
ejpam-1234	106	38	we	we	PRON
ejpam-1234	106	39	need	need	VERB
ejpam-1234	106	40	to	to	PART
ejpam-1234	106	41	show	show	VERB
ejpam-1234	106	42	tr	tr	NOUN
ejpam-1234	106	43	h	h	NOUN
ejpam-1234	106	44	k	k	PROPN
ejpam-1234	107	1	[	[	X
ejpam-1234	107	2	l1	l1	X
ejpam-1234	107	3	]	]	PUNCT
ejpam-1234	107	4	(	(	PUNCT
ejpam-1234	107	5	lvm	lvm	NOUN
ejpam-1234	107	6	◦	◦	NOUN
ejpam-1234	107	7	ρl2	ρl2	PROPN
ejpam-1234	107	8	)	)	PUNCT
ejpam-1234	107	9	=	=	PUNCT
ejpam-1234	108	1	tr	tr	NOUN
ejpam-1234	108	2	h	h	NOUN
ejpam-1234	108	3	k	k	PROPN
ejpam-1234	109	1	[	[	X
ejpam-1234	109	2	l2	l2	NOUN
ejpam-1234	109	3	]	]	PUNCT
ejpam-1234	109	4	(	(	PUNCT
ejpam-1234	109	5	ρl−1	ρl−1	PROPN
ejpam-1234	109	6	1	1	NUM
ejpam-1234	109	7	◦	◦	NOUN
ejpam-1234	109	8	lvm	lvm	NOUN
ejpam-1234	109	9	)	)	PUNCT
ejpam-1234	109	10	,	,	PUNCT
ejpam-1234	109	11	for	for	ADP
ejpam-1234	109	12	l1	l1	PROPN
ejpam-1234	109	13	,	,	PUNCT
ejpam-1234	109	14	l2	l2	NOUN
ejpam-1234	109	15	∈	∈	PROPN
ejpam-1234	109	16	l	l	NOUN
ejpam-1234	109	17	and	and	CCONJ
ejpam-1234	109	18	vm	vm	NOUN
ejpam-1234	109	19	∈h	∈h	NOUN
ejpam-1234	109	20	k	k	PROPN
ejpam-1234	110	1	[	[	X
ejpam-1234	110	2	m	m	X
ejpam-1234	110	3	]	]	X
ejpam-1234	110	4	where	where	SCONJ
ejpam-1234	110	5	m	m	VERB
ejpam-1234	110	6	=	=	PUNCT
ejpam-1234	110	7	[	[	X
ejpam-1234	110	8	l1	l1	PROPN
ejpam-1234	110	9	,	,	PUNCT
ejpam-1234	110	10	l2	l2	NOUN
ejpam-1234	110	11	]	]	PUNCT
ejpam-1234	110	12	.	.	PUNCT
ejpam-1234	111	1	the	the	DET
ejpam-1234	111	2	left	left	ADJ
ejpam-1234	111	3	-	-	PUNCT
ejpam-1234	111	4	hand	hand	NOUN
ejpam-1234	111	5	side	side	NOUN
ejpam-1234	111	6	is	be	AUX
ejpam-1234	111	7	tr	tr	VERB
ejpam-1234	111	8	h	h	NOUN
ejpam-1234	111	9	k	k	PROPN
ejpam-1234	112	1	[	[	X
ejpam-1234	112	2	l1	l1	X
ejpam-1234	112	3	]	]	PUNCT
ejpam-1234	112	4	(	(	PUNCT
ejpam-1234	112	5	lvm	lvm	NOUN
ejpam-1234	112	6	◦	◦	NOUN
ejpam-1234	112	7	ρl2	ρl2	NOUN
ejpam-1234	112	8	)	)	PUNCT
ejpam-1234	112	9	=	=	PUNCT
ejpam-1234	113	1	trh[l1	trh[l1	PROPN
ejpam-1234	113	2	]	]	X
ejpam-1234	113	3	(	(	PUNCT
ejpam-1234	113	4	lvm	lvm	NOUN
ejpam-1234	113	5	◦	◦	NOUN
ejpam-1234	113	6	ρl2	ρl2	NOUN
ejpam-1234	113	7	◦	◦	NOUN
ejpam-1234	113	8	πk	πk	NOUN
ejpam-1234	113	9	)	)	PUNCT
ejpam-1234	113	10	=	=	SYM
ejpam-1234	113	11	1	1	NUM
ejpam-1234	113	12	|k|	|k|	PROPN
ejpam-1234	113	13	∑	∑	PROPN
ejpam-1234	113	14	k1,k	k1,k	PROPN
ejpam-1234	113	15	trhk1	trhk1	PROPN
ejpam-1234	113	16	l1	l1	PROPN
ejpam-1234	113	17	(	(	PUNCT
ejpam-1234	113	18	lvm	lvm	NOUN
ejpam-1234	113	19	◦	◦	NOUN
ejpam-1234	113	20	ρl2	ρl2	NOUN
ejpam-1234	113	21	◦	◦	NOUN
ejpam-1234	113	22	ρk	ρk	NOUN
ejpam-1234	113	23	)	)	PUNCT
ejpam-1234	113	24	=	=	SYM
ejpam-1234	113	25	1	1	NUM
ejpam-1234	113	26	|k|	|k|	NOUN
ejpam-1234	113	27	∑	∑	PUNCT
ejpam-1234	113	28	k1,k2	k1,k2	PROPN
ejpam-1234	113	29	trhk1	trhk1	PROPN
ejpam-1234	113	30	l1	l1	PROPN
ejpam-1234	113	31	(	(	PUNCT
ejpam-1234	113	32	lvm	lvm	NOUN
ejpam-1234	113	33	◦	◦	NOUN
ejpam-1234	113	34	ρk2	ρk2	NOUN
ejpam-1234	113	35	l2	l2	NOUN
ejpam-1234	113	36	)	)	PUNCT
ejpam-1234	113	37	=	=	SYM
ejpam-1234	113	38	1	1	NUM
ejpam-1234	113	39	|k|	|k|	NOUN
ejpam-1234	113	40	∑	∑	PUNCT
ejpam-1234	113	41	k1,k2	k1,k2	PROPN
ejpam-1234	113	42	trhk2	trhk2	NOUN
ejpam-1234	113	43	l2	l2	NOUN
ejpam-1234	113	44	(	(	PUNCT
ejpam-1234	113	45	ρ(k1l1	ρ(k1l1	NOUN
ejpam-1234	113	46	)	)	PUNCT
ejpam-1234	113	47	−1	−1	NOUN
ejpam-1234	113	48	◦	◦	NOUN
ejpam-1234	113	49	lvm	lvm	NOUN
ejpam-1234	113	50	)	)	PUNCT
ejpam-1234	113	51	,	,	PUNCT
ejpam-1234	113	52	where	where	SCONJ
ejpam-1234	113	53	the	the	DET
ejpam-1234	113	54	third	third	ADJ
ejpam-1234	113	55	equality	equality	NOUN
ejpam-1234	113	56	is	be	AUX
ejpam-1234	113	57	obtained	obtain	VERB
ejpam-1234	113	58	by	by	ADP
ejpam-1234	113	59	replacing	replace	VERB
ejpam-1234	113	60	the	the	DET
ejpam-1234	113	61	parameter	parameter	NOUN
ejpam-1234	113	62	kl−1	kl−1	PROPN
ejpam-1234	113	63	2	2	NUM
ejpam-1234	113	64	by	by	ADP
ejpam-1234	113	65	k2	k2	PROPN
ejpam-1234	113	66	and	and	CCONJ
ejpam-1234	113	67	the	the	DET
ejpam-1234	113	68	fourth	fourth	ADJ
ejpam-1234	113	69	equality	equality	NOUN
ejpam-1234	113	70	follows	follow	VERB
ejpam-1234	113	71	from	from	ADP
ejpam-1234	113	72	the	the	DET
ejpam-1234	113	73	trace	trace	NOUN
ejpam-1234	113	74	axiom	axiom	NOUN
ejpam-1234	113	75	for	for	ADP
ejpam-1234	113	76	h	h	NOUN
ejpam-1234	113	77	.	.	PUNCT
ejpam-1234	114	1	the	the	DET
ejpam-1234	114	2	right	right	ADJ
ejpam-1234	114	3	-	-	PUNCT
ejpam-1234	114	4	hand	hand	NOUN
ejpam-1234	114	5	side	side	NOUN
ejpam-1234	114	6	is	be	AUX
ejpam-1234	114	7	tr	tr	VERB
ejpam-1234	114	8	h	h	NOUN
ejpam-1234	114	9	k	k	PROPN
ejpam-1234	115	1	[	[	X
ejpam-1234	115	2	l2	l2	NOUN
ejpam-1234	115	3	]	]	PUNCT
ejpam-1234	115	4	(	(	PUNCT
ejpam-1234	115	5	ρl−1	ρl−1	PROPN
ejpam-1234	115	6	1	1	NUM
ejpam-1234	115	7	◦	◦	NOUN
ejpam-1234	115	8	lvm	lvm	NOUN
ejpam-1234	115	9	)	)	PUNCT
ejpam-1234	115	10	=	=	SYM
ejpam-1234	115	11	1	1	NUM
ejpam-1234	115	12	|k|	|k|	PROPN
ejpam-1234	115	13	∑	∑	PROPN
ejpam-1234	115	14	k	k	PROPN
ejpam-1234	115	15	,	,	PUNCT
ejpam-1234	115	16	k2	k2	ADJ
ejpam-1234	115	17	trhk2	trhk2	NOUN
ejpam-1234	115	18	l2	l2	NOUN
ejpam-1234	115	19	(	(	PUNCT
ejpam-1234	115	20	ρl−1	ρl−1	PROPN
ejpam-1234	115	21	1	1	NUM
ejpam-1234	115	22	◦	◦	NOUN
ejpam-1234	115	23	lvm	lvm	NOUN
ejpam-1234	115	24	◦	◦	NOUN
ejpam-1234	115	25	ρk	ρk	NOUN
ejpam-1234	115	26	)	)	PUNCT
ejpam-1234	115	27	=	=	SYM
ejpam-1234	115	28	1	1	NUM
ejpam-1234	115	29	|k|	|k|	NOUN
ejpam-1234	115	30	∑	∑	PUNCT
ejpam-1234	115	31	k1,k2	k1,k2	PROPN
ejpam-1234	115	32	trhk2	trhk2	NOUN
ejpam-1234	115	33	l2	l2	NOUN
ejpam-1234	115	34	(	(	PUNCT
ejpam-1234	115	35	ρl−1	ρl−1	PROPN
ejpam-1234	115	36	1	1	NUM
ejpam-1234	115	37	k−1	k−1	PROPN
ejpam-1234	115	38	1	1	NUM
ejpam-1234	115	39	◦	◦	NOUN
ejpam-1234	115	40	lvm	lvm	NOUN
ejpam-1234	115	41	)	)	PUNCT
ejpam-1234	115	42	,	,	PUNCT
ejpam-1234	115	43	where	where	SCONJ
ejpam-1234	115	44	the	the	DET
ejpam-1234	115	45	second	second	ADJ
ejpam-1234	115	46	equality	equality	NOUN
ejpam-1234	115	47	follows	follow	VERB
ejpam-1234	115	48	from	from	ADP
ejpam-1234	115	49	the	the	DET
ejpam-1234	115	50	cyclicity	cyclicity	NOUN
ejpam-1234	115	51	of	of	ADP
ejpam-1234	115	52	the	the	DET
ejpam-1234	115	53	trace	trace	NOUN
ejpam-1234	115	54	and	and	CCONJ
ejpam-1234	115	55	by	by	ADP
ejpam-1234	115	56	replacing	replace	VERB
ejpam-1234	115	57	the	the	DET
ejpam-1234	115	58	parameter	parameter	NOUN
ejpam-1234	115	59	k	k	PROPN
ejpam-1234	115	60	l−1	l−1	PROPN
ejpam-1234	115	61	1	1	NUM
ejpam-1234	115	62	1	1	NUM
ejpam-1234	115	63	by	by	ADP
ejpam-1234	115	64	k−1	k−1	PROPN
ejpam-1234	115	65	1	1	NUM
ejpam-1234	115	66	.	.	PUNCT
ejpam-1234	116	1	thus	thus	ADV
ejpam-1234	116	2	,	,	PUNCT
ejpam-1234	116	3	the	the	DET
ejpam-1234	116	4	trace	trace	NOUN
ejpam-1234	116	5	axiom	axiom	NOUN
ejpam-1234	116	6	holds	hold	VERB
ejpam-1234	116	7	for	for	ADP
ejpam-1234	116	8	the	the	DET
ejpam-1234	116	9	k	k	NOUN
ejpam-1234	116	10	-	-	PUNCT
ejpam-1234	116	11	invariants	invariant	NOUN
ejpam-1234	116	12	h	h	PROPN
ejpam-1234	116	13	k.	k.	PROPN
ejpam-1234	116	14	2.2	2.2	NUM
ejpam-1234	116	15	.	.	PUNCT
ejpam-1234	117	1	stringy	stringy	ADJ
ejpam-1234	117	2	and	and	CCONJ
ejpam-1234	117	3	orbifold	orbifold	ADJ
ejpam-1234	117	4	cohomology	cohomology	NOUN
ejpam-1234	117	5	we	we	PRON
ejpam-1234	117	6	review	review	VERB
ejpam-1234	117	7	the	the	DET
ejpam-1234	117	8	definition	definition	NOUN
ejpam-1234	117	9	of	of	ADP
ejpam-1234	117	10	the	the	DET
ejpam-1234	117	11	stringy	stringy	ADJ
ejpam-1234	117	12	and	and	CCONJ
ejpam-1234	117	13	chen	chen	PROPN
ejpam-1234	117	14	-	-	PUNCT
ejpam-1234	117	15	ruan	ruan	PROPN
ejpam-1234	117	16	orbifold	orbifold	PROPN
ejpam-1234	117	17	cohomology	cohomology	NOUN
ejpam-1234	117	18	,	,	PUNCT
ejpam-1234	117	19	following	follow	VERB
ejpam-1234	117	20	[	[	X
ejpam-1234	117	21	7	7	NUM
ejpam-1234	117	22	]	]	PUNCT
ejpam-1234	117	23	and	and	CCONJ
ejpam-1234	117	24	[	[	X
ejpam-1234	117	25	11	11	NUM
ejpam-1234	117	26	]	]	PUNCT
ejpam-1234	117	27	.	.	PUNCT
ejpam-1234	118	1	let	let	VERB
ejpam-1234	118	2	x	x	PRON
ejpam-1234	118	3	be	be	AUX
ejpam-1234	118	4	a	a	DET
ejpam-1234	118	5	compact	compact	ADJ
ejpam-1234	118	6	almost	almost	ADV
ejpam-1234	118	7	complex	complex	ADJ
ejpam-1234	118	8	manifold	manifold	NOUN
ejpam-1234	118	9	of	of	ADP
ejpam-1234	118	10	complex	complex	ADJ
ejpam-1234	118	11	dimension	dimension	NOUN
ejpam-1234	118	12	d	d	NOUN
ejpam-1234	118	13	with	with	ADP
ejpam-1234	118	14	an	an	DET
ejpam-1234	118	15	action	action	NOUN
ejpam-1234	118	16	ρ	ρ	NOUN
ejpam-1234	118	17	of	of	ADP
ejpam-1234	118	18	a	a	DET
ejpam-1234	118	19	finite	finite	ADJ
ejpam-1234	118	20	group	group	NOUN
ejpam-1234	118	21	g	g	PROPN
ejpam-1234	118	22	preserving	preserve	VERB
ejpam-1234	118	23	the	the	DET
ejpam-1234	118	24	almost	almost	ADV
ejpam-1234	118	25	complex	complex	ADJ
ejpam-1234	118	26	structure	structure	NOUN
ejpam-1234	118	27	.	.	PUNCT
ejpam-1234	119	1	let	let	VERB
ejpam-1234	119	2	x	x	PRON
ejpam-1234	119	3	g1	g1	VERB
ejpam-1234	119	4	,	,	PUNCT
ejpam-1234	119	5	·	·	PUNCT
ejpam-1234	119	6	·	·	PUNCT
ejpam-1234	119	7	·	·	PUNCT
ejpam-1234	119	8	,	,	PUNCT
ejpam-1234	119	9	gr	gr	NOUN
ejpam-1234	119	10	be	be	AUX
ejpam-1234	119	11	the	the	DET
ejpam-1234	119	12	submanifold	submanifold	NOUN
ejpam-1234	119	13	of	of	ADP
ejpam-1234	119	14	points	point	NOUN
ejpam-1234	119	15	in	in	ADP
ejpam-1234	119	16	x	x	PUNCT
ejpam-1234	119	17	fixed	fix	VERB
ejpam-1234	119	18	by	by	ADP
ejpam-1234	119	19	the	the	DET
ejpam-1234	119	20	subgroup	subgroup	NOUN
ejpam-1234	119	21	generated	generate	VERB
ejpam-1234	119	22	by	by	ADP
ejpam-1234	119	23	g1	g1	PROPN
ejpam-1234	119	24	,	,	PUNCT
ejpam-1234	119	25	·	·	PUNCT
ejpam-1234	119	26	·	·	PUNCT
ejpam-1234	119	27	·	·	PUNCT
ejpam-1234	120	1	,	,	PUNCT
ejpam-1234	120	2	gr	gr	NUM
ejpam-1234	120	3	∈	∈	PROPN
ejpam-1234	120	4	g.	g.	NOUN
ejpam-1234	120	5	then	then	ADV
ejpam-1234	120	6	h	h	PROPN
ejpam-1234	120	7	(	(	PUNCT
ejpam-1234	120	8	x	x	INTJ
ejpam-1234	120	9	,	,	PUNCT
ejpam-1234	120	10	g	g	NOUN
ejpam-1234	120	11	)	)	PUNCT
ejpam-1234	120	12	:	:	PUNCT
ejpam-1234	120	13	=	=	PROPN
ejpam-1234	120	14	⊕	⊕	PROPN
ejpam-1234	120	15	g∈g	g∈g	NOUN
ejpam-1234	120	16	h∗(x	h∗(x	PROPN
ejpam-1234	120	17	g	g	NOUN
ejpam-1234	120	18	)	)	PUNCT
ejpam-1234	120	19	is	be	AUX
ejpam-1234	120	20	naturally	naturally	ADV
ejpam-1234	120	21	a	a	DET
ejpam-1234	120	22	g	g	NOUN
ejpam-1234	120	23	-	-	PUNCT
ejpam-1234	120	24	graded	grade	VERB
ejpam-1234	120	25	g	g	NOUN
ejpam-1234	120	26	-	-	PUNCT
ejpam-1234	120	27	module	module	NOUN
ejpam-1234	120	28	where	where	SCONJ
ejpam-1234	120	29	ρg	ρg	ADJ
ejpam-1234	120	30	:	:	PUNCT
ejpam-1234	121	1	x	x	PART
ejpam-1234	121	2	h	h	NOUN
ejpam-1234	121	3	−→	−→	ADV
ejpam-1234	121	4	x	x	INTJ
ejpam-1234	121	5	ghg−1	ghg−1	PROPN
ejpam-1234	121	6	(	(	PUNCT
ejpam-1234	121	7	x	x	SYM
ejpam-1234	121	8	7→	7→	NUM
ejpam-1234	121	9	ρg	ρg	NOUN
ejpam-1234	121	10	x	x	NOUN
ejpam-1234	121	11	)	)	PUNCT
ejpam-1234	121	12	.	.	PUNCT
ejpam-1234	122	1	the	the	DET
ejpam-1234	122	2	g	g	NOUN
ejpam-1234	122	3	-	-	PUNCT
ejpam-1234	122	4	equivariant	equivariant	ADJ
ejpam-1234	122	5	multiplication	multiplication	NOUN
ejpam-1234	122	6	requires	require	VERB
ejpam-1234	122	7	the	the	DET
ejpam-1234	122	8	class	class	NOUN
ejpam-1234	122	9	of	of	ADP
ejpam-1234	122	10	the	the	DET
ejpam-1234	122	11	obstruction	obstruction	NOUN
ejpam-1234	122	12	bundle	bundle	NOUN
ejpam-1234	122	13	in	in	ADP
ejpam-1234	122	14	rational	rational	ADJ
ejpam-1234	122	15	k	k	NOUN
ejpam-1234	122	16	-	-	NOUN
ejpam-1234	122	17	theory	theory	NOUN
ejpam-1234	122	18	k(x	k(x	PROPN
ejpam-1234	122	19	g	g	PROPN
ejpam-1234	122	20	,	,	PUNCT
ejpam-1234	122	21	h	h	NOUN
ejpam-1234	122	22	)	)	PUNCT
ejpam-1234	122	23	⊗	⊗	PROPN
ejpam-1234	122	24	q	q	X
ejpam-1234	123	1	[	[	X
ejpam-1234	123	2	7	7	NUM
ejpam-1234	123	3	,	,	PUNCT
ejpam-1234	123	4	11	11	NUM
ejpam-1234	123	5	]	]	PUNCT
ejpam-1234	123	6	:	:	PUNCT
ejpam-1234	123	7	r(g	r(g	NUM
ejpam-1234	123	8	,	,	PUNCT
ejpam-1234	123	9	h	h	NOUN
ejpam-1234	123	10	)	)	PUNCT
ejpam-1234	123	11	=	=	SYM
ejpam-1234	124	1	t	t	NOUN
ejpam-1234	124	2	x	x	SYM
ejpam-1234	124	3	g	g	NOUN
ejpam-1234	124	4	,	,	PUNCT
ejpam-1234	124	5	h⊖	h⊖	PROPN
ejpam-1234	124	6	t	t	NOUN
ejpam-1234	124	7	x	x	X
ejpam-1234	124	8	|x	|x	NOUN
ejpam-1234	124	9	g	g	PROPN
ejpam-1234	124	10	,	,	PUNCT
ejpam-1234	124	11	h	h	PROPN
ejpam-1234	124	12	⊕sg	⊕sg	PROPN
ejpam-1234	124	13	|x	|x	PROPN
ejpam-1234	124	14	g	g	PROPN
ejpam-1234	124	15	,	,	PUNCT
ejpam-1234	124	16	h	h	NOUN
ejpam-1234	124	17	⊕sh|x	⊕sh|x	NOUN
ejpam-1234	124	18	g	g	PROPN
ejpam-1234	124	19	,	,	PUNCT
ejpam-1234	124	20	h	h	NOUN
ejpam-1234	124	21	⊕s(gh)−1	⊕s(gh)−1	VERB
ejpam-1234	124	22	|x	|x	PROPN
ejpam-1234	124	23	g	g	PROPN
ejpam-1234	124	24	,	,	PUNCT
ejpam-1234	124	25	h.	h.	PROPN
ejpam-1234	124	26	(	(	PUNCT
ejpam-1234	124	27	1	1	X
ejpam-1234	124	28	)	)	PUNCT
ejpam-1234	124	29	here	here	ADV
ejpam-1234	124	30	,	,	PUNCT
ejpam-1234	124	31	the	the	DET
ejpam-1234	124	32	class	class	NOUN
ejpam-1234	124	33	sg	sg	ADV
ejpam-1234	124	34	in	in	ADP
ejpam-1234	124	35	k(x	k(x	PROPN
ejpam-1234	124	36	g)⊗q	g)⊗q	PRON
ejpam-1234	124	37	is	be	AUX
ejpam-1234	124	38	given	give	VERB
ejpam-1234	124	39	by	by	ADP
ejpam-1234	124	40	sg	sg	NOUN
ejpam-1234	124	41	:	:	PUNCT
ejpam-1234	124	42	=	=	SYM
ejpam-1234	124	43	r−1	r−1	PROPN
ejpam-1234	124	44	⊕	⊕	PROPN
ejpam-1234	124	45	k=0	k=0	PROPN
ejpam-1234	125	1	k	k	PROPN
ejpam-1234	125	2	r	r	NOUN
ejpam-1234	125	3	wg	wg	PROPN
ejpam-1234	125	4	,	,	PUNCT
ejpam-1234	125	5	k	k	PROPN
ejpam-1234	125	6	(	(	PUNCT
ejpam-1234	125	7	s	s	NOUN
ejpam-1234	125	8	-	-	NOUN
ejpam-1234	125	9	bundle	bundle	NOUN
ejpam-1234	125	10	)	)	PUNCT
ejpam-1234	125	11	(	(	PUNCT
ejpam-1234	125	12	2	2	X
ejpam-1234	125	13	)	)	PUNCT
ejpam-1234	125	14	tomoo	tomoo	VERB
ejpam-1234	125	15	matsumura	matsumura	ADJ
ejpam-1234	125	16	/	/	SYM
ejpam-1234	125	17	eur	eur	PROPN
ejpam-1234	125	18	.	.	PUNCT
ejpam-1234	126	1	j.	j.	PROPN
ejpam-1234	126	2	pure	pure	PROPN
ejpam-1234	126	3	appl	appl	PROPN
ejpam-1234	126	4	.	.	PROPN
ejpam-1234	126	5	math	math	PROPN
ejpam-1234	126	6	,	,	PUNCT
ejpam-1234	126	7	5	5	NUM
ejpam-1234	126	8	(	(	PUNCT
ejpam-1234	126	9	2012	2012	NUM
ejpam-1234	126	10	)	)	PUNCT
ejpam-1234	126	11	,	,	PUNCT
ejpam-1234	126	12	492	492	NUM
ejpam-1234	126	13	-	-	SYM
ejpam-1234	126	14	510	510	NUM
ejpam-1234	126	15	497	497	NUM
ejpam-1234	126	16	where	where	SCONJ
ejpam-1234	126	17	r	r	NOUN
ejpam-1234	126	18	is	be	AUX
ejpam-1234	126	19	the	the	DET
ejpam-1234	126	20	order	order	NOUN
ejpam-1234	126	21	of	of	ADP
ejpam-1234	126	22	g	g	PROPN
ejpam-1234	126	23	(	(	PUNCT
ejpam-1234	126	24	i.e.	i.e.	X
ejpam-1234	126	25	g	g	NOUN
ejpam-1234	126	26	r	r	NOUN
ejpam-1234	126	27	=	=	SYM
ejpam-1234	126	28	1	1	NUM
ejpam-1234	126	29	)	)	PUNCT
ejpam-1234	126	30	,	,	PUNCT
ejpam-1234	126	31	and	and	CCONJ
ejpam-1234	126	32	wg	wg	INTJ
ejpam-1234	126	33	,	,	PUNCT
ejpam-1234	126	34	k	k	PROPN
ejpam-1234	126	35	is	be	AUX
ejpam-1234	126	36	the	the	DET
ejpam-1234	126	37	eigenbundle	eigenbundle	NOUN
ejpam-1234	126	38	of	of	ADP
ejpam-1234	126	39	wg	wg	PROPN
ejpam-1234	126	40	:	:	PUNCT
ejpam-1234	126	41	=	=	SYM
ejpam-1234	126	42	t	t	PROPN
ejpam-1234	126	43	x	x	PUNCT
ejpam-1234	126	44	|x	|x	NOUN
ejpam-1234	126	45	g	g	PROPN
ejpam-1234	126	46	such	such	ADJ
ejpam-1234	126	47	that	that	SCONJ
ejpam-1234	126	48	g	g	PROPN
ejpam-1234	126	49	acts	act	VERB
ejpam-1234	126	50	with	with	ADP
ejpam-1234	126	51	the	the	DET
ejpam-1234	126	52	eigenvalue	eigenvalue	PROPN
ejpam-1234	126	53	exp(2πki	exp(2πki	PROPN
ejpam-1234	126	54	/	/	SYM
ejpam-1234	126	55	r	r	NOUN
ejpam-1234	126	56	)	)	PUNCT
ejpam-1234	126	57	.	.	PUNCT
ejpam-1234	127	1	now	now	ADV
ejpam-1234	127	2	the	the	DET
ejpam-1234	127	3	multiplication	multiplication	NOUN
ejpam-1234	127	4	is	be	AUX
ejpam-1234	127	5	defined	define	VERB
ejpam-1234	127	6	by	by	ADP
ejpam-1234	127	7	,	,	PUNCT
ejpam-1234	127	8	vg	vg	NOUN
ejpam-1234	127	9	·	·	PUNCT
ejpam-1234	127	10	vh	vh	NOUN
ejpam-1234	127	11	:	:	PUNCT
ejpam-1234	127	12	=	=	PUNCT
ejpam-1234	127	13	q∗	q∗	PROPN
ejpam-1234	127	14	�	�	PROPN
ejpam-1234	127	15	vg	vg	NOUN
ejpam-1234	127	16	|x	|x	PROPN
ejpam-1234	127	17	g	g	PROPN
ejpam-1234	127	18	,	,	PUNCT
ejpam-1234	127	19	h	h	NOUN
ejpam-1234	127	20	∪	∪	NOUN
ejpam-1234	127	21	vh|x	vh|x	NOUN
ejpam-1234	128	1	g	g	NOUN
ejpam-1234	128	2	,	,	PUNCT
ejpam-1234	128	3	h	h	NOUN
ejpam-1234	128	4	∪	∪	NOUN
ejpam-1234	128	5	cg	cg	NOUN
ejpam-1234	128	6	,	,	PUNCT
ejpam-1234	128	7	h	h	PROPN
ejpam-1234	128	8	�	�	PROPN
ejpam-1234	128	9	,	,	PUNCT
ejpam-1234	128	10	cg	cg	INTJ
ejpam-1234	128	11	,	,	PUNCT
ejpam-1234	128	12	h	h	NOUN
ejpam-1234	128	13	:	:	PUNCT
ejpam-1234	128	14	=	=	SYM
ejpam-1234	128	15	ctop	ctop	PROPN
ejpam-1234	128	16	�	�	PROPN
ejpam-1234	128	17	r(g	r(g	PROPN
ejpam-1234	128	18	,	,	PUNCT
ejpam-1234	128	19	h	h	NOUN
ejpam-1234	128	20	)	)	PUNCT
ejpam-1234	128	21	�	�	PROPN
ejpam-1234	128	22	(	(	PUNCT
ejpam-1234	128	23	3	3	NUM
ejpam-1234	128	24	)	)	PUNCT
ejpam-1234	128	25	where	where	SCONJ
ejpam-1234	128	26	q	q	NOUN
ejpam-1234	128	27	:	:	PUNCT
ejpam-1234	128	28	x	x	SYM
ejpam-1234	128	29	g	g	NOUN
ejpam-1234	128	30	,	,	PUNCT
ejpam-1234	128	31	h	h	NOUN
ejpam-1234	128	32	,	,	PUNCT
ejpam-1234	128	33	→	→	SYM
ejpam-1234	128	34	x	x	SYM
ejpam-1234	128	35	gh	gh	PROPN
ejpam-1234	128	36	is	be	AUX
ejpam-1234	128	37	the	the	DET
ejpam-1234	128	38	obvious	obvious	ADJ
ejpam-1234	128	39	inclusion	inclusion	NOUN
ejpam-1234	128	40	.	.	PUNCT
ejpam-1234	129	1	the	the	DET
ejpam-1234	129	2	g	g	NOUN
ejpam-1234	129	3	-	-	PUNCT
ejpam-1234	129	4	equivariance	equivariance	NOUN
ejpam-1234	129	5	of	of	ADP
ejpam-1234	129	6	this	this	DET
ejpam-1234	129	7	multiplication	multiplication	NOUN
ejpam-1234	129	8	follows	follow	VERB
ejpam-1234	129	9	from	from	ADP
ejpam-1234	129	10	the	the	DET
ejpam-1234	129	11	g	g	NOUN
ejpam-1234	129	12	-	-	PUNCT
ejpam-1234	129	13	equivariance	equivariance	NOUN
ejpam-1234	129	14	of	of	ADP
ejpam-1234	129	15	s	s	PRON
ejpam-1234	129	16	and	and	CCONJ
ejpam-1234	129	17	r	r	NOUN
ejpam-1234	129	18	:	:	PUNCT
ejpam-1234	129	19	ρ∗msmgm−1	ρ∗msmgm−1	NOUN
ejpam-1234	130	1	=	=	NUM
ejpam-1234	130	2	sg	sg	PROPN
ejpam-1234	130	3	,	,	PUNCT
ejpam-1234	130	4	ρ∗mr(mgm−1	ρ∗mr(mgm−1	PROPN
ejpam-1234	130	5	,	,	PUNCT
ejpam-1234	130	6	mhm−1	mhm−1	PROPN
ejpam-1234	130	7	)	)	PUNCT
ejpam-1234	131	1	=	=	SYM
ejpam-1234	131	2	r(g	r(g	ADJ
ejpam-1234	131	3	,	,	PUNCT
ejpam-1234	131	4	h	h	NOUN
ejpam-1234	131	5	)	)	PUNCT
ejpam-1234	131	6	.	.	PUNCT
ejpam-1234	132	1	(	(	PUNCT
ejpam-1234	132	2	4	4	X
ejpam-1234	132	3	)	)	PUNCT
ejpam-1234	132	4	the	the	DET
ejpam-1234	132	5	metric	metric	PROPN
ejpam-1234	132	6	η	η	PROPN
ejpam-1234	132	7	of	of	ADP
ejpam-1234	132	8	h	h	PROPN
ejpam-1234	132	9	(	(	PUNCT
ejpam-1234	132	10	x	x	SYM
ejpam-1234	132	11	,	,	PUNCT
ejpam-1234	132	12	g	g	NOUN
ejpam-1234	132	13	)	)	PUNCT
ejpam-1234	132	14	is	be	AUX
ejpam-1234	132	15	defined	define	VERB
ejpam-1234	132	16	by	by	ADP
ejpam-1234	132	17	η(vg	η(vg	X
ejpam-1234	132	18	,	,	PUNCT
ejpam-1234	132	19	wg−1	wg−1	PROPN
ejpam-1234	132	20	)	)	PUNCT
ejpam-1234	132	21	:	:	PUNCT
ejpam-1234	133	1	=	=	SYM
ejpam-1234	133	2	∫	∫	PROPN
ejpam-1234	133	3	x	x	SYM
ejpam-1234	133	4	g	g	NOUN
ejpam-1234	133	5	vg	vg	ADP
ejpam-1234	133	6	∪	∪	ADP
ejpam-1234	133	7	ι	ι	PROPN
ejpam-1234	133	8	∗wg−1	∗wg−1	NOUN
ejpam-1234	133	9	,	,	PUNCT
ejpam-1234	133	10	and	and	CCONJ
ejpam-1234	133	11	η(vg	η(vg	NOUN
ejpam-1234	133	12	,	,	PUNCT
ejpam-1234	133	13	wh	wh	NOUN
ejpam-1234	133	14	)	)	PUNCT
ejpam-1234	133	15	=	=	SYM
ejpam-1234	133	16	0	0	PUNCT
ejpam-1234	134	1	if	if	SCONJ
ejpam-1234	134	2	gh	gh	PROPN
ejpam-1234	134	3	6=	6=	ADP
ejpam-1234	134	4	1	1	NUM
ejpam-1234	134	5	(	(	PUNCT
ejpam-1234	134	6	5	5	NUM
ejpam-1234	134	7	)	)	PUNCT
ejpam-1234	134	8	where	where	SCONJ
ejpam-1234	134	9	ι	ι	X
ejpam-1234	134	10	:	:	PUNCT
ejpam-1234	134	11	x	x	PUNCT
ejpam-1234	134	12	g	g	ADP
ejpam-1234	134	13	−→	−→	NOUN
ejpam-1234	134	14	x	x	X
ejpam-1234	134	15	g−1	g−1	PROPN
ejpam-1234	134	16	is	be	AUX
ejpam-1234	134	17	the	the	DET
ejpam-1234	134	18	identity	identity	NOUN
ejpam-1234	134	19	map	map	NOUN
ejpam-1234	134	20	.	.	PUNCT
ejpam-1234	135	1	the	the	DET
ejpam-1234	135	2	orbifold	orbifold	ADJ
ejpam-1234	135	3	q	q	NOUN
ejpam-1234	135	4	-	-	PUNCT
ejpam-1234	135	5	grading	grading	NOUN
ejpam-1234	135	6	is	be	AUX
ejpam-1234	135	7	given	give	VERB
ejpam-1234	135	8	by	by	ADP
ejpam-1234	135	9	degq(vg	degq(vg	PROPN
ejpam-1234	135	10	)	)	PUNCT
ejpam-1234	135	11	:	:	PUNCT
ejpam-1234	135	12	=	=	SYM
ejpam-1234	135	13	|vg	|vg	NUM
ejpam-1234	135	14	|+	|+	NOUN
ejpam-1234	135	15	2	2	NUM
ejpam-1234	135	16	age(g	age(g	NOUN
ejpam-1234	135	17	)	)	PUNCT
ejpam-1234	135	18	,	,	PUNCT
ejpam-1234	135	19	where	where	SCONJ
ejpam-1234	135	20	age(g	age(g	NOUN
ejpam-1234	135	21	)	)	PUNCT
ejpam-1234	135	22	:	:	PUNCT
ejpam-1234	136	1	=	=	PUNCT
ejpam-1234	136	2	rksg	rksg	NOUN
ejpam-1234	136	3	(	(	PUNCT
ejpam-1234	136	4	6	6	NUM
ejpam-1234	136	5	)	)	PUNCT
ejpam-1234	136	6	where	where	SCONJ
ejpam-1234	136	7	|vg	|vg	NUM
ejpam-1234	136	8	|	|	ADV
ejpam-1234	136	9	is	be	AUX
ejpam-1234	136	10	the	the	DET
ejpam-1234	136	11	ordinary	ordinary	ADJ
ejpam-1234	136	12	degree	degree	NOUN
ejpam-1234	136	13	of	of	ADP
ejpam-1234	136	14	the	the	DET
ejpam-1234	136	15	cohomology	cohomology	NOUN
ejpam-1234	136	16	class	class	NOUN
ejpam-1234	136	17	vg	vg	NOUN
ejpam-1234	136	18	.	.	PUNCT
ejpam-1234	137	1	the	the	DET
ejpam-1234	137	2	following	follow	VERB
ejpam-1234	137	3	summarizes	summarize	NOUN
ejpam-1234	137	4	the	the	DET
ejpam-1234	137	5	algebraic	algebraic	ADJ
ejpam-1234	137	6	structure	structure	NOUN
ejpam-1234	137	7	of	of	ADP
ejpam-1234	137	8	h	h	PROPN
ejpam-1234	137	9	(	(	PUNCT
ejpam-1234	137	10	x	x	SYM
ejpam-1234	137	11	,	,	PUNCT
ejpam-1234	137	12	g	g	NOUN
ejpam-1234	137	13	):	):	PUNCT
ejpam-1234	137	14	theorem	theorem	ADJ
ejpam-1234	137	15	2	2	NUM
ejpam-1234	137	16	(	(	PUNCT
ejpam-1234	137	17	[	[	X
ejpam-1234	137	18	7	7	NUM
ejpam-1234	137	19	,	,	PUNCT
ejpam-1234	137	20	10	10	NUM
ejpam-1234	137	21	,	,	PUNCT
ejpam-1234	137	22	11	11	NUM
ejpam-1234	137	23	]	]	NUM
ejpam-1234	137	24	)	)	PUNCT
ejpam-1234	137	25	.	.	PUNCT
ejpam-1234	138	1	(	(	PUNCT
ejpam-1234	138	2	h	h	NOUN
ejpam-1234	138	3	(	(	PUNCT
ejpam-1234	138	4	x	x	NOUN
ejpam-1234	138	5	,	,	PUNCT
ejpam-1234	138	6	g	g	NOUN
ejpam-1234	138	7	)	)	PUNCT
ejpam-1234	138	8	,	,	PUNCT
ejpam-1234	138	9	·	·	PUNCT
ejpam-1234	138	10	,	,	PUNCT
ejpam-1234	138	11	1,η	1,η	NUM
ejpam-1234	138	12	,	,	PUNCT
ejpam-1234	138	13	ρ	ρ	PROPN
ejpam-1234	138	14	,	,	PUNCT
ejpam-1234	138	15	degq	degq	NOUN
ejpam-1234	138	16	)	)	PUNCT
ejpam-1234	138	17	is	be	AUX
ejpam-1234	138	18	a	a	DET
ejpam-1234	138	19	q	q	NOUN
ejpam-1234	138	20	-	-	PUNCT
ejpam-1234	138	21	graded	grade	VERB
ejpam-1234	138	22	g	g	NOUN
ejpam-1234	138	23	-	-	PUNCT
ejpam-1234	138	24	frobenius	frobenius	NOUN
ejpam-1234	138	25	(	(	PUNCT
ejpam-1234	138	26	super-	super-	NOUN
ejpam-1234	138	27	)	)	PUNCT
ejpam-1234	138	28	algebra	algebra	NOUN
ejpam-1234	138	29	of	of	ADP
ejpam-1234	138	30	degree	degree	NOUN
ejpam-1234	138	31	2	2	NUM
ejpam-1234	138	32	dimc	dimc	NOUN
ejpam-1234	138	33	x	x	NOUN
ejpam-1234	138	34	.	.	PUNCT
ejpam-1234	139	1	it	it	PRON
ejpam-1234	139	2	is	be	AUX
ejpam-1234	139	3	called	call	VERB
ejpam-1234	139	4	the	the	DET
ejpam-1234	139	5	stringy	stringy	ADJ
ejpam-1234	139	6	cohomology	cohomology	NOUN
ejpam-1234	139	7	of	of	ADP
ejpam-1234	139	8	g	g	NOUN
ejpam-1234	139	9	-	-	PUNCT
ejpam-1234	139	10	manifold	manifold	ADJ
ejpam-1234	139	11	x	x	X
ejpam-1234	139	12	.	.	PUNCT
ejpam-1234	140	1	the	the	DET
ejpam-1234	140	2	g	g	NOUN
ejpam-1234	140	3	-	-	PUNCT
ejpam-1234	140	4	invariants	invariant	NOUN
ejpam-1234	140	5	of	of	ADP
ejpam-1234	140	6	the	the	DET
ejpam-1234	140	7	stringy	stringy	ADJ
ejpam-1234	140	8	cohomology	cohomology	NOUN
ejpam-1234	140	9	is	be	AUX
ejpam-1234	140	10	isomorphic	isomorphic	ADJ
ejpam-1234	140	11	as	as	ADP
ejpam-1234	140	12	a	a	DET
ejpam-1234	140	13	frobenius	frobenius	NOUN
ejpam-1234	140	14	algebra	algebra	NOUN
ejpam-1234	140	15	to	to	ADP
ejpam-1234	140	16	the	the	DET
ejpam-1234	140	17	orbifold	orbifold	ADJ
ejpam-1234	140	18	cohomology	cohomology	NOUN
ejpam-1234	140	19	of	of	ADP
ejpam-1234	140	20	chen	chen	PROPN
ejpam-1234	140	21	-	-	PUNCT
ejpam-1234	140	22	ruan	ruan	PROPN
ejpam-1234	140	23	[	[	X
ejpam-1234	140	24	4	4	NUM
ejpam-1234	140	25	]	]	PUNCT
ejpam-1234	140	26	,	,	PUNCT
ejpam-1234	140	27	i.e.	i.e.	X
ejpam-1234	140	28	h	h	NOUN
ejpam-1234	140	29	(	(	PUNCT
ejpam-1234	140	30	x	x	NOUN
ejpam-1234	140	31	,	,	PUNCT
ejpam-1234	140	32	g)g	g)g	NOUN
ejpam-1234	140	33	=	=	SYM
ejpam-1234	140	34	h∗	h∗	PROPN
ejpam-1234	140	35	or	or	CCONJ
ejpam-1234	140	36	b	b	PROPN
ejpam-1234	140	37	(	(	PUNCT
ejpam-1234	140	38	[	[	X
ejpam-1234	140	39	x	x	X
ejpam-1234	140	40	/	/	SYM
ejpam-1234	140	41	g	g	NOUN
ejpam-1234	140	42	]	]	PUNCT
ejpam-1234	140	43	)	)	PUNCT
ejpam-1234	140	44	.	.	PUNCT
ejpam-1234	141	1	here	here	ADV
ejpam-1234	141	2	the	the	DET
ejpam-1234	141	3	metric	metric	ADJ
ejpam-1234	141	4	ηcr	ηcr	NOUN
ejpam-1234	141	5	on	on	ADP
ejpam-1234	141	6	h∗	h∗	PROPN
ejpam-1234	141	7	or	or	CCONJ
ejpam-1234	141	8	b	b	PROPN
ejpam-1234	141	9	(	(	PUNCT
ejpam-1234	141	10	[	[	X
ejpam-1234	141	11	x	x	X
ejpam-1234	141	12	/	/	SYM
ejpam-1234	141	13	g	g	NOUN
ejpam-1234	141	14	]	]	PUNCT
ejpam-1234	141	15	)	)	PUNCT
ejpam-1234	141	16	is	be	AUX
ejpam-1234	141	17	given	give	VERB
ejpam-1234	141	18	by	by	ADP
ejpam-1234	141	19	ηcr(v	ηcr(v	PROPN
ejpam-1234	141	20	,	,	PUNCT
ejpam-1234	141	21	w	w	NOUN
ejpam-1234	141	22	)	)	PUNCT
ejpam-1234	141	23	:	:	PUNCT
ejpam-1234	142	1	=	=	SYM
ejpam-1234	142	2	1	1	NUM
ejpam-1234	142	3	|g|	|g|	PROPN
ejpam-1234	142	4	η(v	η(v	PROPN
ejpam-1234	142	5	,	,	PUNCT
ejpam-1234	142	6	w	w	NOUN
ejpam-1234	142	7	)	)	PUNCT
ejpam-1234	142	8	for	for	ADP
ejpam-1234	142	9	v	v	NOUN
ejpam-1234	142	10	,	,	PUNCT
ejpam-1234	142	11	w	w	NOUN
ejpam-1234	142	12	∈h	∈h	NOUN
ejpam-1234	142	13	(	(	PUNCT
ejpam-1234	142	14	x	x	NOUN
ejpam-1234	142	15	,	,	PUNCT
ejpam-1234	142	16	g)g	g)g	NOUN
ejpam-1234	142	17	.	.	PUNCT
ejpam-1234	143	1	(	(	PUNCT
ejpam-1234	143	2	7	7	X
ejpam-1234	143	3	)	)	PUNCT
ejpam-1234	143	4	remark	remark	NOUN
ejpam-1234	143	5	2	2	NUM
ejpam-1234	143	6	.	.	PUNCT
ejpam-1234	144	1	if	if	SCONJ
ejpam-1234	144	2	g	g	NOUN
ejpam-1234	144	3	=	=	SYM
ejpam-1234	144	4	k⋊	k⋊	PROPN
ejpam-1234	144	5	l	l	NOUN
ejpam-1234	144	6	,	,	PUNCT
ejpam-1234	144	7	then	then	ADV
ejpam-1234	144	8	we	we	PRON
ejpam-1234	144	9	have	have	VERB
ejpam-1234	144	10	an	an	DET
ejpam-1234	144	11	action	action	NOUN
ejpam-1234	144	12	of	of	ADP
ejpam-1234	144	13	l	l	NOUN
ejpam-1234	144	14	on	on	ADP
ejpam-1234	144	15	an	an	DET
ejpam-1234	144	16	orbifold	orbifold	NOUN
ejpam-1234	144	17	[	[	X
ejpam-1234	144	18	x	x	X
ejpam-1234	144	19	/	/	SYM
ejpam-1234	144	20	k	k	X
ejpam-1234	144	21	]	]	X
ejpam-1234	144	22	.	.	PUNCT
ejpam-1234	145	1	for	for	ADP
ejpam-1234	145	2	the	the	DET
ejpam-1234	145	3	action	action	NOUN
ejpam-1234	145	4	of	of	ADP
ejpam-1234	145	5	a	a	DET
ejpam-1234	145	6	group	group	NOUN
ejpam-1234	145	7	on	on	ADP
ejpam-1234	145	8	an	an	DET
ejpam-1234	145	9	orbifold	orbifold	NOUN
ejpam-1234	145	10	,	,	PUNCT
ejpam-1234	145	11	see	see	VERB
ejpam-1234	145	12	[	[	X
ejpam-1234	145	13	15	15	NUM
ejpam-1234	145	14	]	]	PUNCT
ejpam-1234	145	15	or	or	CCONJ
ejpam-1234	145	16	[	[	X
ejpam-1234	145	17	21	21	NUM
ejpam-1234	145	18	]	]	PUNCT
ejpam-1234	145	19	for	for	ADP
ejpam-1234	145	20	example	example	NOUN
ejpam-1234	145	21	.	.	PUNCT
ejpam-1234	146	1	by	by	ADP
ejpam-1234	146	2	theorem	theorem	NOUN
ejpam-1234	146	3	1	1	NUM
ejpam-1234	146	4	,	,	PUNCT
ejpam-1234	146	5	we	we	PRON
ejpam-1234	146	6	have	have	VERB
ejpam-1234	146	7	an	an	DET
ejpam-1234	146	8	l	l	ADJ
ejpam-1234	146	9	-	-	ADJ
ejpam-1234	146	10	frobenius	frobenius	ADJ
ejpam-1234	146	11	algebra	algebra	NOUN
ejpam-1234	146	12	h	h	NOUN
ejpam-1234	146	13	(	(	PUNCT
ejpam-1234	146	14	x	x	X
ejpam-1234	146	15	,	,	PUNCT
ejpam-1234	146	16	k⋊l)k	k⋊l)k	PROPN
ejpam-1234	146	17	which	which	PRON
ejpam-1234	146	18	should	should	AUX
ejpam-1234	146	19	play	play	VERB
ejpam-1234	146	20	the	the	DET
ejpam-1234	146	21	role	role	NOUN
ejpam-1234	146	22	of	of	ADP
ejpam-1234	146	23	the	the	DET
ejpam-1234	146	24	stringy	stringy	ADJ
ejpam-1234	146	25	cohomology	cohomology	NOUN
ejpam-1234	146	26	of	of	ADP
ejpam-1234	146	27	l	l	NOUN
ejpam-1234	146	28	-	-	ADJ
ejpam-1234	146	29	orbifold	orbifold	ADJ
ejpam-1234	147	1	[	[	X
ejpam-1234	147	2	x	x	X
ejpam-1234	147	3	/	/	SYM
ejpam-1234	147	4	k	k	X
ejpam-1234	147	5	]	]	X
ejpam-1234	147	6	.	.	PUNCT
ejpam-1234	148	1	in	in	ADP
ejpam-1234	148	2	general	general	ADJ
ejpam-1234	148	3	,	,	PUNCT
ejpam-1234	148	4	when	when	SCONJ
ejpam-1234	148	5	l	l	NOUN
ejpam-1234	148	6	acts	act	VERB
ejpam-1234	148	7	on	on	ADP
ejpam-1234	148	8	an	an	DET
ejpam-1234	148	9	orbifold	orbifold	NOUN
ejpam-1234	148	10	x	x	NOUN
ejpam-1234	148	11	,	,	PUNCT
ejpam-1234	148	12	it	it	PRON
ejpam-1234	148	13	should	should	AUX
ejpam-1234	148	14	be	be	AUX
ejpam-1234	148	15	possible	possible	ADJ
ejpam-1234	148	16	to	to	PART
ejpam-1234	148	17	define	define	VERB
ejpam-1234	148	18	its	its	PRON
ejpam-1234	148	19	stringy	stringy	ADJ
ejpam-1234	148	20	cohomology	cohomology	NOUN
ejpam-1234	148	21	h	h	NOUN
ejpam-1234	148	22	(	(	PUNCT
ejpam-1234	148	23	x	x	NOUN
ejpam-1234	148	24	,	,	PUNCT
ejpam-1234	148	25	l	l	NOUN
ejpam-1234	148	26	)	)	PUNCT
ejpam-1234	148	27	analogously	analogously	ADV
ejpam-1234	148	28	and	and	CCONJ
ejpam-1234	148	29	to	to	PART
ejpam-1234	148	30	show	show	VERB
ejpam-1234	148	31	that	that	SCONJ
ejpam-1234	148	32	it	it	PRON
ejpam-1234	148	33	is	be	AUX
ejpam-1234	148	34	an	an	DET
ejpam-1234	148	35	l	l	ADJ
ejpam-1234	148	36	-	-	ADJ
ejpam-1234	148	37	frobenius	frobenius	ADJ
ejpam-1234	148	38	algebra	algebra	NOUN
ejpam-1234	148	39	.	.	PUNCT
ejpam-1234	149	1	then	then	ADV
ejpam-1234	149	2	our	our	PRON
ejpam-1234	149	3	main	main	ADJ
ejpam-1234	149	4	result	result	NOUN
ejpam-1234	149	5	in	in	ADP
ejpam-1234	149	6	this	this	DET
ejpam-1234	149	7	paper	paper	NOUN
ejpam-1234	149	8	should	should	AUX
ejpam-1234	149	9	be	be	AUX
ejpam-1234	149	10	easily	easily	ADV
ejpam-1234	149	11	generalized	generalize	VERB
ejpam-1234	149	12	for	for	ADP
ejpam-1234	149	13	the	the	DET
ejpam-1234	149	14	symmetric	symmetric	ADJ
ejpam-1234	149	15	product	product	NOUN
ejpam-1234	149	16	of	of	ADP
ejpam-1234	149	17	a	a	DET
ejpam-1234	149	18	global	global	ADJ
ejpam-1234	149	19	quotient	quotient	NOUN
ejpam-1234	149	20	orbifold	orbifold	VERB
ejpam-1234	150	1	[	[	X
ejpam-1234	150	2	x	x	X
ejpam-1234	150	3	/	/	SYM
ejpam-1234	150	4	h	h	NOUN
ejpam-1234	150	5	]	]	X
ejpam-1234	150	6	where	where	SCONJ
ejpam-1234	150	7	h	h	NOUN
ejpam-1234	150	8	is	be	AUX
ejpam-1234	150	9	a	a	DET
ejpam-1234	150	10	lie	lie	NOUN
ejpam-1234	150	11	group	group	NOUN
ejpam-1234	150	12	,	,	PUNCT
ejpam-1234	150	13	namely	namely	ADV
ejpam-1234	150	14	h	h	NOUN
ejpam-1234	150	15	(	(	PUNCT
ejpam-1234	150	16	[	[	X
ejpam-1234	150	17	x	x	X
ejpam-1234	150	18	/	/	SYM
ejpam-1234	150	19	h]n	h]n	ADJ
ejpam-1234	150	20	,	,	PUNCT
ejpam-1234	150	21	σn	σn	NOUN
ejpam-1234	150	22	)	)	PUNCT
ejpam-1234	150	23	∼=	∼=	PROPN
ejpam-1234	150	24	hor	hor	NOUN
ejpam-1234	150	25	b([x	b([x	ADJ
ejpam-1234	150	26	/	/	SYM
ejpam-1234	150	27	h]){σn	h]){σn	NOUN
ejpam-1234	150	28	}	}	PUNCT
ejpam-1234	150	29	with	with	ADP
ejpam-1234	150	30	the	the	DET
ejpam-1234	150	31	help	help	NOUN
ejpam-1234	150	32	of	of	ADP
ejpam-1234	150	33	the	the	DET
ejpam-1234	150	34	explicit	explicit	ADJ
ejpam-1234	150	35	formula	formula	NOUN
ejpam-1234	150	36	for	for	ADP
ejpam-1234	150	37	the	the	DET
ejpam-1234	150	38	obstruction	obstruction	NOUN
ejpam-1234	150	39	bundle	bundle	NOUN
ejpam-1234	150	40	of	of	ADP
ejpam-1234	150	41	[	[	X
ejpam-1234	150	42	x	x	X
ejpam-1234	150	43	/	/	SYM
ejpam-1234	150	44	h	h	NOUN
ejpam-1234	150	45	]	]	X
ejpam-1234	150	46	in	in	ADP
ejpam-1234	150	47	[	[	X
ejpam-1234	150	48	5	5	NUM
ejpam-1234	150	49	]	]	PUNCT
ejpam-1234	150	50	,	,	PUNCT
ejpam-1234	150	51	or	or	CCONJ
ejpam-1234	150	52	if	if	SCONJ
ejpam-1234	150	53	h	h	NOUN
ejpam-1234	150	54	is	be	AUX
ejpam-1234	150	55	a	a	DET
ejpam-1234	150	56	torus	torus	NOUN
ejpam-1234	150	57	,	,	PUNCT
ejpam-1234	150	58	[	[	X
ejpam-1234	150	59	2	2	NUM
ejpam-1234	150	60	,	,	PUNCT
ejpam-1234	150	61	9	9	NUM
ejpam-1234	150	62	]	]	PUNCT
ejpam-1234	150	63	.	.	PUNCT
ejpam-1234	151	1	remark	remark	PROPN
ejpam-1234	151	2	3	3	NUM
ejpam-1234	151	3	.	.	PUNCT
ejpam-1234	152	1	in	in	ADP
ejpam-1234	152	2	the	the	DET
ejpam-1234	152	3	case	case	NOUN
ejpam-1234	152	4	of	of	ADP
ejpam-1234	152	5	the	the	DET
ejpam-1234	152	6	wreath	wreath	NOUN
ejpam-1234	152	7	product	product	NOUN
ejpam-1234	152	8	orbifold	orbifold	VERB
ejpam-1234	152	9	[	[	X
ejpam-1234	152	10	x	x	NOUN
ejpam-1234	152	11	n	n	CCONJ
ejpam-1234	152	12	/	/	SYM
ejpam-1234	152	13	gn	gn	PROPN
ejpam-1234	153	1	⋊	⋊	NUM
ejpam-1234	153	2	σn	σn	NOUN
ejpam-1234	153	3	]	]	PUNCT
ejpam-1234	153	4	that	that	SCONJ
ejpam-1234	153	5	we	we	PRON
ejpam-1234	153	6	study	study	VERB
ejpam-1234	153	7	,	,	PUNCT
ejpam-1234	153	8	the	the	DET
ejpam-1234	153	9	main	main	ADJ
ejpam-1234	153	10	result	result	NOUN
ejpam-1234	153	11	of	of	ADP
ejpam-1234	153	12	this	this	DET
ejpam-1234	153	13	paper	paper	NOUN
ejpam-1234	153	14	implies	imply	VERB
ejpam-1234	153	15	that	that	SCONJ
ejpam-1234	153	16	h	h	NOUN
ejpam-1234	153	17	(	(	PUNCT
ejpam-1234	153	18	x	x	SYM
ejpam-1234	153	19	n	n	CCONJ
ejpam-1234	153	20	,	,	PUNCT
ejpam-1234	153	21	gn	gn	PROPN
ejpam-1234	153	22	⋊σn	⋊σn	PROPN
ejpam-1234	153	23	)	)	PUNCT
ejpam-1234	153	24	gn	gn	PROPN
ejpam-1234	153	25	gives	give	VERB
ejpam-1234	153	26	a	a	DET
ejpam-1234	153	27	geometric	geometric	ADJ
ejpam-1234	153	28	construction	construction	NOUN
ejpam-1234	153	29	of	of	ADP
ejpam-1234	153	30	the	the	DET
ejpam-1234	153	31	second	second	ADJ
ejpam-1234	153	32	quantization	quantization	NOUN
ejpam-1234	153	33	of	of	ADP
ejpam-1234	153	34	an	an	DET
ejpam-1234	153	35	orbifold	orbifold	NOUN
ejpam-1234	154	1	[	[	X
ejpam-1234	154	2	x	x	X
ejpam-1234	154	3	/	/	SYM
ejpam-1234	154	4	g	g	NOUN
ejpam-1234	154	5	]	]	PUNCT
ejpam-1234	154	6	(	(	PUNCT
ejpam-1234	154	7	see	see	VERB
ejpam-1234	154	8	[	[	X
ejpam-1234	154	9	13	13	NUM
ejpam-1234	154	10	]	]	NUM
ejpam-1234	154	11	)	)	PUNCT
ejpam-1234	154	12	.	.	PUNCT
ejpam-1234	155	1	it	it	PRON
ejpam-1234	155	2	is	be	AUX
ejpam-1234	155	3	convenient	convenient	ADJ
ejpam-1234	155	4	to	to	PART
ejpam-1234	155	5	generalize	generalize	VERB
ejpam-1234	155	6	the	the	DET
ejpam-1234	155	7	formula	formula	NOUN
ejpam-1234	155	8	(	(	PUNCT
ejpam-1234	155	9	3	3	NUM
ejpam-1234	155	10	)	)	PUNCT
ejpam-1234	155	11	to	to	ADP
ejpam-1234	155	12	the	the	DET
ejpam-1234	155	13	multi	multi	NOUN
ejpam-1234	155	14	-	-	NOUN
ejpam-1234	155	15	product	product	NOUN
ejpam-1234	155	16	:	:	PUNCT
ejpam-1234	155	17	tomoo	tomoo	VERB
ejpam-1234	155	18	matsumura	matsumura	ADJ
ejpam-1234	155	19	/	/	SYM
ejpam-1234	155	20	eur	eur	PROPN
ejpam-1234	155	21	.	.	PUNCT
ejpam-1234	156	1	j.	j.	PROPN
ejpam-1234	156	2	pure	pure	PROPN
ejpam-1234	156	3	appl	appl	PROPN
ejpam-1234	156	4	.	.	PROPN
ejpam-1234	156	5	math	math	PROPN
ejpam-1234	156	6	,	,	PUNCT
ejpam-1234	156	7	5	5	NUM
ejpam-1234	156	8	(	(	PUNCT
ejpam-1234	156	9	2012	2012	NUM
ejpam-1234	156	10	)	)	PUNCT
ejpam-1234	156	11	,	,	PUNCT
ejpam-1234	156	12	492	492	NUM
ejpam-1234	156	13	-	-	SYM
ejpam-1234	156	14	510	510	NUM
ejpam-1234	156	15	498	498	NUM
ejpam-1234	156	16	lemma	lemma	PROPN
ejpam-1234	156	17	1	1	NUM
ejpam-1234	156	18	.	.	PUNCT
ejpam-1234	157	1	let	let	VERB
ejpam-1234	157	2	g1	g1	PROPN
ejpam-1234	157	3	,	,	PUNCT
ejpam-1234	157	4	·	·	PUNCT
ejpam-1234	157	5	·	·	PUNCT
ejpam-1234	157	6	·	·	PUNCT
ejpam-1234	157	7	,	,	PUNCT
ejpam-1234	157	8	gr	gr	X
ejpam-1234	157	9	∈	∈	PROPN
ejpam-1234	157	10	g	g	NOUN
ejpam-1234	157	11	,	,	PUNCT
ejpam-1234	157	12	q	q	NOUN
ejpam-1234	157	13	:	:	PUNCT
ejpam-1234	157	14	z	z	NOUN
ejpam-1234	157	15	:	:	PUNCT
ejpam-1234	157	16	=	=	SYM
ejpam-1234	157	17	x	x	SYM
ejpam-1234	157	18	g1	g1	PROPN
ejpam-1234	157	19	,	,	PUNCT
ejpam-1234	157	20	·	·	PUNCT
ejpam-1234	157	21	·	·	PUNCT
ejpam-1234	157	22	·	·	PUNCT
ejpam-1234	157	23	,	,	PUNCT
ejpam-1234	157	24	gr	gr	ADV
ejpam-1234	157	25	−→	−→	NOUN
ejpam-1234	157	26	x	x	X
ejpam-1234	157	27	g1···gr	g1···gr	PROPN
ejpam-1234	157	28	.	.	PUNCT
ejpam-1234	158	1	then	then	ADV
ejpam-1234	158	2	vg1	vg1	PROPN
ejpam-1234	158	3	·	·	PUNCT
ejpam-1234	158	4	·	·	PUNCT
ejpam-1234	158	5	·	·	PUNCT
ejpam-1234	158	6	·	·	PUNCT
ejpam-1234	158	7	·	·	PUNCT
ejpam-1234	159	1	vgr	vgr	X
ejpam-1234	159	2	=	=	SYM
ejpam-1234	159	3	q∗	q∗	PROPN
ejpam-1234	159	4	�	�	PROPN
ejpam-1234	159	5	vg1	vg1	PROPN
ejpam-1234	159	6	|z	|z	PROPN
ejpam-1234	159	7	∪	∪	X
ejpam-1234	159	8	·	·	PUNCT
ejpam-1234	159	9	·	·	PUNCT
ejpam-1234	159	10	·	·	PUNCT
ejpam-1234	159	11	∪	∪	ADP
ejpam-1234	159	12	vgr	vgr	PROPN
ejpam-1234	159	13	|z	|z	PROPN
ejpam-1234	159	14	∪	∪	ADP
ejpam-1234	159	15	c(g1	c(g1	NOUN
ejpam-1234	159	16	,	,	PUNCT
ejpam-1234	159	17	·	·	PUNCT
ejpam-1234	159	18	·	·	PUNCT
ejpam-1234	159	19	·	·	PUNCT
ejpam-1234	159	20	,	,	PUNCT
ejpam-1234	159	21	gr	gr	PROPN
ejpam-1234	159	22	)	)	PUNCT
ejpam-1234	159	23	�	�	PROPN
ejpam-1234	159	24	,	,	PUNCT
ejpam-1234	159	25	where	where	SCONJ
ejpam-1234	159	26	r(g1	r(g1	NOUN
ejpam-1234	159	27	,	,	PUNCT
ejpam-1234	159	28	·	·	PUNCT
ejpam-1234	159	29	·	·	PUNCT
ejpam-1234	159	30	·	·	PUNCT
ejpam-1234	159	31	,	,	PUNCT
ejpam-1234	159	32	gr	gr	NOUN
ejpam-1234	159	33	)	)	PUNCT
ejpam-1234	159	34	:	:	PUNCT
ejpam-1234	160	1	=	=	X
ejpam-1234	160	2	t	t	X
ejpam-1234	160	3	z	z	X
ejpam-1234	160	4	⊖	⊖	SYM
ejpam-1234	160	5	t	t	PROPN
ejpam-1234	160	6	x	x	SYM
ejpam-1234	160	7	|z	|z	PROPN
ejpam-1234	160	8	⊕sg1	⊕sg1	NUM
ejpam-1234	160	9	⊕	⊕	PROPN
ejpam-1234	160	10	·	·	PUNCT
ejpam-1234	160	11	·	·	PUNCT
ejpam-1234	160	12	·	·	PUNCT
ejpam-1234	160	13	⊕sgr	⊕sgr	NUM
ejpam-1234	160	14	⊕s(g1···gr	⊕s(g1···gr	NOUN
ejpam-1234	160	15	)	)	PUNCT
ejpam-1234	160	16	−1	−1	NOUN
ejpam-1234	160	17	c(g1	c(g1	NOUN
ejpam-1234	160	18	,	,	PUNCT
ejpam-1234	160	19	·	·	PUNCT
ejpam-1234	160	20	·	·	PUNCT
ejpam-1234	160	21	·	·	PUNCT
ejpam-1234	160	22	,	,	PUNCT
ejpam-1234	160	23	gr	gr	NOUN
ejpam-1234	160	24	)	)	PUNCT
ejpam-1234	160	25	:	:	PUNCT
ejpam-1234	160	26	=	=	SYM
ejpam-1234	160	27	ctop(r(g1	ctop(r(g1	NOUN
ejpam-1234	160	28	,	,	PUNCT
ejpam-1234	160	29	·	·	PUNCT
ejpam-1234	160	30	·	·	PUNCT
ejpam-1234	160	31	·	·	PUNCT
ejpam-1234	160	32	,	,	PUNCT
ejpam-1234	160	33	gr	gr	NOUN
ejpam-1234	160	34	)	)	PUNCT
ejpam-1234	160	35	)	)	PUNCT
ejpam-1234	160	36	.	.	PUNCT
ejpam-1234	161	1	the	the	DET
ejpam-1234	161	2	proof	proof	NOUN
ejpam-1234	161	3	of	of	ADP
ejpam-1234	161	4	the	the	DET
ejpam-1234	161	5	associativity	associativity	NOUN
ejpam-1234	161	6	of	of	ADP
ejpam-1234	161	7	the	the	DET
ejpam-1234	161	8	product	product	NOUN
ejpam-1234	161	9	in	in	ADP
ejpam-1234	161	10	[	[	X
ejpam-1234	161	11	11	11	NUM
ejpam-1234	161	12	]	]	PUNCT
ejpam-1234	161	13	can	can	AUX
ejpam-1234	161	14	be	be	AUX
ejpam-1234	161	15	easily	easily	ADV
ejpam-1234	161	16	generalized	generalize	VERB
ejpam-1234	161	17	to	to	ADP
ejpam-1234	161	18	the	the	DET
ejpam-1234	161	19	proof	proof	NOUN
ejpam-1234	161	20	of	of	ADP
ejpam-1234	161	21	this	this	DET
ejpam-1234	161	22	lemma	lemma	PROPN
ejpam-1234	161	23	(	(	PUNCT
ejpam-1234	161	24	c.f	c.f	PROPN
ejpam-1234	161	25	.	.	PROPN
ejpam-1234	161	26	proposition	proposition	NOUN
ejpam-1234	161	27	5.3	5.3	NUM
ejpam-1234	161	28	of	of	ADP
ejpam-1234	161	29	[	[	X
ejpam-1234	161	30	17	17	NUM
ejpam-1234	161	31	]	]	NUM
ejpam-1234	161	32	)	)	PUNCT
ejpam-1234	161	33	.	.	PUNCT
ejpam-1234	162	1	3	3	X
ejpam-1234	162	2	.	.	X
ejpam-1234	162	3	the	the	DET
ejpam-1234	162	4	wreath	wreath	NOUN
ejpam-1234	162	5	product	product	NOUN
ejpam-1234	162	6	orbifold	orbifold	VERB
ejpam-1234	162	7	in	in	ADP
ejpam-1234	162	8	this	this	DET
ejpam-1234	162	9	section	section	NOUN
ejpam-1234	162	10	,	,	PUNCT
ejpam-1234	162	11	we	we	PRON
ejpam-1234	162	12	review	review	VERB
ejpam-1234	162	13	the	the	DET
ejpam-1234	162	14	wreath	wreath	NOUN
ejpam-1234	162	15	product	product	NOUN
ejpam-1234	162	16	orbifold	orbifold	VERB
ejpam-1234	162	17	to	to	PART
ejpam-1234	162	18	fix	fix	VERB
ejpam-1234	162	19	the	the	DET
ejpam-1234	162	20	notation	notation	NOUN
ejpam-1234	162	21	(	(	PUNCT
ejpam-1234	163	1	cf	cf	NOUN
ejpam-1234	163	2	.	.	PUNCT
ejpam-1234	163	3	section	section	NOUN
ejpam-1234	163	4	1	1	NUM
ejpam-1234	163	5	of	of	ADP
ejpam-1234	163	6	[	[	X
ejpam-1234	163	7	25	25	NUM
ejpam-1234	163	8	]	]	PUNCT
ejpam-1234	163	9	)	)	PUNCT
ejpam-1234	163	10	and	and	CCONJ
ejpam-1234	163	11	then	then	ADV
ejpam-1234	163	12	compute	compute	VERB
ejpam-1234	163	13	the	the	DET
ejpam-1234	163	14	obstruction	obstruction	NOUN
ejpam-1234	163	15	bundle	bundle	NOUN
ejpam-1234	163	16	in	in	ADP
ejpam-1234	163	17	certain	certain	ADJ
ejpam-1234	163	18	cases	case	NOUN
ejpam-1234	163	19	.	.	PUNCT
ejpam-1234	164	1	notation	notation	NOUN
ejpam-1234	164	2	1	1	NUM
ejpam-1234	164	3	.	.	PUNCT
ejpam-1234	165	1	the	the	DET
ejpam-1234	165	2	set	set	NOUN
ejpam-1234	165	3	of	of	ADP
ejpam-1234	165	4	conjugacy	conjugacy	PROPN
ejpam-1234	165	5	classes	class	NOUN
ejpam-1234	165	6	of	of	ADP
ejpam-1234	165	7	g	g	PROPN
ejpam-1234	165	8	is	be	AUX
ejpam-1234	165	9	denoted	denote	VERB
ejpam-1234	165	10	by	by	ADP
ejpam-1234	165	11	ḡ.	ḡ.	PROPN
ejpam-1234	165	12	for	for	ADP
ejpam-1234	165	13	all	all	PRON
ejpam-1234	165	14	α	α	NOUN
ejpam-1234	165	15	∈	∈	NOUN
ejpam-1234	165	16	g	g	NOUN
ejpam-1234	165	17	,	,	PUNCT
ejpam-1234	165	18	let	let	VERB
ejpam-1234	165	19	zg(α	zg(α	NOUN
ejpam-1234	165	20	)	)	PUNCT
ejpam-1234	165	21	be	be	AUX
ejpam-1234	165	22	the	the	DET
ejpam-1234	165	23	centralizer	centralizer	NOUN
ejpam-1234	165	24	of	of	ADP
ejpam-1234	165	25	α	α	PROPN
ejpam-1234	165	26	in	in	ADP
ejpam-1234	165	27	g.	g.	PROPN
ejpam-1234	165	28	the	the	DET
ejpam-1234	165	29	subgroup	subgroup	NOUN
ejpam-1234	165	30	generated	generate	VERB
ejpam-1234	165	31	by	by	ADP
ejpam-1234	165	32	the	the	DET
ejpam-1234	165	33	subset	subset	NOUN
ejpam-1234	165	34	{	{	PUNCT
ejpam-1234	165	35	αk}k=1	αk}k=1	PROPN
ejpam-1234	165	36	,	,	PUNCT
ejpam-1234	165	37	·	·	PUNCT
ejpam-1234	165	38	·	·	PUNCT
ejpam-1234	165	39	·	·	PUNCT
ejpam-1234	165	40	,	,	PUNCT
ejpam-1234	165	41	r	r	NOUN
ejpam-1234	165	42	of	of	ADP
ejpam-1234	165	43	g	g	PROPN
ejpam-1234	165	44	is	be	AUX
ejpam-1234	165	45	denoted	denote	VERB
ejpam-1234	165	46	by	by	ADP
ejpam-1234	165	47	〈	〈	NOUN
ejpam-1234	165	48	α1	α1	PROPN
ejpam-1234	165	49	,	,	PUNCT
ejpam-1234	165	50	·	·	PUNCT
ejpam-1234	165	51	·	·	PUNCT
ejpam-1234	165	52	·	·	PUNCT
ejpam-1234	165	53	,	,	PUNCT
ejpam-1234	165	54	αr	αr	X
ejpam-1234	165	55	〉	〉	NOUN
ejpam-1234	165	56	.	.	PUNCT
ejpam-1234	166	1	for	for	ADP
ejpam-1234	166	2	a	a	DET
ejpam-1234	166	3	finite	finite	PROPN
ejpam-1234	166	4	set	set	VERB
ejpam-1234	166	5	j	j	PROPN
ejpam-1234	166	6	,	,	PUNCT
ejpam-1234	166	7	let	let	VERB
ejpam-1234	166	8	gj	gj	NOUN
ejpam-1234	166	9	be	be	AUX
ejpam-1234	166	10	the	the	DET
ejpam-1234	166	11	set	set	NOUN
ejpam-1234	166	12	of	of	ADP
ejpam-1234	166	13	maps	map	NOUN
ejpam-1234	166	14	,	,	PUNCT
ejpam-1234	166	15	map(j	map(j	PROPN
ejpam-1234	166	16	,	,	PUNCT
ejpam-1234	166	17	g	g	NOUN
ejpam-1234	166	18	)	)	PUNCT
ejpam-1234	166	19	∼=	∼=	PART
ejpam-1234	166	20	g|j	g|j	NOUN
ejpam-1234	167	1	|	|	ADV
ejpam-1234	168	1	and	and	CCONJ
ejpam-1234	168	2	let	let	VERB
ejpam-1234	168	3	gi	gi	VERB
ejpam-1234	169	1	:	:	PUNCT
ejpam-1234	169	2	=	=	SYM
ejpam-1234	169	3	g(i	g(i	PROPN
ejpam-1234	169	4	)	)	PUNCT
ejpam-1234	169	5	for	for	ADP
ejpam-1234	169	6	g	g	PROPN
ejpam-1234	169	7	∈	∈	PROPN
ejpam-1234	169	8	gj	gj	NOUN
ejpam-1234	169	9	and	and	CCONJ
ejpam-1234	169	10	i	i	PRON
ejpam-1234	169	11	∈	∈	PROPN
ejpam-1234	170	1	j.	j.	PROPN
ejpam-1234	170	2	if	if	SCONJ
ejpam-1234	170	3	g	g	PROPN
ejpam-1234	170	4	∈	∈	PROPN
ejpam-1234	170	5	gj	gj	NOUN
ejpam-1234	170	6	,	,	PUNCT
ejpam-1234	170	7	then	then	ADV
ejpam-1234	170	8	ḡ	ḡ	VERB
ejpam-1234	170	9	∈	∈	PROPN
ejpam-1234	170	10	ḡj	ḡj	PROPN
ejpam-1234	170	11	is	be	AUX
ejpam-1234	170	12	defined	define	VERB
ejpam-1234	170	13	by	by	ADP
ejpam-1234	170	14	(	(	PUNCT
ejpam-1234	170	15	ḡ)i	ḡ)i	NOUN
ejpam-1234	170	16	:	:	PUNCT
ejpam-1234	170	17	=	=	PUNCT
ejpam-1234	170	18	ḡi	ḡi	PROPN
ejpam-1234	170	19	∈	∈	PROPN
ejpam-1234	170	20	g.	g.	NOUN
ejpam-1234	170	21	let	let	VERB
ejpam-1234	170	22	∆j	∆j	PROPN
ejpam-1234	170	23	:	:	PUNCT
ejpam-1234	170	24	g→	g→	NOUN
ejpam-1234	170	25	gj	gj	NOUN
ejpam-1234	170	26	be	be	AUX
ejpam-1234	170	27	the	the	DET
ejpam-1234	170	28	diagonal	diagonal	ADJ
ejpam-1234	170	29	map	map	NOUN
ejpam-1234	170	30	and	and	CCONJ
ejpam-1234	170	31	let	let	VERB
ejpam-1234	170	32	∆j	∆j	PROPN
ejpam-1234	170	33	g	g	NOUN
ejpam-1234	170	34	:	:	PUNCT
ejpam-1234	170	35	=	=	SYM
ejpam-1234	170	36	∆j(g	∆j(g	NOUN
ejpam-1234	170	37	)	)	PUNCT
ejpam-1234	170	38	.	.	PUNCT
ejpam-1234	171	1	the	the	DET
ejpam-1234	171	2	same	same	ADJ
ejpam-1234	171	3	notation	notation	NOUN
ejpam-1234	171	4	is	be	AUX
ejpam-1234	171	5	applied	apply	VERB
ejpam-1234	171	6	to	to	ADP
ejpam-1234	171	7	any	any	DET
ejpam-1234	171	8	set	set	NOUN
ejpam-1234	171	9	,	,	PUNCT
ejpam-1234	171	10	i.e.	i.e.	X
ejpam-1234	171	11	if	if	SCONJ
ejpam-1234	171	12	x	x	PRON
ejpam-1234	171	13	is	be	AUX
ejpam-1234	171	14	a	a	DET
ejpam-1234	171	15	manifold	manifold	ADJ
ejpam-1234	171	16	,	,	PUNCT
ejpam-1234	171	17	then	then	ADV
ejpam-1234	171	18	x	x	X
ejpam-1234	171	19	j	j	NOUN
ejpam-1234	171	20	:	:	PUNCT
ejpam-1234	171	21	=	=	SYM
ejpam-1234	171	22	map(j	map(j	NOUN
ejpam-1234	171	23	,	,	PUNCT
ejpam-1234	171	24	x	x	PROPN
ejpam-1234	171	25	)	)	PUNCT
ejpam-1234	171	26	,	,	PUNCT
ejpam-1234	171	27	x	x	X
ejpam-1234	172	1	i	i	PRON
ejpam-1234	172	2	:	:	PUNCT
ejpam-1234	172	3	=	=	SYM
ejpam-1234	172	4	x(i	x(i	PROPN
ejpam-1234	172	5	)	)	PUNCT
ejpam-1234	172	6	for	for	ADP
ejpam-1234	172	7	x	x	SYM
ejpam-1234	172	8	∈	∈	PROPN
ejpam-1234	172	9	x	x	SYM
ejpam-1234	172	10	j	j	PROPN
ejpam-1234	172	11	and	and	CCONJ
ejpam-1234	172	12	∆j	∆j	PROPN
ejpam-1234	172	13	x	x	PUNCT
ejpam-1234	172	14	:	:	PUNCT
ejpam-1234	172	15	=	=	SYM
ejpam-1234	172	16	∆j	∆j	NOUN
ejpam-1234	172	17	where	where	SCONJ
ejpam-1234	172	18	∆j	∆j	VERB
ejpam-1234	172	19	:	:	PUNCT
ejpam-1234	172	20	x	x	X
ejpam-1234	172	21	→	→	SYM
ejpam-1234	172	22	x	x	SYM
ejpam-1234	172	23	j	j	PROPN
ejpam-1234	172	24	is	be	AUX
ejpam-1234	172	25	the	the	DET
ejpam-1234	172	26	diagonal	diagonal	ADJ
ejpam-1234	172	27	map	map	NOUN
ejpam-1234	172	28	.	.	PUNCT
ejpam-1234	173	1	definition	definition	NOUN
ejpam-1234	173	2	4	4	NUM
ejpam-1234	173	3	(	(	PUNCT
ejpam-1234	173	4	wreath	wreath	NOUN
ejpam-1234	173	5	product	product	NOUN
ejpam-1234	173	6	and	and	CCONJ
ejpam-1234	173	7	wreath	wreath	NOUN
ejpam-1234	173	8	product	product	NOUN
ejpam-1234	173	9	orbifold	orbifold	NOUN
ejpam-1234	173	10	)	)	PUNCT
ejpam-1234	173	11	.	.	PUNCT
ejpam-1234	174	1	fix	fix	VERB
ejpam-1234	174	2	a	a	DET
ejpam-1234	174	3	finite	finite	NOUN
ejpam-1234	174	4	set	set	VERB
ejpam-1234	174	5	i	i	PRON
ejpam-1234	174	6	of	of	ADP
ejpam-1234	174	7	cardinality	cardinality	PROPN
ejpam-1234	174	8	n	n	PROPN
ejpam-1234	174	9	and	and	CCONJ
ejpam-1234	174	10	let	let	VERB
ejpam-1234	174	11	σi	σi	PRON
ejpam-1234	174	12	be	be	AUX
ejpam-1234	174	13	the	the	DET
ejpam-1234	174	14	permutation	permutation	NOUN
ejpam-1234	174	15	group	group	NOUN
ejpam-1234	174	16	of	of	ADP
ejpam-1234	174	17	the	the	DET
ejpam-1234	174	18	set	set	NOUN
ejpam-1234	174	19	i.	i.	NOUN
ejpam-1234	174	20	for	for	ADP
ejpam-1234	174	21	all	all	DET
ejpam-1234	174	22	σ	σ	PROPN
ejpam-1234	174	23	,	,	PUNCT
ejpam-1234	174	24	τ	τ	PROPN
ejpam-1234	174	25	∈	∈	PROPN
ejpam-1234	174	26	σi	σi	X
ejpam-1234	174	27	,	,	PUNCT
ejpam-1234	174	28	let	let	VERB
ejpam-1234	174	29	iσ	iσ	VERB
ejpam-1234	174	30	:	:	PUNCT
ejpam-1234	174	31	=	=	SYM
ejpam-1234	175	1	i/〈σ	i/〈σ	NUM
ejpam-1234	175	2	〉	〉	NOUN
ejpam-1234	175	3	be	be	VERB
ejpam-1234	175	4	the	the	DET
ejpam-1234	175	5	set	set	NOUN
ejpam-1234	175	6	of	of	ADP
ejpam-1234	175	7	orbits	orbit	NOUN
ejpam-1234	175	8	in	in	ADP
ejpam-1234	175	9	i	i	PRON
ejpam-1234	175	10	under	under	ADP
ejpam-1234	175	11	the	the	DET
ejpam-1234	175	12	action	action	NOUN
ejpam-1234	175	13	of	of	ADP
ejpam-1234	175	14	the	the	DET
ejpam-1234	175	15	subgroup	subgroup	NOUN
ejpam-1234	175	16	〈	〈	PROPN
ejpam-1234	175	17	σ	σ	NOUN
ejpam-1234	175	18	〉	〉	NOUN
ejpam-1234	175	19	and	and	CCONJ
ejpam-1234	175	20	similarly	similarly	ADV
ejpam-1234	175	21	let	let	VERB
ejpam-1234	175	22	iσ	iσ	VERB
ejpam-1234	175	23	,	,	PUNCT
ejpam-1234	175	24	τ	τ	X
ejpam-1234	175	25	:	:	PUNCT
ejpam-1234	175	26	=	=	SYM
ejpam-1234	175	27	i/〈σ	i/〈σ	PROPN
ejpam-1234	175	28	,	,	PUNCT
ejpam-1234	175	29	τ	τ	X
ejpam-1234	175	30	〉	〉	NOUN
ejpam-1234	175	31	.	.	PUNCT
ejpam-1234	176	1	let	let	VERB
ejpam-1234	176	2	|σ|	|σ|	PROPN
ejpam-1234	176	3	be	be	AUX
ejpam-1234	176	4	the	the	DET
ejpam-1234	176	5	minimum	minimum	ADJ
ejpam-1234	176	6	number	number	NOUN
ejpam-1234	176	7	of	of	ADP
ejpam-1234	176	8	transpositions	transposition	NOUN
ejpam-1234	176	9	to	to	PART
ejpam-1234	176	10	express	express	VERB
ejpam-1234	176	11	σ	σ	PROPN
ejpam-1234	176	12	and	and	CCONJ
ejpam-1234	176	13	then	then	ADV
ejpam-1234	176	14	|σ|=	|σ|=	PROPN
ejpam-1234	176	15	n−	n−	PROPN
ejpam-1234	176	16	|iσ|	|iσ|	PROPN
ejpam-1234	176	17	.	.	PUNCT
ejpam-1234	177	1	the	the	DET
ejpam-1234	177	2	natural	natural	ADJ
ejpam-1234	177	3	left	left	ADJ
ejpam-1234	177	4	action	action	NOUN
ejpam-1234	177	5	of	of	ADP
ejpam-1234	177	6	σi	σi	PRON
ejpam-1234	177	7	on	on	ADP
ejpam-1234	177	8	gi	gi	PROPN
ejpam-1234	177	9	is	be	AUX
ejpam-1234	177	10	given	give	VERB
ejpam-1234	177	11	by	by	ADP
ejpam-1234	177	12	σ	σ	NOUN
ejpam-1234	177	13	:	:	PUNCT
ejpam-1234	177	14	gi	gi	ADP
ejpam-1234	177	15	7→	7→	NUM
ejpam-1234	177	16	gσ−1(i	gσ−1(i	NOUN
ejpam-1234	177	17	)	)	PUNCT
ejpam-1234	177	18	for	for	ADP
ejpam-1234	177	19	all	all	DET
ejpam-1234	177	20	σ	σ	NOUN
ejpam-1234	177	21	∈	∈	PROPN
ejpam-1234	177	22	σi	σi	X
ejpam-1234	177	23	and	and	CCONJ
ejpam-1234	177	24	g	g	PROPN
ejpam-1234	177	25	∈	∈	PROPN
ejpam-1234	177	26	gi	gi	X
ejpam-1234	177	27	.	.	PUNCT
ejpam-1234	178	1	the	the	DET
ejpam-1234	178	2	semidirect	semidirect	NOUN
ejpam-1234	178	3	product	product	NOUN
ejpam-1234	178	4	gi	gi	VERB
ejpam-1234	178	5	⋊	⋊	NUM
ejpam-1234	178	6	σi	σi	PRON
ejpam-1234	178	7	is	be	AUX
ejpam-1234	178	8	called	call	VERB
ejpam-1234	178	9	the	the	DET
ejpam-1234	178	10	wreath	wreath	NOUN
ejpam-1234	178	11	product	product	NOUN
ejpam-1234	178	12	of	of	ADP
ejpam-1234	178	13	g.	g.	PROPN
ejpam-1234	178	14	let	let	VERB
ejpam-1234	178	15	x	x	PRON
ejpam-1234	178	16	be	be	AUX
ejpam-1234	178	17	a	a	DET
ejpam-1234	178	18	compact	compact	ADJ
ejpam-1234	178	19	almost	almost	ADV
ejpam-1234	178	20	complex	complex	ADJ
ejpam-1234	178	21	manifold	manifold	ADJ
ejpam-1234	178	22	with	with	ADP
ejpam-1234	178	23	a	a	DET
ejpam-1234	178	24	left	left	ADJ
ejpam-1234	178	25	action	action	NOUN
ejpam-1234	178	26	ρ	ρ	PROPN
ejpam-1234	178	27	of	of	ADP
ejpam-1234	178	28	g.	g.	PROPN
ejpam-1234	178	29	there	there	PRON
ejpam-1234	178	30	is	be	VERB
ejpam-1234	178	31	a	a	DET
ejpam-1234	178	32	natural	natural	ADJ
ejpam-1234	178	33	left	left	ADJ
ejpam-1234	178	34	action	action	NOUN
ejpam-1234	178	35	of	of	ADP
ejpam-1234	178	36	the	the	DET
ejpam-1234	178	37	wreath	wreath	NOUN
ejpam-1234	178	38	product	product	NOUN
ejpam-1234	178	39	gi	gi	VERB
ejpam-1234	178	40	⋊σi	⋊σi	NOUN
ejpam-1234	178	41	on	on	ADP
ejpam-1234	178	42	x	x	PROPN
ejpam-1234	178	43	i	i	PRON
ejpam-1234	178	44	,	,	PUNCT
ejpam-1234	178	45	which	which	PRON
ejpam-1234	178	46	we	we	PRON
ejpam-1234	178	47	also	also	ADV
ejpam-1234	178	48	denote	denote	VERB
ejpam-1234	178	49	by	by	ADP
ejpam-1234	178	50	ρ	ρ	PROPN
ejpam-1234	178	51	.	.	PUNCT
ejpam-1234	179	1	namely	namely	ADV
ejpam-1234	179	2	,	,	PUNCT
ejpam-1234	179	3	for	for	ADP
ejpam-1234	179	4	gσ	gσ	NOUN
ejpam-1234	179	5	∈	∈	PROPN
ejpam-1234	179	6	gi	gi	NOUN
ejpam-1234	179	7	⋊σi	⋊σi	NOUN
ejpam-1234	179	8	,	,	PUNCT
ejpam-1234	179	9	ρgσ(x	ρgσ(x	X
ejpam-1234	179	10	)	)	PUNCT
ejpam-1234	179	11	∈	∈	PROPN
ejpam-1234	179	12	x	x	X
ejpam-1234	179	13	i	i	PRON
ejpam-1234	179	14	is	be	AUX
ejpam-1234	179	15	defined	define	VERB
ejpam-1234	179	16	by	by	ADP
ejpam-1234	179	17	(	(	PUNCT
ejpam-1234	179	18	ρgσ(x))i	ρgσ(x))i	PROPN
ejpam-1234	179	19	:	:	PUNCT
ejpam-1234	179	20	=	=	NUM
ejpam-1234	179	21	ρgi	ρgi	NOUN
ejpam-1234	179	22	(	(	PUNCT
ejpam-1234	179	23	xσ−1(i	xσ−1(i	PROPN
ejpam-1234	179	24	)	)	PUNCT
ejpam-1234	179	25	)	)	PUNCT
ejpam-1234	179	26	.	.	PUNCT
ejpam-1234	180	1	thus	thus	ADV
ejpam-1234	180	2	,	,	PUNCT
ejpam-1234	180	3	we	we	PRON
ejpam-1234	180	4	have	have	VERB
ejpam-1234	180	5	an	an	DET
ejpam-1234	180	6	orbifold	orbifold	NOUN
ejpam-1234	180	7	[	[	X
ejpam-1234	180	8	x	x	X
ejpam-1234	180	9	i	i	NOUN
ejpam-1234	180	10	/	/	SYM
ejpam-1234	180	11	g	g	PROPN
ejpam-1234	180	12	i	i	PROPN
ejpam-1234	180	13	⋊σi	⋊σi	NOUN
ejpam-1234	180	14	]	]	PUNCT
ejpam-1234	180	15	which	which	PRON
ejpam-1234	180	16	we	we	PRON
ejpam-1234	180	17	call	call	VERB
ejpam-1234	180	18	the	the	DET
ejpam-1234	180	19	wreath	wreath	NOUN
ejpam-1234	180	20	product	product	NOUN
ejpam-1234	180	21	orbifold	orbifold	NOUN
ejpam-1234	180	22	associated	associate	VERB
ejpam-1234	180	23	to	to	ADP
ejpam-1234	180	24	[	[	X
ejpam-1234	180	25	x	x	X
ejpam-1234	180	26	/	/	SYM
ejpam-1234	180	27	g	g	NOUN
ejpam-1234	180	28	]	]	PUNCT
ejpam-1234	180	29	.	.	PUNCT
ejpam-1234	181	1	definition	definition	NOUN
ejpam-1234	181	2	5	5	NUM
ejpam-1234	181	3	(	(	PUNCT
ejpam-1234	181	4	cycle	cycle	NOUN
ejpam-1234	181	5	product	product	NOUN
ejpam-1234	181	6	)	)	PUNCT
ejpam-1234	181	7	.	.	PUNCT
ejpam-1234	182	1	for	for	ADP
ejpam-1234	182	2	each	each	PRON
ejpam-1234	182	3	a	a	DET
ejpam-1234	182	4	∈	∈	PROPN
ejpam-1234	182	5	iσ	iσ	ADV
ejpam-1234	182	6	,	,	PUNCT
ejpam-1234	182	7	choose	choose	VERB
ejpam-1234	182	8	a	a	DET
ejpam-1234	182	9	representative	representative	ADJ
ejpam-1234	182	10	ia	ia	PROPN
ejpam-1234	182	11	∈	∈	PROPN
ejpam-1234	182	12	a.	a.	NOUN
ejpam-1234	182	13	for	for	ADP
ejpam-1234	182	14	each	each	DET
ejpam-1234	182	15	σ	σ	PROPN
ejpam-1234	182	16	∈	∈	PROPN
ejpam-1234	182	17	σi	σi	X
ejpam-1234	182	18	,	,	PUNCT
ejpam-1234	182	19	define	define	VERB
ejpam-1234	182	20	a	a	DET
ejpam-1234	182	21	map	map	NOUN
ejpam-1234	182	22	θσ	θσ	ADP
ejpam-1234	182	23	:	:	PUNCT
ejpam-1234	183	1	gi	gi	VERB
ejpam-1234	183	2	−→	−→	PROPN
ejpam-1234	183	3	giσ	giσ	PROPN
ejpam-1234	183	4	(	(	PUNCT
ejpam-1234	183	5	g	g	PROPN
ejpam-1234	183	6	7→	7→	PROPN
ejpam-1234	183	7	θσg	θσg	NOUN
ejpam-1234	183	8	)	)	PUNCT
ejpam-1234	183	9	where	where	SCONJ
ejpam-1234	183	10	(	(	PUNCT
ejpam-1234	183	11	θσg	θσg	NOUN
ejpam-1234	183	12	)	)	PUNCT
ejpam-1234	183	13	a	a	DET
ejpam-1234	183	14	:	:	PUNCT
ejpam-1234	183	15	=	=	NUM
ejpam-1234	183	16	gσ|a|−1(ia	gσ|a|−1(ia	VERB
ejpam-1234	183	17	)	)	PUNCT
ejpam-1234	183	18	gσ|a|−2(ia	gσ|a|−2(ia	PROPN
ejpam-1234	183	19	)	)	PUNCT
ejpam-1234	183	20	·	·	PUNCT
ejpam-1234	183	21	·	·	PUNCT
ejpam-1234	183	22	·	·	PUNCT
ejpam-1234	183	23	gσ0(ia	gσ0(ia	X
ejpam-1234	183	24	)	)	PUNCT
ejpam-1234	183	25	,	,	PUNCT
ejpam-1234	183	26	∀a	∀a	NOUN
ejpam-1234	183	27	∈	∈	NOUN
ejpam-1234	183	28	iσ	iσ	VERB
ejpam-1234	183	29	.	.	PUNCT
ejpam-1234	184	1	(	(	PUNCT
ejpam-1234	184	2	8)	8)	NUM
ejpam-1234	184	3	θσg	θσg	NOUN
ejpam-1234	184	4	is	be	AUX
ejpam-1234	184	5	a	a	DET
ejpam-1234	184	6	cycle	cycle	NOUN
ejpam-1234	184	7	product	product	NOUN
ejpam-1234	184	8	of	of	ADP
ejpam-1234	184	9	g	g	NOUN
ejpam-1234	184	10	with	with	ADP
ejpam-1234	184	11	respect	respect	NOUN
ejpam-1234	184	12	to	to	ADP
ejpam-1234	184	13	σ	σ	PROPN
ejpam-1234	184	14	.	.	PUNCT
ejpam-1234	185	1	the	the	DET
ejpam-1234	185	2	map	map	NOUN
ejpam-1234	185	3	θσ	θσ	ADP
ejpam-1234	185	4	depends	depend	VERB
ejpam-1234	185	5	on	on	ADP
ejpam-1234	185	6	the	the	DET
ejpam-1234	185	7	choice	choice	NOUN
ejpam-1234	185	8	of	of	ADP
ejpam-1234	185	9	representatives	representative	NOUN
ejpam-1234	185	10	{	{	PUNCT
ejpam-1234	185	11	ia	ia	PROPN
ejpam-1234	185	12	}	}	PUNCT
ejpam-1234	185	13	,	,	PUNCT
ejpam-1234	185	14	but	but	CCONJ
ejpam-1234	185	15	if	if	SCONJ
ejpam-1234	185	16	we	we	PRON
ejpam-1234	185	17	choose	choose	VERB
ejpam-1234	185	18	different	different	ADJ
ejpam-1234	185	19	representatives	representative	NOUN
ejpam-1234	185	20	,	,	PUNCT
ejpam-1234	185	21	then	then	ADV
ejpam-1234	185	22	each	each	DET
ejpam-1234	185	23	(	(	PUNCT
ejpam-1234	185	24	θσg	θσg	NOUN
ejpam-1234	185	25	)	)	PUNCT
ejpam-1234	185	26	a	a	PRON
ejpam-1234	185	27	is	be	AUX
ejpam-1234	185	28	conjugated	conjugate	VERB
ejpam-1234	185	29	by	by	ADP
ejpam-1234	185	30	some	some	DET
ejpam-1234	185	31	element	element	NOUN
ejpam-1234	185	32	in	in	ADP
ejpam-1234	185	33	g.	g.	PROPN
ejpam-1234	185	34	hence	hence	ADV
ejpam-1234	185	35	θ̄σg	θ̄σg	PROPN
ejpam-1234	185	36	∈	∈	PROPN
ejpam-1234	185	37	ḡ	ḡ	VERB
ejpam-1234	185	38	iσ	iσ	VERB
ejpam-1234	185	39	is	be	AUX
ejpam-1234	185	40	independent	independent	ADJ
ejpam-1234	185	41	of	of	ADP
ejpam-1234	185	42	the	the	DET
ejpam-1234	185	43	choice	choice	NOUN
ejpam-1234	185	44	of	of	ADP
ejpam-1234	185	45	representatives	representative	NOUN
ejpam-1234	185	46	{	{	PUNCT
ejpam-1234	185	47	ia	ia	PROPN
ejpam-1234	185	48	}	}	PUNCT
ejpam-1234	185	49	.	.	PUNCT
ejpam-1234	186	1	tomoo	tomoo	VERB
ejpam-1234	186	2	matsumura	matsumura	ADJ
ejpam-1234	186	3	/	/	SYM
ejpam-1234	186	4	eur	eur	PROPN
ejpam-1234	186	5	.	.	PUNCT
ejpam-1234	187	1	j.	j.	PROPN
ejpam-1234	187	2	pure	pure	PROPN
ejpam-1234	187	3	appl	appl	PROPN
ejpam-1234	187	4	.	.	PROPN
ejpam-1234	187	5	math	math	PROPN
ejpam-1234	187	6	,	,	PUNCT
ejpam-1234	187	7	5	5	NUM
ejpam-1234	187	8	(	(	PUNCT
ejpam-1234	187	9	2012	2012	NUM
ejpam-1234	187	10	)	)	PUNCT
ejpam-1234	187	11	,	,	PUNCT
ejpam-1234	187	12	492	492	NUM
ejpam-1234	187	13	-	-	SYM
ejpam-1234	187	14	510	510	NUM
ejpam-1234	187	15	499	499	NUM
ejpam-1234	187	16	now	now	ADV
ejpam-1234	187	17	we	we	PRON
ejpam-1234	187	18	compute	compute	VERB
ejpam-1234	187	19	the	the	DET
ejpam-1234	187	20	orbits	orbit	NOUN
ejpam-1234	187	21	of	of	ADP
ejpam-1234	187	22	the	the	DET
ejpam-1234	187	23	action	action	NOUN
ejpam-1234	187	24	of	of	ADP
ejpam-1234	187	25	gi	gi	NOUN
ejpam-1234	187	26	by	by	ADP
ejpam-1234	187	27	conjugation	conjugation	NOUN
ejpam-1234	187	28	on	on	ADP
ejpam-1234	187	29	gi	gi	PROPN
ejpam-1234	187	30	⋊σi	⋊σi	PROPN
ejpam-1234	187	31	.	.	PUNCT
ejpam-1234	188	1	proposition	proposition	NOUN
ejpam-1234	188	2	1	1	NUM
ejpam-1234	188	3	.	.	PUNCT
ejpam-1234	188	4	choose	choose	VERB
ejpam-1234	188	5	a	a	DET
ejpam-1234	188	6	representative	representative	ADJ
ejpam-1234	188	7	ia	ia	NOUN
ejpam-1234	188	8	in	in	ADP
ejpam-1234	188	9	a	a	PRON
ejpam-1234	188	10	for	for	SCONJ
ejpam-1234	188	11	each	each	DET
ejpam-1234	188	12	a	a	DET
ejpam-1234	188	13	∈	∈	NOUN
ejpam-1234	188	14	iσ	iσ	VERB
ejpam-1234	188	15	.	.	PUNCT
ejpam-1234	189	1	for	for	ADP
ejpam-1234	189	2	gσ	gσ	NOUN
ejpam-1234	189	3	∈	∈	PROPN
ejpam-1234	189	4	gi	gi	NOUN
ejpam-1234	189	5	⋊σi	⋊σi	NOUN
ejpam-1234	189	6	,	,	PUNCT
ejpam-1234	189	7	let	let	VERB
ejpam-1234	189	8	g	g	NOUN
ejpam-1234	189	9	:	:	PUNCT
ejpam-1234	189	10	=	=	PUNCT
ejpam-1234	189	11	θσg	θσg	NOUN
ejpam-1234	189	12	∈	∈	PROPN
ejpam-1234	189	13	g	g	NOUN
ejpam-1234	189	14	iσ	iσ	VERB
ejpam-1234	189	15	.	.	PUNCT
ejpam-1234	190	1	the	the	DET
ejpam-1234	190	2	orbit	orbit	NOUN
ejpam-1234	190	3	of	of	ADP
ejpam-1234	190	4	gσ	gσ	NOUN
ejpam-1234	190	5	under	under	ADP
ejpam-1234	190	6	the	the	DET
ejpam-1234	190	7	action	action	NOUN
ejpam-1234	190	8	of	of	ADP
ejpam-1234	190	9	gi	gi	NOUN
ejpam-1234	190	10	by	by	ADP
ejpam-1234	190	11	conjugation	conjugation	NOUN
ejpam-1234	190	12	is	be	AUX
ejpam-1234	190	13	given	give	VERB
ejpam-1234	190	14	by	by	ADP
ejpam-1234	190	15	ogσ	ogσ	ADJ
ejpam-1234	190	16	:	:	PUNCT
ejpam-1234	190	17	=	=	SYM
ejpam-1234	190	18	n	n	NUM
ejpam-1234	190	19	g′σ	g′σ	NOUN
ejpam-1234	190	20	∈	∈	PROPN
ejpam-1234	190	21	giσ	giσ	PROPN
ejpam-1234	190	22	�	�	PROPN
ejpam-1234	190	23	�	�	PROPN
ejpam-1234	190	24	θ̄σ	θ̄σ	VERB
ejpam-1234	190	25	g	g	NOUN
ejpam-1234	190	26	′	′	NOUN
ejpam-1234	190	27	=	=	PUNCT
ejpam-1234	190	28	ḡ	ḡ	VERB
ejpam-1234	190	29	o	o	NOUN
ejpam-1234	190	30	.	.	PUNCT
ejpam-1234	191	1	(	(	PUNCT
ejpam-1234	191	2	9	9	X
ejpam-1234	191	3	)	)	PUNCT
ejpam-1234	191	4	proof	proof	NOUN
ejpam-1234	191	5	.	.	PUNCT
ejpam-1234	192	1	define	define	VERB
ejpam-1234	192	2	εg	εg	ADP
ejpam-1234	192	3	∈	∈	PROPN
ejpam-1234	192	4	g	g	PROPN
ejpam-1234	192	5	i	i	PRON
ejpam-1234	192	6	by	by	ADP
ejpam-1234	192	7	(	(	PUNCT
ejpam-1234	192	8	εg)i	εg)i	PROPN
ejpam-1234	192	9	:	:	PUNCT
ejpam-1234	193	1	=	=	PUNCT
ejpam-1234	193	2	ga	ga	PROPN
ejpam-1234	193	3	if	if	SCONJ
ejpam-1234	193	4	i	i	PRON
ejpam-1234	193	5	=	=	SYM
ejpam-1234	193	6	ia	ia	PROPN
ejpam-1234	193	7	for	for	ADP
ejpam-1234	193	8	some	some	DET
ejpam-1234	193	9	a	a	DET
ejpam-1234	193	10	∈	∈	NOUN
ejpam-1234	193	11	iσ	iσ	ADV
ejpam-1234	194	1	and	and	CCONJ
ejpam-1234	194	2	otherwise	otherwise	ADV
ejpam-1234	194	3	(	(	PUNCT
ejpam-1234	194	4	εg)i	εg)i	NOUN
ejpam-1234	194	5	=	=	SYM
ejpam-1234	194	6	1	1	X
ejpam-1234	194	7	.	.	PUNCT
ejpam-1234	195	1	then	then	ADV
ejpam-1234	195	2	it	it	PRON
ejpam-1234	195	3	is	be	AUX
ejpam-1234	195	4	easy	easy	ADJ
ejpam-1234	195	5	to	to	PART
ejpam-1234	195	6	check	check	VERB
ejpam-1234	195	7	(	(	PUNCT
ejpam-1234	195	8	νσg	νσg	PROPN
ejpam-1234	195	9	)	)	PUNCT
ejpam-1234	195	10	−1	−1	NOUN
ejpam-1234	195	11	·	·	PUNCT
ejpam-1234	196	1	gσ	gσ	NUM
ejpam-1234	196	2	·	·	PUNCT
ejpam-1234	196	3	νσg	νσg	X
ejpam-1234	196	4	=	=	PUNCT
ejpam-1234	196	5	εgσ	εgσ	VERB
ejpam-1234	196	6	where	where	SCONJ
ejpam-1234	196	7	νσg	νσg	PROPN
ejpam-1234	196	8	is	be	AUX
ejpam-1234	196	9	given	give	VERB
ejpam-1234	196	10	by	by	ADP
ejpam-1234	196	11	(	(	PUNCT
ejpam-1234	196	12	νσg	νσg	PROPN
ejpam-1234	196	13	)	)	PUNCT
ejpam-1234	196	14	σm(ia	σm(ia	PROPN
ejpam-1234	196	15	)	)	PUNCT
ejpam-1234	196	16	:	:	PUNCT
ejpam-1234	196	17	=	=	SYM
ejpam-1234	196	18	gσm(ia	gσm(ia	X
ejpam-1234	196	19	)	)	PUNCT
ejpam-1234	196	20	gσm−1(ia	gσm−1(ia	PROPN
ejpam-1234	196	21	)	)	PUNCT
ejpam-1234	196	22	·	·	PUNCT
ejpam-1234	196	23	·	·	PUNCT
ejpam-1234	196	24	·	·	PUNCT
ejpam-1234	196	25	gσ0(ia	gσ0(ia	X
ejpam-1234	196	26	)	)	PUNCT
ejpam-1234	196	27	,	,	PUNCT
ejpam-1234	196	28	m=	m=	X
ejpam-1234	196	29	0	0	NUM
ejpam-1234	196	30	,	,	PUNCT
ejpam-1234	196	31	·	·	PUNCT
ejpam-1234	196	32	·	·	PUNCT
ejpam-1234	196	33	·	·	PUNCT
ejpam-1234	196	34	,	,	PUNCT
ejpam-1234	196	35	|a|	|a|	NOUN
ejpam-1234	196	36	−	−	PROPN
ejpam-1234	196	37	1	1	NUM
ejpam-1234	196	38	.	.	PUNCT
ejpam-1234	197	1	(	(	PUNCT
ejpam-1234	197	2	10	10	NUM
ejpam-1234	197	3	)	)	PUNCT
ejpam-1234	197	4	therefore	therefore	ADV
ejpam-1234	197	5	gσ	gσ	NOUN
ejpam-1234	197	6	and	and	CCONJ
ejpam-1234	197	7	εgσ	εgσ	VERB
ejpam-1234	197	8	are	be	AUX
ejpam-1234	197	9	in	in	ADP
ejpam-1234	197	10	the	the	DET
ejpam-1234	197	11	same	same	ADJ
ejpam-1234	197	12	orbit	orbit	NOUN
ejpam-1234	197	13	.	.	PUNCT
ejpam-1234	198	1	on	on	ADP
ejpam-1234	198	2	the	the	DET
ejpam-1234	198	3	other	other	ADJ
ejpam-1234	198	4	hand	hand	NOUN
ejpam-1234	198	5	,	,	PUNCT
ejpam-1234	198	6	for	for	ADP
ejpam-1234	198	7	g	g	NOUN
ejpam-1234	198	8	,	,	PUNCT
ejpam-1234	198	9	g′	g′	NOUN
ejpam-1234	198	10	in	in	ADP
ejpam-1234	198	11	g	g	PROPN
ejpam-1234	198	12	iσ	iσ	ADV
ejpam-1234	198	13	,	,	PUNCT
ejpam-1234	198	14	f	f	PROPN
ejpam-1234	198	15	∈	∈	PROPN
ejpam-1234	198	16	gi	gi	NOUN
ejpam-1234	198	17	satisfies	satisfie	NOUN
ejpam-1234	198	18	εgσ	εgσ	VERB
ejpam-1234	198	19	=	=	SYM
ejpam-1234	199	1	f	f	PROPN
ejpam-1234	199	2	−1εg′σ	−1εg′σ	PROPN
ejpam-1234	199	3	f	f	PROPN
ejpam-1234	200	1	if	if	SCONJ
ejpam-1234	200	2	and	and	CCONJ
ejpam-1234	200	3	only	only	ADV
ejpam-1234	200	4	if	if	SCONJ
ejpam-1234	200	5	f	f	PROPN
ejpam-1234	200	6	∈	∈	PROPN
ejpam-1234	200	7	∏	∏	PROPN
ejpam-1234	200	8	a∈iσ	a∈iσ	NOUN
ejpam-1234	200	9	∆a	∆a	PROPN
ejpam-1234	200	10	g	g	NOUN
ejpam-1234	200	11	and	and	CCONJ
ejpam-1234	200	12	ga	ga	PROPN
ejpam-1234	200	13	=	=	SYM
ejpam-1234	200	14	f	f	PROPN
ejpam-1234	200	15	−1	−1	PROPN
ejpam-1234	200	16	ia	ia	PROPN
ejpam-1234	200	17	g′a	g′a	PROPN
ejpam-1234	200	18	fia	fia	PROPN
ejpam-1234	200	19	.	.	PUNCT
ejpam-1234	201	1	thus	thus	ADV
ejpam-1234	201	2	,	,	PUNCT
ejpam-1234	201	3	gσ	gσ	NOUN
ejpam-1234	201	4	and	and	CCONJ
ejpam-1234	201	5	g′σ	g′σ	NOUN
ejpam-1234	201	6	are	be	AUX
ejpam-1234	201	7	in	in	ADP
ejpam-1234	201	8	the	the	DET
ejpam-1234	201	9	same	same	ADJ
ejpam-1234	201	10	orbit	orbit	NOUN
ejpam-1234	201	11	if	if	SCONJ
ejpam-1234	201	12	and	and	CCONJ
ejpam-1234	201	13	only	only	ADV
ejpam-1234	201	14	if	if	SCONJ
ejpam-1234	201	15	θ̄σg	θ̄σg	PROPN
ejpam-1234	201	16	=	=	PUNCT
ejpam-1234	201	17	θ̄	θ̄	PROPN
ejpam-1234	201	18	σ	σ	NOUN
ejpam-1234	201	19	g	g	NOUN
ejpam-1234	201	20	′	′	NOUN
ejpam-1234	201	21	.	.	PUNCT
ejpam-1234	202	1	remark	remark	NOUN
ejpam-1234	202	2	4	4	NUM
ejpam-1234	202	3	.	.	PUNCT
ejpam-1234	202	4	from	from	ADP
ejpam-1234	202	5	the	the	DET
ejpam-1234	202	6	above	above	ADJ
ejpam-1234	202	7	proof	proof	NOUN
ejpam-1234	202	8	,	,	PUNCT
ejpam-1234	202	9	it	it	PRON
ejpam-1234	202	10	is	be	AUX
ejpam-1234	202	11	clear	clear	ADJ
ejpam-1234	202	12	that	that	SCONJ
ejpam-1234	202	13	zgi	zgi	PROPN
ejpam-1234	202	14	(	(	PUNCT
ejpam-1234	202	15	εgσ	εgσ	NOUN
ejpam-1234	202	16	)	)	PUNCT
ejpam-1234	202	17	=	=	SYM
ejpam-1234	202	18	∏	∏	PROPN
ejpam-1234	202	19	a∈iσ	a∈iσ	NOUN
ejpam-1234	202	20	∆a	∆a	PROPN
ejpam-1234	202	21	zg(ga	zg(ga	NOUN
ejpam-1234	202	22	)	)	PUNCT
ejpam-1234	202	23	.	.	PUNCT
ejpam-1234	203	1	lemma	lemma	PROPN
ejpam-1234	203	2	2	2	NUM
ejpam-1234	203	3	(	(	PUNCT
ejpam-1234	203	4	[	[	X
ejpam-1234	203	5	lemma	lemma	X
ejpam-1234	203	6	4	4	NUM
ejpam-1234	203	7	and	and	CCONJ
ejpam-1234	203	8	5	5	NUM
ejpam-1234	203	9	,	,	PUNCT
ejpam-1234	203	10	25	25	NUM
ejpam-1234	203	11	]	]	PUNCT
ejpam-1234	203	12	)	)	PUNCT
ejpam-1234	203	13	.	.	PUNCT
ejpam-1234	204	1	for	for	ADP
ejpam-1234	204	2	gσ	gσ	NOUN
ejpam-1234	204	3	∈	∈	NOUN
ejpam-1234	204	4	gi	gi	NOUN
ejpam-1234	204	5	⋊	⋊	PUNCT
ejpam-1234	204	6	σi	σi	NOUN
ejpam-1234	204	7	,	,	PUNCT
ejpam-1234	204	8	we	we	PRON
ejpam-1234	204	9	have	have	VERB
ejpam-1234	204	10	(	(	PUNCT
ejpam-1234	204	11	x	x	X
ejpam-1234	204	12	i)gσ	i)gσ	PROPN
ejpam-1234	204	13	=	=	SYM
ejpam-1234	204	14	ρνσg	ρνσg	PROPN
ejpam-1234	204	15	�	�	PROPN
ejpam-1234	204	16	∏	∏	PROPN
ejpam-1234	204	17	a∈iσ	a∈iσ	NOUN
ejpam-1234	204	18	∆a	∆a	PROPN
ejpam-1234	204	19	xga	xga	PROPN
ejpam-1234	204	20	�	�	PROPN
ejpam-1234	204	21	where	where	SCONJ
ejpam-1234	204	22	g	g	NOUN
ejpam-1234	204	23	:	:	PUNCT
ejpam-1234	204	24	=	=	X
ejpam-1234	204	25	θσg	θσg	NOUN
ejpam-1234	204	26	.	.	PUNCT
ejpam-1234	205	1	proof	proof	NOUN
ejpam-1234	205	2	.	.	PUNCT
ejpam-1234	206	1	when	when	SCONJ
ejpam-1234	206	2	gσ	gσ	NOUN
ejpam-1234	206	3	=	=	SYM
ejpam-1234	206	4	εgσ	εgσ	NOUN
ejpam-1234	206	5	,	,	PUNCT
ejpam-1234	206	6	it	it	PRON
ejpam-1234	206	7	follows	follow	VERB
ejpam-1234	206	8	from	from	ADP
ejpam-1234	206	9	[	[	X
ejpam-1234	206	10	lemma	lemma	PROPN
ejpam-1234	206	11	4	4	NUM
ejpam-1234	206	12	,	,	PUNCT
ejpam-1234	206	13	25	25	NUM
ejpam-1234	206	14	]	]	PUNCT
ejpam-1234	206	15	.	.	PUNCT
ejpam-1234	207	1	in	in	ADP
ejpam-1234	207	2	general	general	ADJ
ejpam-1234	207	3	,	,	PUNCT
ejpam-1234	207	4	it	it	PRON
ejpam-1234	207	5	follows	follow	VERB
ejpam-1234	207	6	from	from	ADP
ejpam-1234	207	7	the	the	DET
ejpam-1234	207	8	definition	definition	NOUN
ejpam-1234	207	9	(	(	PUNCT
ejpam-1234	207	10	10	10	NUM
ejpam-1234	207	11	)	)	PUNCT
ejpam-1234	207	12	of	of	ADP
ejpam-1234	207	13	νσg	νσg	PROPN
ejpam-1234	207	14	.	.	PUNCT
ejpam-1234	208	1	indeed	indeed	ADV
ejpam-1234	208	2	,	,	PUNCT
ejpam-1234	208	3	(	(	PUNCT
ejpam-1234	208	4	x	x	X
ejpam-1234	208	5	i)gσ	i)gσ	PROPN
ejpam-1234	208	6	=	=	SYM
ejpam-1234	208	7	(	(	PUNCT
ejpam-1234	208	8	x	x	SYM
ejpam-1234	208	9	i	i	NOUN
ejpam-1234	208	10	)	)	PUNCT
ejpam-1234	208	11	νσg	νσg	PROPN
ejpam-1234	208	12	·	·	PUNCT
ejpam-1234	208	13	εgσ·(ν	εgσ·(ν	NOUN
ejpam-1234	208	14	σ	σ	NOUN
ejpam-1234	208	15	g	g	NOUN
ejpam-1234	208	16	)	)	PUNCT
ejpam-1234	208	17	−1	−1	NOUN
ejpam-1234	209	1	=	=	PROPN
ejpam-1234	209	2	ρνσg	ρνσg	PROPN
ejpam-1234	209	3	�	�	PROPN
ejpam-1234	209	4	(	(	PUNCT
ejpam-1234	209	5	x	x	SYM
ejpam-1234	209	6	i)εgσ	i)εgσ	PROPN
ejpam-1234	209	7	�	�	PROPN
ejpam-1234	209	8	.	.	PUNCT
ejpam-1234	210	1	3.1	3.1	NUM
ejpam-1234	210	2	.	.	PUNCT
ejpam-1234	211	1	the	the	DET
ejpam-1234	211	2	obstruction	obstruction	NOUN
ejpam-1234	211	3	bundle	bundle	NOUN
ejpam-1234	211	4	of	of	ADP
ejpam-1234	211	5	the	the	DET
ejpam-1234	211	6	wreath	wreath	NOUN
ejpam-1234	211	7	product	product	NOUN
ejpam-1234	211	8	orbifold	orbifold	VERB
ejpam-1234	211	9	now	now	ADV
ejpam-1234	211	10	we	we	PRON
ejpam-1234	211	11	will	will	AUX
ejpam-1234	211	12	compute	compute	VERB
ejpam-1234	211	13	the	the	DET
ejpam-1234	211	14	obstruction	obstruction	NOUN
ejpam-1234	211	15	bundle	bundle	NOUN
ejpam-1234	211	16	of	of	ADP
ejpam-1234	211	17	the	the	DET
ejpam-1234	211	18	wreath	wreath	NOUN
ejpam-1234	211	19	product	product	NOUN
ejpam-1234	211	20	orbifold	orbifold	VERB
ejpam-1234	211	21	in	in	ADP
ejpam-1234	211	22	certain	certain	ADJ
ejpam-1234	211	23	cases	case	NOUN
ejpam-1234	211	24	.	.	PUNCT
ejpam-1234	212	1	theorem	theorem	NOUN
ejpam-1234	212	2	3	3	NUM
ejpam-1234	212	3	is	be	AUX
ejpam-1234	212	4	crucial	crucial	ADJ
ejpam-1234	212	5	because	because	SCONJ
ejpam-1234	212	6	it	it	PRON
ejpam-1234	212	7	roughly	roughly	ADV
ejpam-1234	212	8	says	say	VERB
ejpam-1234	212	9	that	that	SCONJ
ejpam-1234	212	10	the	the	DET
ejpam-1234	212	11	s	s	NOUN
ejpam-1234	212	12	-	-	NOUN
ejpam-1234	212	13	bundles	bundle	NOUN
ejpam-1234	212	14	for	for	ADP
ejpam-1234	212	15	the	the	DET
ejpam-1234	212	16	wreath	wreath	NOUN
ejpam-1234	212	17	product	product	NOUN
ejpam-1234	213	1	[	[	X
ejpam-1234	213	2	x	x	X
ejpam-1234	213	3	i	i	PROPN
ejpam-1234	213	4	/	/	SYM
ejpam-1234	213	5	gi⋊σi	gi⋊σi	PROPN
ejpam-1234	213	6	]	]	PUNCT
ejpam-1234	213	7	can	can	AUX
ejpam-1234	213	8	be	be	AUX
ejpam-1234	213	9	written	write	VERB
ejpam-1234	213	10	in	in	ADP
ejpam-1234	213	11	terms	term	NOUN
ejpam-1234	213	12	of	of	ADP
ejpam-1234	213	13	the	the	DET
ejpam-1234	213	14	s	s	NOUN
ejpam-1234	213	15	-	-	NOUN
ejpam-1234	213	16	bundles	bundle	NOUN
ejpam-1234	213	17	of	of	ADP
ejpam-1234	213	18	[	[	X
ejpam-1234	213	19	x	x	X
ejpam-1234	213	20	/	/	SYM
ejpam-1234	213	21	g	g	NOUN
ejpam-1234	213	22	]	]	PUNCT
ejpam-1234	213	23	and	and	CCONJ
ejpam-1234	213	24	[	[	X
ejpam-1234	213	25	x	x	X
ejpam-1234	213	26	i	i	NOUN
ejpam-1234	213	27	/	/	SYM
ejpam-1234	213	28	σi	σi	NOUN
ejpam-1234	213	29	]	]	X
ejpam-1234	213	30	.	.	PUNCT
ejpam-1234	214	1	we	we	PRON
ejpam-1234	214	2	use	use	VERB
ejpam-1234	214	3	lemma	lemma	PROPN
ejpam-1234	214	4	3	3	NUM
ejpam-1234	214	5	in	in	ADP
ejpam-1234	214	6	the	the	DET
ejpam-1234	214	7	proof	proof	NOUN
ejpam-1234	214	8	of	of	ADP
ejpam-1234	214	9	our	our	PRON
ejpam-1234	214	10	main	main	ADJ
ejpam-1234	214	11	theorem	theorem	NOUN
ejpam-1234	214	12	,	,	PUNCT
ejpam-1234	214	13	in	in	ADP
ejpam-1234	214	14	particular	particular	ADJ
ejpam-1234	214	15	,	,	PUNCT
ejpam-1234	214	16	in	in	ADP
ejpam-1234	214	17	the	the	DET
ejpam-1234	214	18	proof	proof	NOUN
ejpam-1234	214	19	of	of	ADP
ejpam-1234	214	20	proposition	proposition	NOUN
ejpam-1234	214	21	3	3	NUM
ejpam-1234	214	22	.	.	PUNCT
ejpam-1234	214	23	theorem	theorem	NOUN
ejpam-1234	214	24	3	3	X
ejpam-1234	214	25	.	.	PUNCT
ejpam-1234	215	1	let	let	VERB
ejpam-1234	215	2	σ	σ	X
ejpam-1234	215	3	∈	∈	PROPN
ejpam-1234	215	4	σi	σi	X
ejpam-1234	215	5	,	,	PUNCT
ejpam-1234	215	6	g	g	PROPN
ejpam-1234	215	7	∈	∈	PROPN
ejpam-1234	215	8	g	g	NOUN
ejpam-1234	215	9	iσ	iσ	VERB
ejpam-1234	215	10	.	.	PUNCT
ejpam-1234	216	1	let	let	VERB
ejpam-1234	217	1	εg	εg	PRON
ejpam-1234	217	2	∈	∈	VERB
ejpam-1234	218	1	g	g	PROPN
ejpam-1234	219	1	i	i	PRON
ejpam-1234	219	2	be	be	VERB
ejpam-1234	219	3	the	the	DET
ejpam-1234	219	4	element	element	NOUN
ejpam-1234	219	5	defined	define	VERB
ejpam-1234	219	6	in	in	ADP
ejpam-1234	219	7	the	the	DET
ejpam-1234	219	8	proof	proof	NOUN
ejpam-1234	219	9	of	of	ADP
ejpam-1234	219	10	proposition	proposition	NOUN
ejpam-1234	219	11	1	1	X
ejpam-1234	219	12	.	.	PUNCT
ejpam-1234	220	1	we	we	PRON
ejpam-1234	220	2	have	have	VERB
ejpam-1234	220	3	sεgσ	sεgσ	PRON
ejpam-1234	220	4	=	=	SYM
ejpam-1234	220	5	∏	∏	PROPN
ejpam-1234	220	6	a∈iσ	a∈iσ	NOUN
ejpam-1234	220	7	�	�	PROPN
ejpam-1234	220	8	∆a	∆a	PROPN
ejpam-1234	220	9	∗	∗	PROPN
ejpam-1234	220	10	�	�	PROPN
ejpam-1234	220	11	sga	sga	PROPN
ejpam-1234	220	12	⊕	⊕	PROPN
ejpam-1234	220	13	|a|	|a|	PROPN
ejpam-1234	220	14	−	−	PROPN
ejpam-1234	220	15	1	1	NUM
ejpam-1234	220	16	2	2	NUM
ejpam-1234	220	17	t	t	NOUN
ejpam-1234	220	18	x	x	PUNCT
ejpam-1234	220	19	|xga	|xga	PROPN
ejpam-1234	220	20	�	�	PROPN
ejpam-1234	220	21	�	�	PROPN
ejpam-1234	220	22	where	where	SCONJ
ejpam-1234	220	23	sga	sga	PROPN
ejpam-1234	220	24	∈	∈	PROPN
ejpam-1234	220	25	k(x	k(x	PROPN
ejpam-1234	220	26	ga	ga	PROPN
ejpam-1234	220	27	)	)	PUNCT
ejpam-1234	220	28	is	be	AUX
ejpam-1234	220	29	the	the	DET
ejpam-1234	220	30	s	s	NOUN
ejpam-1234	220	31	-	-	NOUN
ejpam-1234	220	32	bundle	bundle	NOUN
ejpam-1234	220	33	with	with	ADP
ejpam-1234	220	34	respect	respect	NOUN
ejpam-1234	220	35	to	to	ADP
ejpam-1234	220	36	the	the	DET
ejpam-1234	220	37	action	action	NOUN
ejpam-1234	220	38	of	of	ADP
ejpam-1234	220	39	g	g	NOUN
ejpam-1234	220	40	on	on	ADP
ejpam-1234	220	41	x	x	PUNCT
ejpam-1234	220	42	and	and	CCONJ
ejpam-1234	220	43	∆a	∆a	VERB
ejpam-1234	220	44	:	:	PUNCT
ejpam-1234	220	45	x	x	X
ejpam-1234	220	46	ga	ga	PROPN
ejpam-1234	220	47	∼=∆a	∼=∆a	VERB
ejpam-1234	220	48	xga	xga	PROPN
ejpam-1234	220	49	.	.	PUNCT
ejpam-1234	221	1	proof	proof	NOUN
ejpam-1234	221	2	.	.	PUNCT
ejpam-1234	222	1	without	without	ADP
ejpam-1234	222	2	loss	loss	NOUN
ejpam-1234	222	3	of	of	ADP
ejpam-1234	222	4	generality	generality	NOUN
ejpam-1234	222	5	,	,	PUNCT
ejpam-1234	222	6	we	we	PRON
ejpam-1234	222	7	can	can	AUX
ejpam-1234	222	8	assume	assume	VERB
ejpam-1234	222	9	i	i	PRON
ejpam-1234	222	10	=	=	PUNCT
ejpam-1234	222	11	{	{	PUNCT
ejpam-1234	222	12	1	1	NUM
ejpam-1234	222	13	,	,	PUNCT
ejpam-1234	222	14	·	·	PUNCT
ejpam-1234	222	15	·	·	PUNCT
ejpam-1234	222	16	·	·	PUNCT
ejpam-1234	222	17	,	,	PUNCT
ejpam-1234	222	18	n	n	CCONJ
ejpam-1234	222	19	}	}	PUNCT
ejpam-1234	222	20	and	and	CCONJ
ejpam-1234	222	21	σ	σ	NUM
ejpam-1234	222	22	=	=	SYM
ejpam-1234	222	23	(	(	PUNCT
ejpam-1234	222	24	12	12	NUM
ejpam-1234	222	25	·	·	PUNCT
ejpam-1234	222	26	·	·	PUNCT
ejpam-1234	222	27	·	·	PUNCT
ejpam-1234	222	28	n	n	CCONJ
ejpam-1234	222	29	)	)	PUNCT
ejpam-1234	222	30	.	.	PUNCT
ejpam-1234	223	1	let	let	VERB
ejpam-1234	223	2	εg	εg	NOUN
ejpam-1234	223	3	=	=	PUNCT
ejpam-1234	223	4	(	(	PUNCT
ejpam-1234	223	5	g	g	PROPN
ejpam-1234	223	6	,	,	PUNCT
ejpam-1234	223	7	1	1	NUM
ejpam-1234	223	8	,	,	PUNCT
ejpam-1234	223	9	·	·	PUNCT
ejpam-1234	223	10	·	·	PUNCT
ejpam-1234	223	11	·	·	PUNCT
ejpam-1234	223	12	,	,	PUNCT
ejpam-1234	223	13	1	1	X
ejpam-1234	223	14	)	)	PUNCT
ejpam-1234	223	15	∈	∈	NOUN
ejpam-1234	223	16	gi	gi	INTJ
ejpam-1234	223	17	.	.	PUNCT
ejpam-1234	224	1	let	let	VERB
ejpam-1234	224	2	ρ	ρ	NOUN
ejpam-1234	224	3	be	be	AUX
ejpam-1234	224	4	the	the	DET
ejpam-1234	224	5	natural	natural	ADJ
ejpam-1234	224	6	left	left	ADJ
ejpam-1234	224	7	action	action	NOUN
ejpam-1234	224	8	of	of	ADP
ejpam-1234	224	9	σi	σi	PRON
ejpam-1234	224	10	on	on	ADP
ejpam-1234	224	11	v	v	ADP
ejpam-1234	224	12	:	:	PUNCT
ejpam-1234	225	1	=	=	SYM
ejpam-1234	225	2	cn	cn	VERB
ejpam-1234	225	3	so	so	SCONJ
ejpam-1234	225	4	that	that	SCONJ
ejpam-1234	225	5	ρσ(e	ρσ(e	PUNCT
ejpam-1234	225	6	j	j	NOUN
ejpam-1234	225	7	)	)	PUNCT
ejpam-1234	226	1	=	=	SYM
ejpam-1234	226	2	eσ−1	eσ−1	PROPN
ejpam-1234	226	3	(	(	PUNCT
ejpam-1234	226	4	j	j	NOUN
ejpam-1234	226	5	)	)	PUNCT
ejpam-1234	226	6	where	where	SCONJ
ejpam-1234	226	7	{	{	PUNCT
ejpam-1234	226	8	e1	e1	NOUN
ejpam-1234	226	9	,	,	PUNCT
ejpam-1234	226	10	·	·	PUNCT
ejpam-1234	226	11	·	·	PUNCT
ejpam-1234	226	12	·	·	PUNCT
ejpam-1234	226	13	,	,	PUNCT
ejpam-1234	226	14	en	en	ADP
ejpam-1234	226	15	}	}	PUNCT
ejpam-1234	226	16	is	be	AUX
ejpam-1234	226	17	the	the	DET
ejpam-1234	226	18	standard	standard	ADJ
ejpam-1234	226	19	basis	basis	NOUN
ejpam-1234	226	20	of	of	ADP
ejpam-1234	226	21	v	v	NOUN
ejpam-1234	226	22	.	.	PUNCT
ejpam-1234	227	1	as	as	ADP
ejpam-1234	227	2	a	a	DET
ejpam-1234	227	3	〈	〈	NOUN
ejpam-1234	227	4	εgσ〉-equivariant	εgσ〉-equivariant	NOUN
ejpam-1234	227	5	vector	vector	NOUN
ejpam-1234	227	6	bundle	bundle	NOUN
ejpam-1234	227	7	,	,	PUNCT
ejpam-1234	227	8	t	t	NOUN
ejpam-1234	227	9	x	x	PROPN
ejpam-1234	228	1	i	i	PRON
ejpam-1234	228	2	|(x	|(x	ADP
ejpam-1234	228	3	i	i	PRON
ejpam-1234	228	4	)	)	PUNCT
ejpam-1234	228	5	εgσ	εgσ	VERB
ejpam-1234	228	6	can	can	AUX
ejpam-1234	228	7	be	be	AUX
ejpam-1234	228	8	identified	identify	VERB
ejpam-1234	228	9	to	to	ADP
ejpam-1234	228	10	(	(	PUNCT
ejpam-1234	228	11	t∆x⊗v	t∆x⊗v	PROPN
ejpam-1234	228	12	)	)	PUNCT
ejpam-1234	228	13	|∆xg	|∆xg	NOUN
ejpam-1234	228	14	.	.	PUNCT
ejpam-1234	229	1	explicitly	explicitly	ADV
ejpam-1234	229	2	,	,	PUNCT
ejpam-1234	229	3	εgσ	εgσ	VERB
ejpam-1234	229	4	acts	act	VERB
ejpam-1234	229	5	on	on	ADP
ejpam-1234	229	6	u⊗v	u⊗v	PROPN
ejpam-1234	229	7	∈	∈	PROPN
ejpam-1234	229	8	tp∆x⊗v	tp∆x⊗v	PUNCT
ejpam-1234	229	9	as	as	ADP
ejpam-1234	229	10	ρεgσ(u⊗	ρεgσ(u⊗	PROPN
ejpam-1234	229	11	v	v	NOUN
ejpam-1234	229	12	)	)	PUNCT
ejpam-1234	229	13	=	=	SYM
ejpam-1234	229	14	ρgu⊗	ρgu⊗	NOUN
ejpam-1234	229	15	v1en+	v1en+	NOUN
ejpam-1234	229	16	∑n	∑n	PROPN
ejpam-1234	229	17	j=2	j=2	PROPN
ejpam-1234	229	18	u⊗	u⊗	NOUN
ejpam-1234	229	19	v	v	X
ejpam-1234	229	20	je	je	X
ejpam-1234	230	1	j−1	j−1	PROPN
ejpam-1234	230	2	where	where	SCONJ
ejpam-1234	230	3	v=	v=	VERB
ejpam-1234	230	4	∑	∑	PROPN
ejpam-1234	230	5	j	j	PROPN
ejpam-1234	230	6	vjej	vjej	NOUN
ejpam-1234	230	7	.	.	PUNCT
ejpam-1234	231	1	let	let	VERB
ejpam-1234	231	2	r	r	NOUN
ejpam-1234	231	3	be	be	AUX
ejpam-1234	231	4	the	the	DET
ejpam-1234	231	5	order	order	NOUN
ejpam-1234	231	6	of	of	ADP
ejpam-1234	231	7	g	g	PROPN
ejpam-1234	231	8	∈	∈	PROPN
ejpam-1234	231	9	g	g	PROPN
ejpam-1234	231	10	and	and	CCONJ
ejpam-1234	231	11	let	let	VERB
ejpam-1234	231	12	t∆x	t∆x	NOUN
ejpam-1234	231	13	|∆xg	|∆xg	NOUN
ejpam-1234	231	14	=	=	SYM
ejpam-1234	232	1	⊕r−1	⊕r−1	X
ejpam-1234	232	2	l=0	l=0	PROPN
ejpam-1234	232	3	ul	ul	INTJ
ejpam-1234	232	4	be	be	AUX
ejpam-1234	232	5	the	the	DET
ejpam-1234	232	6	eigenbundle	eigenbundle	ADJ
ejpam-1234	232	7	decomposition	decomposition	NOUN
ejpam-1234	232	8	of	of	ADP
ejpam-1234	232	9	the	the	DET
ejpam-1234	232	10	diagonal	diagonal	ADJ
ejpam-1234	232	11	action	action	NOUN
ejpam-1234	232	12	of	of	ADP
ejpam-1234	232	13	g	g	PROPN
ejpam-1234	232	14	tomoo	tomoo	VERB
ejpam-1234	232	15	matsumura	matsumura	ADV
ejpam-1234	232	16	/	/	SYM
ejpam-1234	232	17	eur	eur	PROPN
ejpam-1234	232	18	.	.	PUNCT
ejpam-1234	233	1	j.	j.	PROPN
ejpam-1234	233	2	pure	pure	PROPN
ejpam-1234	233	3	appl	appl	PROPN
ejpam-1234	233	4	.	.	PROPN
ejpam-1234	233	5	math	math	PROPN
ejpam-1234	233	6	,	,	PUNCT
ejpam-1234	233	7	5	5	NUM
ejpam-1234	233	8	(	(	PUNCT
ejpam-1234	233	9	2012	2012	NUM
ejpam-1234	233	10	)	)	PUNCT
ejpam-1234	233	11	,	,	PUNCT
ejpam-1234	233	12	492	492	NUM
ejpam-1234	233	13	-	-	SYM
ejpam-1234	233	14	510	510	NUM
ejpam-1234	233	15	500	500	NUM
ejpam-1234	233	16	where	where	SCONJ
ejpam-1234	233	17	the	the	DET
ejpam-1234	233	18	eigenvalue	eigenvalue	PROPN
ejpam-1234	233	19	on	on	ADP
ejpam-1234	233	20	ul	ul	PROPN
ejpam-1234	233	21	is	be	AUX
ejpam-1234	233	22	e2πi	e2πi	X
ejpam-1234	233	23	l	l	NOUN
ejpam-1234	233	24	r	r	NOUN
ejpam-1234	233	25	.	.	PUNCT
ejpam-1234	234	1	on	on	ADP
ejpam-1234	234	2	the	the	DET
ejpam-1234	234	3	other	other	ADJ
ejpam-1234	234	4	hand	hand	NOUN
ejpam-1234	234	5	,	,	PUNCT
ejpam-1234	234	6	the	the	DET
ejpam-1234	234	7	eigenvalues	eigenvalue	NOUN
ejpam-1234	234	8	of	of	ADP
ejpam-1234	234	9	the	the	DET
ejpam-1234	234	10	action	action	NOUN
ejpam-1234	234	11	of	of	ADP
ejpam-1234	234	12	σ	σ	PROPN
ejpam-1234	234	13	on	on	ADP
ejpam-1234	234	14	v	v	NUM
ejpam-1234	234	15	are	be	AUX
ejpam-1234	234	16	e2πi	e2πi	X
ejpam-1234	234	17	k	k	PROPN
ejpam-1234	234	18	n	n	PROPN
ejpam-1234	234	19	,	,	PUNCT
ejpam-1234	234	20	k	k	PROPN
ejpam-1234	235	1	=	=	SYM
ejpam-1234	236	1	0	0	NUM
ejpam-1234	236	2	,	,	PUNCT
ejpam-1234	236	3	·	·	PUNCT
ejpam-1234	236	4	·	·	PUNCT
ejpam-1234	236	5	·	·	PUNCT
ejpam-1234	236	6	,	,	PUNCT
ejpam-1234	236	7	n−	n−	NOUN
ejpam-1234	236	8	1	1	NUM
ejpam-1234	236	9	and	and	CCONJ
ejpam-1234	236	10	the	the	DET
ejpam-1234	236	11	corresponding	corresponding	ADJ
ejpam-1234	236	12	eigenvectors	eigenvector	NOUN
ejpam-1234	236	13	are	be	AUX
ejpam-1234	236	14	vk	vk	ADP
ejpam-1234	236	15	:	:	PUNCT
ejpam-1234	236	16	=	=	SYM
ejpam-1234	236	17	∑n	∑n	PROPN
ejpam-1234	236	18	j=1	j=1	PROPN
ejpam-1234	236	19	�	�	PROPN
ejpam-1234	236	20	e2πi	e2πi	PROPN
ejpam-1234	236	21	k	k	PROPN
ejpam-1234	236	22	n	n	X
ejpam-1234	236	23	�	�	PROPN
ejpam-1234	236	24	j	j	PROPN
ejpam-1234	236	25	e	e	PROPN
ejpam-1234	236	26	j.	j.	PROPN
ejpam-1234	236	27	for	for	ADP
ejpam-1234	236	28	each	each	DET
ejpam-1234	236	29	l	l	NOUN
ejpam-1234	236	30	=	=	SYM
ejpam-1234	236	31	0	0	NUM
ejpam-1234	236	32	,	,	PUNCT
ejpam-1234	236	33	·	·	PUNCT
ejpam-1234	236	34	·	·	PUNCT
ejpam-1234	236	35	·	·	PUNCT
ejpam-1234	236	36	,	,	PUNCT
ejpam-1234	236	37	r	r	NOUN
ejpam-1234	236	38	−	−	PROPN
ejpam-1234	236	39	1	1	NUM
ejpam-1234	236	40	,	,	PUNCT
ejpam-1234	236	41	define	define	VERB
ejpam-1234	236	42	vk	vk	NOUN
ejpam-1234	236	43	,	,	PUNCT
ejpam-1234	236	44	l	l	NOUN
ejpam-1234	236	45	=	=	PUNCT
ejpam-1234	236	46	∑n	∑n	PROPN
ejpam-1234	236	47	j=1	j=1	PROPN
ejpam-1234	236	48	�	�	PROPN
ejpam-1234	236	49	e2πi	e2πi	ADP
ejpam-1234	236	50	�	�	PROPN
ejpam-1234	236	51	l	l	PROPN
ejpam-1234	236	52	rn	rn	PROPN
ejpam-1234	237	1	+	+	CCONJ
ejpam-1234	237	2	k	k	PROPN
ejpam-1234	237	3	n	n	SYM
ejpam-1234	237	4	�	�	PROPN
ejpam-1234	237	5	�	�	PROPN
ejpam-1234	237	6	j	j	PROPN
ejpam-1234	237	7	e	e	PROPN
ejpam-1234	237	8	j	j	PROPN
ejpam-1234	237	9	and	and	CCONJ
ejpam-1234	237	10	then	then	ADV
ejpam-1234	237	11	{	{	PUNCT
ejpam-1234	237	12	vk	vk	INTJ
ejpam-1234	237	13	,	,	PUNCT
ejpam-1234	237	14	l	l	NOUN
ejpam-1234	237	15	,	,	PUNCT
ejpam-1234	237	16	k	k	PROPN
ejpam-1234	237	17	=	=	SYM
ejpam-1234	237	18	0	0	NUM
ejpam-1234	237	19	,	,	PUNCT
ejpam-1234	237	20	·	·	PUNCT
ejpam-1234	237	21	·	·	PUNCT
ejpam-1234	237	22	·	·	PUNCT
ejpam-1234	237	23	,	,	PUNCT
ejpam-1234	237	24	n−	n−	NOUN
ejpam-1234	237	25	1	1	NUM
ejpam-1234	237	26	}	}	PUNCT
ejpam-1234	237	27	forms	form	VERB
ejpam-1234	237	28	a	a	DET
ejpam-1234	237	29	basis	basis	NOUN
ejpam-1234	237	30	of	of	ADP
ejpam-1234	237	31	v	v	NOUN
ejpam-1234	237	32	.	.	PUNCT
ejpam-1234	238	1	thus	thus	ADV
ejpam-1234	238	2	we	we	PRON
ejpam-1234	238	3	have	have	VERB
ejpam-1234	238	4	the	the	DET
ejpam-1234	238	5	following	follow	VERB
ejpam-1234	238	6	decomposition	decomposition	NOUN
ejpam-1234	238	7	t	t	NOUN
ejpam-1234	238	8	x	x	X
ejpam-1234	239	1	i	i	PRON
ejpam-1234	239	2	|(x	|(x	ADP
ejpam-1234	239	3	i	i	PRON
ejpam-1234	239	4	)	)	PUNCT
ejpam-1234	239	5	εgσ	εgσ	PROPN
ejpam-1234	239	6	=	=	SYM
ejpam-1234	239	7	n−1	n−1	PROPN
ejpam-1234	239	8	⊕	⊕	PROPN
ejpam-1234	239	9	k=0	k=0	PROPN
ejpam-1234	240	1	r−1	r−1	PROPN
ejpam-1234	240	2	⊕	⊕	PROPN
ejpam-1234	241	1	l=0	l=0	PROPN
ejpam-1234	241	2	ul	ul	PROPN
ejpam-1234	242	1	⊗	⊗	PROPN
ejpam-1234	242	2	vk	vk	PROPN
ejpam-1234	242	3	,	,	PUNCT
ejpam-1234	242	4	l	l	NOUN
ejpam-1234	242	5	!	!	PUNCT
ejpam-1234	242	6	.	.	PUNCT
ejpam-1234	243	1	(	(	PUNCT
ejpam-1234	243	2	11	11	NUM
ejpam-1234	243	3	)	)	PUNCT
ejpam-1234	243	4	where	where	SCONJ
ejpam-1234	243	5	vk	vk	X
ejpam-1234	243	6	,	,	PUNCT
ejpam-1234	243	7	l	l	NOUN
ejpam-1234	243	8	is	be	AUX
ejpam-1234	243	9	the	the	DET
ejpam-1234	243	10	1	1	NUM
ejpam-1234	243	11	-	-	PUNCT
ejpam-1234	243	12	dimensional	dimensional	ADJ
ejpam-1234	243	13	subspace	subspace	NOUN
ejpam-1234	243	14	spanned	span	VERB
ejpam-1234	243	15	by	by	ADP
ejpam-1234	243	16	vk	vk	NOUN
ejpam-1234	243	17	,	,	PUNCT
ejpam-1234	243	18	l	l	NOUN
ejpam-1234	243	19	.	.	PUNCT
ejpam-1234	244	1	this	this	PRON
ejpam-1234	244	2	turns	turn	VERB
ejpam-1234	244	3	out	out	ADP
ejpam-1234	244	4	to	to	PART
ejpam-1234	244	5	be	be	AUX
ejpam-1234	244	6	the	the	DET
ejpam-1234	244	7	eigenbundle	eigenbundle	ADJ
ejpam-1234	244	8	decomposition	decomposition	NOUN
ejpam-1234	244	9	of	of	ADP
ejpam-1234	244	10	the	the	DET
ejpam-1234	244	11	action	action	NOUN
ejpam-1234	244	12	of	of	ADP
ejpam-1234	244	13	εgσ	εgσ	NOUN
ejpam-1234	244	14	where	where	SCONJ
ejpam-1234	244	15	the	the	DET
ejpam-1234	244	16	eigenvalue	eigenvalue	PROPN
ejpam-1234	244	17	of	of	ADP
ejpam-1234	244	18	ul	ul	PROPN
ejpam-1234	244	19	⊗	⊗	PROPN
ejpam-1234	244	20	vk	vk	PROPN
ejpam-1234	244	21	,	,	PUNCT
ejpam-1234	244	22	l	l	PROPN
ejpam-1234	244	23	is	be	AUX
ejpam-1234	244	24	e2πi	e2πi	X
ejpam-1234	244	25	�	�	PROPN
ejpam-1234	244	26	l	l	NOUN
ejpam-1234	244	27	nr	nr	PROPN
ejpam-1234	245	1	+	+	CCONJ
ejpam-1234	245	2	k	k	PROPN
ejpam-1234	245	3	n	n	PRON
ejpam-1234	245	4	�	�	PROPN
ejpam-1234	245	5	.	.	PUNCT
ejpam-1234	246	1	indeed	indeed	ADV
ejpam-1234	246	2	,	,	PUNCT
ejpam-1234	246	3	if	if	SCONJ
ejpam-1234	246	4	ul	ul	PROPN
ejpam-1234	246	5	⊗	⊗	PROPN
ejpam-1234	246	6	vk	vk	PROPN
ejpam-1234	246	7	,	,	PUNCT
ejpam-1234	246	8	l	l	PROPN
ejpam-1234	246	9	∈	∈	PROPN
ejpam-1234	246	10	ul	ul	INTJ
ejpam-1234	246	11	⊗	⊗	PROPN
ejpam-1234	246	12	vk	vk	PROPN
ejpam-1234	246	13	,	,	PUNCT
ejpam-1234	246	14	l	l	PROPN
ejpam-1234	246	15	,	,	PUNCT
ejpam-1234	246	16	ρεgσ(ul	ρεgσ(ul	PROPN
ejpam-1234	246	17	⊗	⊗	PROPN
ejpam-1234	246	18	vk	vk	PROPN
ejpam-1234	246	19	,	,	PUNCT
ejpam-1234	246	20	l	l	NOUN
ejpam-1234	246	21	)	)	PUNCT
ejpam-1234	246	22	=	=	SYM
ejpam-1234	246	23	e2πi	e2πi	X
ejpam-1234	246	24	�	�	PROPN
ejpam-1234	246	25	l	l	PROPN
ejpam-1234	246	26	rn	rn	PROPN
ejpam-1234	247	1	+	+	CCONJ
ejpam-1234	247	2	k	k	PROPN
ejpam-1234	247	3	n	n	SYM
ejpam-1234	247	4	�	�	PROPN
ejpam-1234	247	5	�	�	PROPN
ejpam-1234	247	6	e2πi	e2πi	X
ejpam-1234	247	7	l	l	NOUN
ejpam-1234	247	8	r	r	NOUN
ejpam-1234	247	9	�	�	PROPN
ejpam-1234	247	10	ul	ul	PROPN
ejpam-1234	247	11	⊗	⊗	PROPN
ejpam-1234	247	12	en+	en+	PROPN
ejpam-1234	247	13	n	n	PROPN
ejpam-1234	247	14	∑	∑	PROPN
ejpam-1234	247	15	j=2	j=2	PROPN
ejpam-1234	247	16	�	�	PROPN
ejpam-1234	247	17	e2πi	e2πi	X
ejpam-1234	247	18	�	�	PROPN
ejpam-1234	247	19	l	l	PROPN
ejpam-1234	247	20	rn	rn	PROPN
ejpam-1234	248	1	+	+	CCONJ
ejpam-1234	248	2	k	k	PROPN
ejpam-1234	248	3	n	n	SYM
ejpam-1234	248	4	�	�	PROPN
ejpam-1234	248	5	�	�	PROPN
ejpam-1234	248	6	j	j	PROPN
ejpam-1234	248	7	ul	ul	PROPN
ejpam-1234	248	8	⊗	⊗	NOUN
ejpam-1234	249	1	e	e	PROPN
ejpam-1234	249	2	j−1	j−1	PROPN
ejpam-1234	249	3	=	=	SYM
ejpam-1234	249	4	e2πi	e2πi	X
ejpam-1234	249	5	�	�	PROPN
ejpam-1234	249	6	l	l	PROPN
ejpam-1234	249	7	rn	rn	PROPN
ejpam-1234	250	1	+	+	CCONJ
ejpam-1234	250	2	k	k	PROPN
ejpam-1234	250	3	n	n	CCONJ
ejpam-1234	250	4	�	�	PROPN
ejpam-1234	250	5			PROPN
ejpam-1234	250	6			PROPN
ejpam-1234	250	7			PROPN
ejpam-1234	250	8	�	�	PROPN
ejpam-1234	250	9	e2πi	e2πi	X
ejpam-1234	250	10	l	l	NOUN
ejpam-1234	250	11	r	r	NOUN
ejpam-1234	250	12	�	�	PROPN
ejpam-1234	250	13	ul	ul	NOUN
ejpam-1234	250	14	⊗	⊗	PROPN
ejpam-1234	250	15	en	en	PROPN
ejpam-1234	250	16	+	+	CCONJ
ejpam-1234	250	17	n	n	CCONJ
ejpam-1234	250	18	∑	∑	PROPN
ejpam-1234	250	19	j=2	j=2	PROPN
ejpam-1234	250	20	�	�	PROPN
ejpam-1234	250	21	e2πi	e2πi	X
ejpam-1234	250	22	�	�	PROPN
ejpam-1234	250	23	l	l	PROPN
ejpam-1234	250	24	rn	rn	PROPN
ejpam-1234	251	1	+	+	CCONJ
ejpam-1234	251	2	k	k	PROPN
ejpam-1234	251	3	n	n	SYM
ejpam-1234	251	4	�	�	PROPN
ejpam-1234	251	5	�	�	PROPN
ejpam-1234	251	6	j−1	j−1	PROPN
ejpam-1234	251	7	ul	ul	INTJ
ejpam-1234	252	1	⊗	⊗	PROPN
ejpam-1234	252	2	e	e	PROPN
ejpam-1234	252	3	j−1	j−1	PROPN
ejpam-1234	252	4			PROPN
ejpam-1234	252	5			PROPN
ejpam-1234	252	6			PROPN
ejpam-1234	252	7	=	=	SYM
ejpam-1234	252	8	e2πi	e2πi	X
ejpam-1234	252	9	�	�	PROPN
ejpam-1234	252	10	l	l	PROPN
ejpam-1234	252	11	rn	rn	PROPN
ejpam-1234	253	1	+	+	CCONJ
ejpam-1234	253	2	k	k	PROPN
ejpam-1234	253	3	n	n	PRON
ejpam-1234	253	4	�	�	PROPN
ejpam-1234	253	5	·	·	PUNCT
ejpam-1234	253	6	ul	ul	PROPN
ejpam-1234	253	7	⊗	⊗	PROPN
ejpam-1234	253	8	vk	vk	PROPN
ejpam-1234	253	9	,	,	PUNCT
ejpam-1234	253	10	l	l	NOUN
ejpam-1234	253	11	thus	thus	ADV
ejpam-1234	253	12	we	we	PRON
ejpam-1234	253	13	have	have	VERB
ejpam-1234	253	14	sεgσ	sεgσ	NOUN
ejpam-1234	253	15	=	=	SYM
ejpam-1234	253	16	n−1	n−1	PROPN
ejpam-1234	253	17	⊕	⊕	PROPN
ejpam-1234	253	18	k=0	k=0	PROPN
ejpam-1234	254	1	r−1	r−1	PROPN
ejpam-1234	254	2	⊕	⊕	PROPN
ejpam-1234	254	3	l=0	l=0	PROPN
ejpam-1234	254	4	�	�	PROPN
ejpam-1234	254	5	l	l	NOUN
ejpam-1234	254	6	nr	nr	PROPN
ejpam-1234	255	1	+	+	CCONJ
ejpam-1234	255	2	k	k	PROPN
ejpam-1234	255	3	n	n	PRON
ejpam-1234	255	4	�	�	PROPN
ejpam-1234	255	5	ul	ul	NOUN
ejpam-1234	255	6	⊗	⊗	PROPN
ejpam-1234	255	7	v	v	NUM
ejpam-1234	256	1	l	l	NOUN
ejpam-1234	256	2	k	k	NOUN
ejpam-1234	256	3	=	=	PUNCT
ejpam-1234	256	4	r−1	r−1	PROPN
ejpam-1234	256	5	⊕	⊕	NOUN
ejpam-1234	256	6	l=0	l=0	PROPN
ejpam-1234	257	1	l	l	NOUN
ejpam-1234	258	1	r	r	NOUN
ejpam-1234	258	2	ul	ul	NOUN
ejpam-1234	258	3	⊕	⊕	PROPN
ejpam-1234	258	4	n−1	n−1	PROPN
ejpam-1234	258	5	⊕	⊕	PROPN
ejpam-1234	258	6	k=0	k=0	PROPN
ejpam-1234	259	1	k	k	PROPN
ejpam-1234	260	1	n	n	PROPN
ejpam-1234	260	2	t∆x	t∆x	VERB
ejpam-1234	260	3	|∆xga	|∆xga	PROPN
ejpam-1234	260	4	=	=	VERB
ejpam-1234	260	5	∆∗	∆∗	ADP
ejpam-1234	260	6	�	�	PROPN
ejpam-1234	260	7	sg	sg	ADP
ejpam-1234	260	8	⊕	⊕	PROPN
ejpam-1234	260	9	n−	n−	NOUN
ejpam-1234	260	10	1	1	NUM
ejpam-1234	260	11	2	2	NUM
ejpam-1234	260	12	t	t	NOUN
ejpam-1234	260	13	x	x	SYM
ejpam-1234	260	14	|xg	|xg	PROPN
ejpam-1234	260	15	�	�	PROPN
ejpam-1234	260	16	,	,	PUNCT
ejpam-1234	260	17	where	where	SCONJ
ejpam-1234	260	18	the	the	DET
ejpam-1234	260	19	second	second	ADJ
ejpam-1234	260	20	equality	equality	NOUN
ejpam-1234	260	21	follows	follow	VERB
ejpam-1234	260	22	from	from	ADP
ejpam-1234	260	23	forgetting	forget	VERB
ejpam-1234	260	24	the	the	DET
ejpam-1234	260	25	group	group	NOUN
ejpam-1234	260	26	action	action	NOUN
ejpam-1234	260	27	and	and	CCONJ
ejpam-1234	260	28	identifying	identify	VERB
ejpam-1234	260	29	vk	vk	NOUN
ejpam-1234	260	30	,	,	PUNCT
ejpam-1234	260	31	l	l	NOUN
ejpam-1234	260	32	with	with	ADP
ejpam-1234	260	33	c.	c.	PROPN
ejpam-1234	260	34	corollary	corollary	PROPN
ejpam-1234	260	35	1	1	PROPN
ejpam-1234	260	36	.	.	PUNCT
ejpam-1234	261	1	theorem	theorem	VERB
ejpam-1234	261	2	3	3	NUM
ejpam-1234	261	3	leads	lead	VERB
ejpam-1234	261	4	to	to	ADP
ejpam-1234	261	5	the	the	DET
ejpam-1234	261	6	following	follow	VERB
ejpam-1234	261	7	formula	formula	NOUN
ejpam-1234	261	8	obtained	obtain	VERB
ejpam-1234	261	9	in	in	ADP
ejpam-1234	261	10	[	[	X
ejpam-1234	261	11	26	26	NUM
ejpam-1234	261	12	]	]	PUNCT
ejpam-1234	261	13	through	through	ADP
ejpam-1234	261	14	the	the	DET
ejpam-1234	261	15	direct	direct	ADJ
ejpam-1234	261	16	calculation	calculation	NOUN
ejpam-1234	261	17	:	:	PUNCT
ejpam-1234	261	18	age(gσ	age(gσ	NOUN
ejpam-1234	261	19	)	)	PUNCT
ejpam-1234	261	20	:	:	PUNCT
ejpam-1234	261	21	=	=	SYM
ejpam-1234	261	22	rksεgσ	rksεgσ	NOUN
ejpam-1234	261	23	=	=	PUNCT
ejpam-1234	261	24	dimc	dimc	ADJ
ejpam-1234	261	25	x	x	X
ejpam-1234	261	26	·	·	PUNCT
ejpam-1234	261	27	|σ|	|σ|	PROPN
ejpam-1234	261	28	2	2	NUM
ejpam-1234	261	29	+	+	CCONJ
ejpam-1234	261	30	∑	∑	ADJ
ejpam-1234	261	31	a∈iσ	a∈iσ	NOUN
ejpam-1234	261	32	age(ga	age(ga	X
ejpam-1234	261	33	)	)	PUNCT
ejpam-1234	261	34	where	where	SCONJ
ejpam-1234	261	35	age(ga	age(ga	X
ejpam-1234	261	36	)	)	PUNCT
ejpam-1234	261	37	is	be	AUX
ejpam-1234	261	38	the	the	DET
ejpam-1234	261	39	age	age	NOUN
ejpam-1234	261	40	of	of	ADP
ejpam-1234	261	41	ga	ga	PROPN
ejpam-1234	261	42	with	with	ADP
ejpam-1234	261	43	respect	respect	NOUN
ejpam-1234	261	44	to	to	ADP
ejpam-1234	261	45	the	the	DET
ejpam-1234	261	46	action	action	NOUN
ejpam-1234	261	47	g	g	NOUN
ejpam-1234	261	48	on	on	ADP
ejpam-1234	261	49	x	x	X
ejpam-1234	261	50	.	.	PUNCT
ejpam-1234	262	1	we	we	PRON
ejpam-1234	262	2	need	need	VERB
ejpam-1234	262	3	the	the	DET
ejpam-1234	262	4	following	follow	VERB
ejpam-1234	262	5	lemma	lemma	PROPN
ejpam-1234	262	6	to	to	PART
ejpam-1234	262	7	compute	compute	VERB
ejpam-1234	262	8	the	the	DET
ejpam-1234	262	9	action	action	NOUN
ejpam-1234	262	10	of	of	ADP
ejpam-1234	262	11	the	the	DET
ejpam-1234	262	12	untwisted	untwist	VERB
ejpam-1234	262	13	sector	sector	NOUN
ejpam-1234	262	14	of	of	ADP
ejpam-1234	262	15	h	h	NOUN
ejpam-1234	262	16	(	(	PUNCT
ejpam-1234	262	17	x	x	PROPN
ejpam-1234	262	18	i	i	PRON
ejpam-1234	262	19	,	,	PUNCT
ejpam-1234	262	20	gi	gi	VERB
ejpam-1234	262	21	⋊σi	⋊σi	NOUN
ejpam-1234	262	22	)	)	PUNCT
ejpam-1234	262	23	gi	gi	INTJ
ejpam-1234	262	24	.	.	PUNCT
ejpam-1234	263	1	lemma	lemma	PROPN
ejpam-1234	263	2	3	3	X
ejpam-1234	263	3	.	.	PUNCT
ejpam-1234	264	1	for	for	ADP
ejpam-1234	264	2	every	every	DET
ejpam-1234	264	3	h	h	NOUN
ejpam-1234	264	4	∈	∈	NOUN
ejpam-1234	264	5	gi	gi	NOUN
ejpam-1234	264	6	and	and	CCONJ
ejpam-1234	264	7	g	g	PROPN
ejpam-1234	264	8	∈	∈	PROPN
ejpam-1234	264	9	giσ	giσ	PROPN
ejpam-1234	264	10	,	,	PUNCT
ejpam-1234	264	11	let	let	VERB
ejpam-1234	264	12	za	za	NOUN
ejpam-1234	264	13	:	:	PUNCT
ejpam-1234	264	14	=	=	SYM
ejpam-1234	264	15	x	x	SYM
ejpam-1234	264	16	ga	ga	PROPN
ejpam-1234	264	17	,	,	PUNCT
ejpam-1234	264	18	hi	hi	INTJ
ejpam-1234	264	19	,	,	PUNCT
ejpam-1234	264	20	i∈a	i∈a	ADJ
ejpam-1234	264	21	for	for	ADP
ejpam-1234	264	22	a	a	DET
ejpam-1234	264	23	∈	∈	PROPN
ejpam-1234	264	24	iσ	iσ	ADV
ejpam-1234	264	25	,	,	PUNCT
ejpam-1234	264	26	then	then	ADV
ejpam-1234	264	27	(	(	PUNCT
ejpam-1234	264	28	x	x	X
ejpam-1234	264	29	i)h	i)h	NOUN
ejpam-1234	264	30	∩	∩	NOUN
ejpam-1234	264	31	(	(	PUNCT
ejpam-1234	264	32	x	x	PUNCT
ejpam-1234	264	33	i)εgσ	i)εgσ	PROPN
ejpam-1234	264	34	=	=	SYM
ejpam-1234	264	35	∏	∏	PROPN
ejpam-1234	264	36	a∈iσ	a∈iσ	NOUN
ejpam-1234	264	37	∆a	∆a	PROPN
ejpam-1234	264	38	za	za	PROPN
ejpam-1234	264	39	and	and	CCONJ
ejpam-1234	264	40	r(h	r(h	PROPN
ejpam-1234	264	41	,	,	PUNCT
ejpam-1234	264	42	εgσ	εgσ	NOUN
ejpam-1234	264	43	)	)	PUNCT
ejpam-1234	264	44	=	=	SYM
ejpam-1234	264	45	∏	∏	NUM
ejpam-1234	264	46	a∈iσ	a∈iσ	NOUN
ejpam-1234	264	47	∆a	∆a	PROPN
ejpam-1234	264	48	∗r(hσ|a|−1(ia	∗r(hσ|a|−1(ia	NOUN
ejpam-1234	264	49	)	)	PUNCT
ejpam-1234	264	50	,	,	PUNCT
ejpam-1234	264	51	·	·	PUNCT
ejpam-1234	264	52	·	·	PUNCT
ejpam-1234	264	53	·	·	PUNCT
ejpam-1234	264	54	,	,	PUNCT
ejpam-1234	264	55	hσ0(ia	hσ0(ia	NOUN
ejpam-1234	264	56	)	)	PUNCT
ejpam-1234	264	57	,	,	PUNCT
ejpam-1234	264	58	ga	ga	PROPN
ejpam-1234	264	59	)	)	PUNCT
ejpam-1234	264	60	tomoo	tomoo	VERB
ejpam-1234	264	61	matsumura	matsumura	ADJ
ejpam-1234	264	62	/	/	SYM
ejpam-1234	264	63	eur	eur	PROPN
ejpam-1234	264	64	.	.	PUNCT
ejpam-1234	265	1	j.	j.	PROPN
ejpam-1234	265	2	pure	pure	PROPN
ejpam-1234	265	3	appl	appl	PROPN
ejpam-1234	265	4	.	.	PROPN
ejpam-1234	265	5	math	math	PROPN
ejpam-1234	265	6	,	,	PUNCT
ejpam-1234	265	7	5	5	NUM
ejpam-1234	265	8	(	(	PUNCT
ejpam-1234	265	9	2012	2012	NUM
ejpam-1234	265	10	)	)	PUNCT
ejpam-1234	265	11	,	,	PUNCT
ejpam-1234	265	12	492	492	NUM
ejpam-1234	265	13	-	-	SYM
ejpam-1234	265	14	510	510	NUM
ejpam-1234	265	15	501	501	NUM
ejpam-1234	265	16	proof	proof	NOUN
ejpam-1234	265	17	.	.	PUNCT
ejpam-1234	266	1	the	the	DET
ejpam-1234	266	2	first	first	ADJ
ejpam-1234	266	3	statement	statement	NOUN
ejpam-1234	266	4	follows	follow	VERB
ejpam-1234	266	5	immediately	immediately	ADV
ejpam-1234	266	6	from	from	ADP
ejpam-1234	266	7	lemma	lemma	PROPN
ejpam-1234	266	8	2	2	NUM
ejpam-1234	266	9	.	.	PUNCT
ejpam-1234	267	1	for	for	ADP
ejpam-1234	267	2	the	the	DET
ejpam-1234	267	3	second	second	ADJ
ejpam-1234	267	4	claim	claim	NOUN
ejpam-1234	267	5	,	,	PUNCT
ejpam-1234	267	6	without	without	ADP
ejpam-1234	267	7	loss	loss	NOUN
ejpam-1234	267	8	of	of	ADP
ejpam-1234	267	9	generality	generality	NOUN
ejpam-1234	267	10	we	we	PRON
ejpam-1234	267	11	can	can	AUX
ejpam-1234	267	12	assume	assume	VERB
ejpam-1234	267	13	that	that	SCONJ
ejpam-1234	267	14	i	i	PRON
ejpam-1234	267	15	=	=	PUNCT
ejpam-1234	267	16	{	{	PUNCT
ejpam-1234	267	17	1	1	NUM
ejpam-1234	267	18	,	,	PUNCT
ejpam-1234	267	19	·	·	PUNCT
ejpam-1234	267	20	·	·	PUNCT
ejpam-1234	267	21	·	·	PUNCT
ejpam-1234	267	22	,	,	PUNCT
ejpam-1234	267	23	n	n	CCONJ
ejpam-1234	267	24	}	}	PUNCT
ejpam-1234	267	25	,	,	PUNCT
ejpam-1234	267	26	σ	σ	PROPN
ejpam-1234	267	27	=	=	PUNCT
ejpam-1234	267	28	(	(	PUNCT
ejpam-1234	267	29	12	12	NUM
ejpam-1234	267	30	·	·	PUNCT
ejpam-1234	267	31	·	·	PUNCT
ejpam-1234	267	32	·	·	PUNCT
ejpam-1234	267	33	n	n	CCONJ
ejpam-1234	267	34	)	)	PUNCT
ejpam-1234	267	35	and	and	CCONJ
ejpam-1234	267	36	εg	εg	ADV
ejpam-1234	268	1	=	=	PUNCT
ejpam-1234	268	2	(	(	PUNCT
ejpam-1234	268	3	g	g	PROPN
ejpam-1234	268	4	,	,	PUNCT
ejpam-1234	268	5	1	1	NUM
ejpam-1234	268	6	,	,	PUNCT
ejpam-1234	268	7	·	·	PUNCT
ejpam-1234	268	8	·	·	PUNCT
ejpam-1234	268	9	·	·	PUNCT
ejpam-1234	268	10	,	,	PUNCT
ejpam-1234	268	11	1	1	NUM
ejpam-1234	268	12	)	)	PUNCT
ejpam-1234	268	13	.	.	PUNCT
ejpam-1234	269	1	since	since	SCONJ
ejpam-1234	269	2	(	(	PUNCT
ejpam-1234	269	3	hεgσ	hεgσ	ADJ
ejpam-1234	269	4	)	)	PUNCT
ejpam-1234	269	5	−1	−1	NOUN
ejpam-1234	269	6	=	=	PUNCT
ejpam-1234	269	7	(	(	PUNCT
ejpam-1234	269	8	h−1	h−1	PROPN
ejpam-1234	269	9	2	2	NUM
ejpam-1234	269	10	,	,	PUNCT
ejpam-1234	269	11	·	·	PUNCT
ejpam-1234	269	12	·	·	PUNCT
ejpam-1234	269	13	·	·	PUNCT
ejpam-1234	269	14	,	,	PUNCT
ejpam-1234	269	15	h−1	h−1	PROPN
ejpam-1234	269	16	n	n	INTJ
ejpam-1234	269	17	,	,	PUNCT
ejpam-1234	269	18	g−1h−1	g−1h−1	NOUN
ejpam-1234	269	19	1	1	NUM
ejpam-1234	269	20	)	)	PUNCT
ejpam-1234	269	21	σ−1	σ−1	PROPN
ejpam-1234	269	22	,	,	PUNCT
ejpam-1234	269	23	we	we	PRON
ejpam-1234	269	24	have	have	VERB
ejpam-1234	269	25	m	m	PRON
ejpam-1234	269	26	·	·	PUNCT
ejpam-1234	269	27	(	(	PUNCT
ejpam-1234	269	28	hεgσ	hεgσ	ADJ
ejpam-1234	269	29	)	)	PUNCT
ejpam-1234	269	30	−1	−1	NOUN
ejpam-1234	269	31	·	·	PUNCT
ejpam-1234	269	32	m−1	m−1	PROPN
ejpam-1234	269	33	=	=	PUNCT
ejpam-1234	269	34	ε(hn···h2h1	ε(hn···h2h1	PROPN
ejpam-1234	269	35	g	g	NOUN
ejpam-1234	269	36	)	)	PUNCT
ejpam-1234	269	37	−1σ−1	−1σ−1	PROPN
ejpam-1234	269	38	for	for	ADP
ejpam-1234	269	39	some	some	DET
ejpam-1234	269	40	m	m	NOUN
ejpam-1234	269	41	∈	∈	PROPN
ejpam-1234	269	42	〈	〈	NOUN
ejpam-1234	269	43	h1	h1	PROPN
ejpam-1234	269	44	,	,	PUNCT
ejpam-1234	269	45	·	·	PUNCT
ejpam-1234	269	46	·	·	PUNCT
ejpam-1234	269	47	·	·	PUNCT
ejpam-1234	269	48	,	,	PUNCT
ejpam-1234	269	49	hn	hn	PROPN
ejpam-1234	269	50	,	,	PUNCT
ejpam-1234	269	51	g〉i	g〉i	PROPN
ejpam-1234	269	52	.	.	PUNCT
ejpam-1234	270	1	now	now	ADV
ejpam-1234	270	2	compute	compute	VERB
ejpam-1234	270	3	r(h	r(h	NOUN
ejpam-1234	270	4	,	,	PUNCT
ejpam-1234	270	5	εgσ	εgσ	NOUN
ejpam-1234	270	6	)	)	PUNCT
ejpam-1234	271	1	=	=	NOUN
ejpam-1234	271	2	t∆z	t∆z	NOUN
ejpam-1234	271	3	⊖	⊖	VERB
ejpam-1234	271	4	t	t	NOUN
ejpam-1234	271	5	x	x	SYM
ejpam-1234	271	6	i	i	PRON
ejpam-1234	271	7	|∆z	|∆z	PROPN
ejpam-1234	271	8	⊕∆∗	⊕∆∗	NOUN
ejpam-1234	271	9	�	�	PROPN
ejpam-1234	271	10	sh1	sh1	PROPN
ejpam-1234	271	11	|z	|z	PROPN
ejpam-1234	271	12	⊕	⊕	PROPN
ejpam-1234	271	13	·	·	PUNCT
ejpam-1234	271	14	·	·	PUNCT
ejpam-1234	271	15	·	·	PUNCT
ejpam-1234	272	1	⊕shn	⊕shn	NUM
ejpam-1234	272	2	|z	|z	PROPN
ejpam-1234	272	3	�	�	PROPN
ejpam-1234	272	4	⊕∆∗	⊕∆∗	PROPN
ejpam-1234	272	5	�	�	PROPN
ejpam-1234	272	6	sg|z	sg|z	NOUN
ejpam-1234	272	7	⊕	⊕	PROPN
ejpam-1234	272	8	n−	n−	NOUN
ejpam-1234	272	9	1	1	NUM
ejpam-1234	272	10	2	2	NUM
ejpam-1234	272	11	t	t	NOUN
ejpam-1234	272	12	x	x	SYM
ejpam-1234	272	13	|z	|z	PROPN
ejpam-1234	272	14	�	�	PROPN
ejpam-1234	272	15	⊕ρ∗m∆∗	⊕ρ∗m∆∗	PROPN
ejpam-1234	272	16	�	�	PROPN
ejpam-1234	272	17	s(hn···h2h1	s(hn···h2h1	NOUN
ejpam-1234	272	18	g	g	NOUN
ejpam-1234	272	19	)	)	PUNCT
ejpam-1234	272	20	−1	−1	NOUN
ejpam-1234	272	21	|z	|z	PROPN
ejpam-1234	272	22	⊕	⊕	PROPN
ejpam-1234	272	23	n−	n−	NOUN
ejpam-1234	272	24	1	1	NUM
ejpam-1234	272	25	2	2	NUM
ejpam-1234	272	26	t	t	NOUN
ejpam-1234	272	27	x	x	SYM
ejpam-1234	272	28	|z	|z	PROPN
ejpam-1234	272	29	�	�	PROPN
ejpam-1234	272	30	where	where	SCONJ
ejpam-1234	272	31	z	z	NOUN
ejpam-1234	272	32	:	:	PUNCT
ejpam-1234	272	33	=	=	SYM
ejpam-1234	272	34	x	x	SYM
ejpam-1234	272	35	g	g	PROPN
ejpam-1234	272	36	,	,	PUNCT
ejpam-1234	272	37	h1	h1	PROPN
ejpam-1234	272	38	,	,	PUNCT
ejpam-1234	272	39	·	·	PUNCT
ejpam-1234	272	40	·	·	PUNCT
ejpam-1234	272	41	·	·	PUNCT
ejpam-1234	272	42	,	,	PUNCT
ejpam-1234	272	43	hn	hn	PROPN
ejpam-1234	272	44	.	.	PUNCT
ejpam-1234	273	1	since	since	SCONJ
ejpam-1234	273	2	mi	mi	PROPN
ejpam-1234	273	3	fixes	fix	NOUN
ejpam-1234	273	4	z	z	NOUN
ejpam-1234	273	5	,	,	PUNCT
ejpam-1234	273	6	ρm|∆z	ρm|∆z	X
ejpam-1234	274	1	=	=	PUNCT
ejpam-1234	274	2	i	i	PROPN
ejpam-1234	274	3	d	d	PROPN
ejpam-1234	274	4	and	and	CCONJ
ejpam-1234	274	5	therefore	therefore	ADV
ejpam-1234	274	6	r(h	r(h	PROPN
ejpam-1234	274	7	,	,	PUNCT
ejpam-1234	274	8	εgσ	εgσ	NOUN
ejpam-1234	274	9	)	)	PUNCT
ejpam-1234	274	10	=	=	VERB
ejpam-1234	274	11	∆∗	∆∗	ADP
ejpam-1234	274	12	�	�	PROPN
ejpam-1234	274	13	t	t	PROPN
ejpam-1234	274	14	z	z	PROPN
ejpam-1234	274	15	⊖	⊖	SYM
ejpam-1234	274	16	t	t	PROPN
ejpam-1234	274	17	x	x	SYM
ejpam-1234	274	18	|z	|z	PROPN
ejpam-1234	274	19	⊕sh1	⊕sh1	PROPN
ejpam-1234	274	20	|z	|z	PROPN
ejpam-1234	274	21	⊕	⊕	PROPN
ejpam-1234	274	22	·	·	PUNCT
ejpam-1234	274	23	·	·	PUNCT
ejpam-1234	274	24	·	·	PUNCT
ejpam-1234	275	1	⊕shn	⊕shn	NUM
ejpam-1234	275	2	|z	|z	PROPN
ejpam-1234	275	3	⊕sg|z	⊕sg|z	PROPN
ejpam-1234	275	4	⊕s(hn···h2h1	⊕s(hn···h2h1	NOUN
ejpam-1234	275	5	g	g	NOUN
ejpam-1234	275	6	)	)	PUNCT
ejpam-1234	275	7	−1	−1	NOUN
ejpam-1234	275	8	|z	|z	PROPN
ejpam-1234	275	9	�	�	PROPN
ejpam-1234	275	10	=	=	SYM
ejpam-1234	275	11	∆∗r(hn	∆∗r(hn	PROPN
ejpam-1234	275	12	,	,	PUNCT
ejpam-1234	275	13	·	·	PUNCT
ejpam-1234	275	14	·	·	PUNCT
ejpam-1234	275	15	·	·	PUNCT
ejpam-1234	275	16	,	,	PUNCT
ejpam-1234	275	17	h1,g	h1,g	NOUN
ejpam-1234	275	18	)	)	PUNCT
ejpam-1234	275	19	.	.	PUNCT
ejpam-1234	276	1	the	the	DET
ejpam-1234	276	2	next	next	ADJ
ejpam-1234	276	3	lemma	lemma	PROPN
ejpam-1234	276	4	is	be	AUX
ejpam-1234	276	5	only	only	ADV
ejpam-1234	276	6	related	relate	VERB
ejpam-1234	276	7	to	to	PART
ejpam-1234	276	8	proposition	proposition	VERB
ejpam-1234	276	9	4	4	NUM
ejpam-1234	276	10	.	.	PUNCT
ejpam-1234	277	1	lemma	lemma	PROPN
ejpam-1234	277	2	4	4	X
ejpam-1234	277	3	.	.	PUNCT
ejpam-1234	278	1	let	let	VERB
ejpam-1234	278	2	σ	σ	PROPN
ejpam-1234	278	3	∈	∈	PROPN
ejpam-1234	278	4	σ	σ	NOUN
ejpam-1234	278	5	and	and	CCONJ
ejpam-1234	278	6	let	let	VERB
ejpam-1234	278	7	τ	τ	PROPN
ejpam-1234	278	8	=	=	PUNCT
ejpam-1234	278	9	(	(	PUNCT
ejpam-1234	278	10	i	i	PROPN
ejpam-1234	278	11	j	j	NOUN
ejpam-1234	278	12	)	)	PUNCT
ejpam-1234	278	13	be	be	VERB
ejpam-1234	278	14	a	a	DET
ejpam-1234	278	15	transposition	transposition	NOUN
ejpam-1234	278	16	.	.	PUNCT
ejpam-1234	279	1	suppose	suppose	VERB
ejpam-1234	279	2	that	that	SCONJ
ejpam-1234	279	3	σ	σ	PROPN
ejpam-1234	279	4	,	,	PUNCT
ejpam-1234	279	5	τ	τ	PROPN
ejpam-1234	279	6	are	be	AUX
ejpam-1234	279	7	transversal	transversal	ADJ
ejpam-1234	279	8	,	,	PUNCT
ejpam-1234	279	9	i.e.	i.e.	X
ejpam-1234	279	10	|σ|+	|σ|+	ADJ
ejpam-1234	279	11	|τ|=	|τ|=	PROPN
ejpam-1234	279	12	|στ|	|στ|	PROPN
ejpam-1234	279	13	and	and	CCONJ
ejpam-1234	279	14	let	let	VERB
ejpam-1234	279	15	i	i	PRON
ejpam-1234	279	16	∈	∈	VERB
ejpam-1234	279	17	a	a	PRON
ejpam-1234	279	18	and	and	CCONJ
ejpam-1234	279	19	j	j	PROPN
ejpam-1234	279	20	∈	∈	PROPN
ejpam-1234	279	21	b	b	PROPN
ejpam-1234	279	22	for	for	ADP
ejpam-1234	279	23	a	a	PRON
ejpam-1234	279	24	,	,	PUNCT
ejpam-1234	279	25	b	b	X
ejpam-1234	279	26	∈	∈	NOUN
ejpam-1234	279	27	iσ	iσ	VERB
ejpam-1234	279	28	.	.	PUNCT
ejpam-1234	280	1	then	then	ADV
ejpam-1234	280	2	(	(	PUNCT
ejpam-1234	280	3	x	x	X
ejpam-1234	280	4	i)σ	i)σ	NOUN
ejpam-1234	280	5	∩	∩	NOUN
ejpam-1234	280	6	(	(	PUNCT
ejpam-1234	280	7	x	x	SYM
ejpam-1234	280	8	i)gτg−1	i)gτg−1	PROPN
ejpam-1234	280	9	=	=	SYM
ejpam-1234	280	10			PROPN
ejpam-1234	280	11			NOUN
ejpam-1234	280	12			NOUN
ejpam-1234	280	13	∏	∏	PROPN
ejpam-1234	280	14	c∈iσ\{a	c∈iσ\{a	NOUN
ejpam-1234	280	15	,	,	PUNCT
ejpam-1234	280	16	b	b	NOUN
ejpam-1234	280	17	}	}	PUNCT
ejpam-1234	280	18	∆c	∆c	NOUN
ejpam-1234	280	19	x	x	SYM
ejpam-1234	280	20			NOUN
ejpam-1234	280	21			NOUN
ejpam-1234	280	22			PUNCT
ejpam-1234	281	1	×ρg	×ρg	INTJ
ejpam-1234	281	2	′	′	NUM
ejpam-1234	281	3	�	�	PROPN
ejpam-1234	281	4	∆a∪b	∆a∪b	PROPN
ejpam-1234	281	5	x	x	PROPN
ejpam-1234	281	6	�	�	PROPN
ejpam-1234	281	7	where	where	SCONJ
ejpam-1234	281	8	g′	g′	NOUN
ejpam-1234	281	9	∈	∈	PROPN
ejpam-1234	281	10	ga∪b	ga∪b	PROPN
ejpam-1234	281	11	is	be	AUX
ejpam-1234	281	12	given	give	VERB
ejpam-1234	281	13	by	by	ADP
ejpam-1234	281	14	g′	g′	NOUN
ejpam-1234	281	15	l	l	NOUN
ejpam-1234	282	1	=	=	PUNCT
ejpam-1234	282	2	gi	gi	INTJ
ejpam-1234	282	3	if	if	SCONJ
ejpam-1234	282	4	l	l	PROPN
ejpam-1234	282	5	∈	∈	PROPN
ejpam-1234	282	6	a	a	PRON
ejpam-1234	282	7	and	and	CCONJ
ejpam-1234	282	8	g′	g′	NOUN
ejpam-1234	282	9	l	l	NOUN
ejpam-1234	283	1	=	=	PUNCT
ejpam-1234	284	1	g	g	PROPN
ejpam-1234	284	2	j	j	PROPN
ejpam-1234	284	3	if	if	SCONJ
ejpam-1234	284	4	l	l	PROPN
ejpam-1234	284	5	∈	∈	PROPN
ejpam-1234	284	6	b.	b.	PROPN
ejpam-1234	285	1	moreover	moreover	ADV
ejpam-1234	285	2	,	,	PUNCT
ejpam-1234	285	3	rkr(σ	rkr(σ	PROPN
ejpam-1234	285	4	,	,	PUNCT
ejpam-1234	285	5	gτg−1	gτg−1	PROPN
ejpam-1234	285	6	)	)	PUNCT
ejpam-1234	285	7	=	=	SYM
ejpam-1234	285	8	0	0	NUM
ejpam-1234	285	9	and	and	CCONJ
ejpam-1234	285	10	so	so	ADV
ejpam-1234	285	11	c(σ	c(σ	PROPN
ejpam-1234	285	12	,	,	PUNCT
ejpam-1234	285	13	gτg−1	gτg−1	PROPN
ejpam-1234	285	14	)	)	PUNCT
ejpam-1234	285	15	=	=	SYM
ejpam-1234	285	16	1	1	X
ejpam-1234	285	17	.	.	PUNCT
ejpam-1234	285	18	proof	proof	NOUN
ejpam-1234	285	19	.	.	PUNCT
ejpam-1234	286	1	the	the	DET
ejpam-1234	286	2	first	first	ADJ
ejpam-1234	286	3	statement	statement	NOUN
ejpam-1234	286	4	is	be	AUX
ejpam-1234	286	5	straightforward	straightforward	ADJ
ejpam-1234	286	6	.	.	PUNCT
ejpam-1234	287	1	without	without	ADP
ejpam-1234	287	2	loss	loss	NOUN
ejpam-1234	287	3	of	of	ADP
ejpam-1234	287	4	generality	generality	NOUN
ejpam-1234	287	5	,	,	PUNCT
ejpam-1234	287	6	we	we	PRON
ejpam-1234	287	7	can	can	AUX
ejpam-1234	287	8	assume	assume	VERB
ejpam-1234	287	9	that	that	SCONJ
ejpam-1234	287	10	iσ	iσ	VERB
ejpam-1234	287	11	,	,	PUNCT
ejpam-1234	287	12	τ	τ	PROPN
ejpam-1234	287	13	=	=	PUNCT
ejpam-1234	287	14	{	{	PUNCT
ejpam-1234	287	15	i	i	NOUN
ejpam-1234	287	16	}	}	PUNCT
ejpam-1234	287	17	.	.	PUNCT
ejpam-1234	288	1	also	also	ADV
ejpam-1234	288	2	we	we	PRON
ejpam-1234	288	3	can	can	AUX
ejpam-1234	288	4	assume	assume	VERB
ejpam-1234	288	5	that	that	SCONJ
ejpam-1234	288	6	g	g	PROPN
ejpam-1234	288	7	=	=	SYM
ejpam-1234	288	8	g′	g′	NOUN
ejpam-1234	288	9	,	,	PUNCT
ejpam-1234	288	10	since	since	SCONJ
ejpam-1234	288	11	gτg−1	gτg−1	PROPN
ejpam-1234	288	12	=	=	SYM
ejpam-1234	288	13	g′τ(g′)−1	g′τ(g′)−1	NOUN
ejpam-1234	288	14	.	.	PUNCT
ejpam-1234	289	1	since	since	SCONJ
ejpam-1234	289	2	gσg−1	gσg−1	PROPN
ejpam-1234	289	3	=	=	SYM
ejpam-1234	289	4	σ	σ	PROPN
ejpam-1234	289	5	,	,	PUNCT
ejpam-1234	289	6	we	we	PRON
ejpam-1234	289	7	have	have	VERB
ejpam-1234	289	8	r(σ	r(σ	PROPN
ejpam-1234	289	9	,	,	PUNCT
ejpam-1234	289	10	gτg−1	gτg−1	PROPN
ejpam-1234	289	11	)	)	PUNCT
ejpam-1234	289	12	=	=	PUNCT
ejpam-1234	289	13	ρg∗r(σ	ρg∗r(σ	PROPN
ejpam-1234	289	14	,	,	PUNCT
ejpam-1234	289	15	τ	τ	X
ejpam-1234	289	16	)	)	PUNCT
ejpam-1234	289	17	.	.	PUNCT
ejpam-1234	290	1	however	however	ADV
ejpam-1234	290	2	,	,	PUNCT
ejpam-1234	290	3	from	from	ADP
ejpam-1234	290	4	corollary	corollary	ADJ
ejpam-1234	290	5	1	1	NUM
ejpam-1234	290	6	we	we	PRON
ejpam-1234	290	7	can	can	AUX
ejpam-1234	290	8	compute	compute	VERB
ejpam-1234	290	9	that	that	DET
ejpam-1234	290	10	rkr(σ	rkr(σ	PROPN
ejpam-1234	290	11	,	,	PUNCT
ejpam-1234	290	12	τ	τ	X
ejpam-1234	290	13	)	)	PUNCT
ejpam-1234	290	14	=	=	SYM
ejpam-1234	290	15	0	0	NUM
ejpam-1234	290	16	and	and	CCONJ
ejpam-1234	290	17	thus	thus	ADV
ejpam-1234	290	18	c(σ	c(σ	PROPN
ejpam-1234	290	19	,	,	PUNCT
ejpam-1234	290	20	gτg−1)=1	gτg−1)=1	PROPN
ejpam-1234	290	21	.	.	PUNCT
ejpam-1234	291	1	remark	remark	PROPN
ejpam-1234	291	2	5	5	NUM
ejpam-1234	291	3	.	.	PUNCT
ejpam-1234	292	1	if	if	SCONJ
ejpam-1234	292	2	g	g	PROPN
ejpam-1234	292	3	is	be	AUX
ejpam-1234	292	4	abelian	abelian	ADJ
ejpam-1234	292	5	,	,	PUNCT
ejpam-1234	292	6	the	the	DET
ejpam-1234	292	7	general	general	ADJ
ejpam-1234	292	8	computation	computation	NOUN
ejpam-1234	292	9	of	of	ADP
ejpam-1234	292	10	the	the	DET
ejpam-1234	292	11	obstruction	obstruction	NOUN
ejpam-1234	292	12	bundle	bundle	NOUN
ejpam-1234	292	13	is	be	AUX
ejpam-1234	292	14	available	available	ADJ
ejpam-1234	292	15	in	in	ADP
ejpam-1234	292	16	[	[	X
ejpam-1234	292	17	17	17	NUM
ejpam-1234	292	18	]	]	SYM
ejpam-1234	292	19	.	.	PUNCT
ejpam-1234	293	1	4	4	X
ejpam-1234	293	2	.	.	X
ejpam-1234	293	3	lehn	lehn	NOUN
ejpam-1234	293	4	-	-	PUNCT
ejpam-1234	293	5	sorger	sorger	NOUN
ejpam-1234	293	6	’s	’s	PART
ejpam-1234	293	7	algebras	algebras	NOUN
ejpam-1234	293	8	and	and	CCONJ
ejpam-1234	293	9	g	g	NOUN
ejpam-1234	293	10	i	i	PRON
ejpam-1234	293	11	-invariants	-invariant	NOUN
ejpam-1234	293	12	of	of	ADP
ejpam-1234	293	13	stringy	stringy	ADJ
ejpam-1234	293	14	cohomology	cohomology	NOUN
ejpam-1234	293	15	in	in	ADP
ejpam-1234	293	16	this	this	DET
ejpam-1234	293	17	section	section	NOUN
ejpam-1234	293	18	,	,	PUNCT
ejpam-1234	293	19	we	we	PRON
ejpam-1234	293	20	prove	prove	VERB
ejpam-1234	293	21	our	our	PRON
ejpam-1234	293	22	main	main	ADJ
ejpam-1234	293	23	theorem	theorem	NOUN
ejpam-1234	293	24	.	.	PUNCT
ejpam-1234	294	1	since	since	SCONJ
ejpam-1234	294	2	our	our	PRON
ejpam-1234	294	3	g	g	NOUN
ejpam-1234	294	4	-	-	PUNCT
ejpam-1234	294	5	frobenius	frobenius	NOUN
ejpam-1234	294	6	algebras	algebra	NOUN
ejpam-1234	294	7	are	be	AUX
ejpam-1234	294	8	special	special	ADJ
ejpam-1234	294	9	g	g	NOUN
ejpam-1234	294	10	-	-	PUNCT
ejpam-1234	294	11	frobenius	frobenius	NOUN
ejpam-1234	294	12	algebras	algebra	NOUN
ejpam-1234	294	13	,	,	PUNCT
ejpam-1234	294	14	we	we	PRON
ejpam-1234	294	15	can	can	AUX
ejpam-1234	294	16	use	use	VERB
ejpam-1234	294	17	the	the	DET
ejpam-1234	294	18	structure	structure	NOUN
ejpam-1234	294	19	theorems	theorem	NOUN
ejpam-1234	294	20	in	in	ADP
ejpam-1234	294	21	[	[	X
ejpam-1234	294	22	12	12	NUM
ejpam-1234	294	23	]	]	PUNCT
ejpam-1234	294	24	and	and	CCONJ
ejpam-1234	294	25	[	[	X
ejpam-1234	294	26	13	13	NUM
ejpam-1234	294	27	]	]	PUNCT
ejpam-1234	294	28	.	.	PUNCT
ejpam-1234	295	1	for	for	ADP
ejpam-1234	295	2	the	the	DET
ejpam-1234	295	3	summary	summary	NOUN
ejpam-1234	295	4	of	of	ADP
ejpam-1234	295	5	definitions	definition	NOUN
ejpam-1234	295	6	and	and	CCONJ
ejpam-1234	295	7	theorems	theorem	NOUN
ejpam-1234	295	8	,	,	PUNCT
ejpam-1234	295	9	please	please	INTJ
ejpam-1234	295	10	see	see	VERB
ejpam-1234	295	11	the	the	DET
ejpam-1234	295	12	appendix	appendix	NOUN
ejpam-1234	295	13	.	.	PUNCT
ejpam-1234	296	1	let	let	VERB
ejpam-1234	296	2	h	h	NOUN
ejpam-1234	296	3	(	(	PUNCT
ejpam-1234	296	4	x	x	X
ejpam-1234	296	5	i	i	PRON
ejpam-1234	296	6	,	,	PUNCT
ejpam-1234	296	7	gi	gi	VERB
ejpam-1234	296	8	⋊	⋊	PROPN
ejpam-1234	296	9	σi	σi	NOUN
ejpam-1234	296	10	)	)	PUNCT
ejpam-1234	296	11	be	be	AUX
ejpam-1234	296	12	the	the	DET
ejpam-1234	296	13	stringy	stringy	ADJ
ejpam-1234	296	14	cohomology	cohomology	NOUN
ejpam-1234	296	15	of	of	ADP
ejpam-1234	296	16	the	the	DET
ejpam-1234	296	17	(	(	PUNCT
ejpam-1234	296	18	g	g	NOUN
ejpam-1234	296	19	i	i	PRON
ejpam-1234	296	20	⋊σi)-space	⋊σi)-space	VERB
ejpam-1234	296	21	x	x	VERB
ejpam-1234	297	1	i	i	PRON
ejpam-1234	297	2	reviewed	review	VERB
ejpam-1234	297	3	in	in	ADP
ejpam-1234	297	4	section	section	NOUN
ejpam-1234	297	5	2.2	2.2	NUM
ejpam-1234	297	6	and	and	CCONJ
ejpam-1234	297	7	let	let	VERB
ejpam-1234	297	8	h∗	h∗	NOUN
ejpam-1234	297	9	or	or	CCONJ
ejpam-1234	297	10	b	b	PROPN
ejpam-1234	297	11	(	(	PUNCT
ejpam-1234	297	12	[	[	X
ejpam-1234	297	13	x	x	X
ejpam-1234	297	14	/	/	SYM
ejpam-1234	297	15	g]){σi	g]){σi	NOUN
ejpam-1234	297	16	}	}	PUNCT
ejpam-1234	297	17	be	be	AUX
ejpam-1234	297	18	the	the	DET
ejpam-1234	297	19	lehn	lehn	ADJ
ejpam-1234	297	20	-	-	PUNCT
ejpam-1234	297	21	sorger	sorger	NOUN
ejpam-1234	297	22	algebra	algebra	NOUN
ejpam-1234	297	23	associated	associate	VERB
ejpam-1234	297	24	to	to	ADP
ejpam-1234	297	25	h∗	h∗	PROPN
ejpam-1234	297	26	or	or	CCONJ
ejpam-1234	297	27	b	b	PROPN
ejpam-1234	297	28	(	(	PUNCT
ejpam-1234	297	29	[	[	X
ejpam-1234	297	30	x	x	X
ejpam-1234	297	31	/	/	SYM
ejpam-1234	297	32	g	g	NOUN
ejpam-1234	297	33	]	]	PUNCT
ejpam-1234	297	34	)	)	PUNCT
ejpam-1234	297	35	reviewed	review	VERB
ejpam-1234	297	36	in	in	ADP
ejpam-1234	297	37	section	section	NOUN
ejpam-1234	297	38	5	5	NUM
ejpam-1234	297	39	.	.	PUNCT
ejpam-1234	297	40	by	by	ADP
ejpam-1234	297	41	proposition	proposition	NOUN
ejpam-1234	297	42	1	1	NUM
ejpam-1234	297	43	,	,	PUNCT
ejpam-1234	297	44	the	the	DET
ejpam-1234	297	45	gi	gi	ADJ
ejpam-1234	297	46	-invariants	-invariant	NOUN
ejpam-1234	297	47	of	of	ADP
ejpam-1234	297	48	h	h	NOUN
ejpam-1234	297	49	(	(	PUNCT
ejpam-1234	297	50	x	x	PROPN
ejpam-1234	297	51	i	i	PRON
ejpam-1234	297	52	,	,	PUNCT
ejpam-1234	297	53	gi	gi	VERB
ejpam-1234	297	54	⋊σi	⋊σi	NOUN
ejpam-1234	297	55	)	)	PUNCT
ejpam-1234	297	56	is	be	AUX
ejpam-1234	297	57	h	h	NOUN
ejpam-1234	297	58	(	(	PUNCT
ejpam-1234	297	59	x	x	PROPN
ejpam-1234	297	60	i	i	PRON
ejpam-1234	297	61	,	,	PUNCT
ejpam-1234	297	62	gi	gi	VERB
ejpam-1234	297	63	⋊σi	⋊σi	NOUN
ejpam-1234	297	64	)	)	PUNCT
ejpam-1234	297	65	gi	gi	NOUN
ejpam-1234	298	1	=	=	PUNCT
ejpam-1234	298	2	⊕	⊕	PROPN
ejpam-1234	298	3	σ∈σi	σ∈σi	PROPN
ejpam-1234	298	4	⊕	⊕	PROPN
ejpam-1234	298	5	ḡ∈ḡiσ	ḡ∈ḡiσ	PROPN
ejpam-1234	298	6	hḡ,σ	hḡ,σ	PROPN
ejpam-1234	298	7	,	,	PUNCT
ejpam-1234	298	8	hḡ,σ	hḡ,σ	VERB
ejpam-1234	298	9	:	:	PUNCT
ejpam-1234	298	10	=	=	SYM
ejpam-1234	298	11			PROPN
ejpam-1234	298	12			NOUN
ejpam-1234	298	13			NOUN
ejpam-1234	298	14	⊕	⊕	NOUN
ejpam-1234	298	15	gσ∈ogσ	gσ∈ogσ	X
ejpam-1234	298	16	h∗((x	h∗((x	VERB
ejpam-1234	298	17	i)gσ	i)gσ	PROPN
ejpam-1234	298	18	)	)	PUNCT
ejpam-1234	298	19			NOUN
ejpam-1234	298	20			NOUN
ejpam-1234	298	21			PUNCT
ejpam-1234	299	1	gi	gi	X
ejpam-1234	299	2	.	.	PUNCT
ejpam-1234	300	1	tomoo	tomoo	VERB
ejpam-1234	300	2	matsumura	matsumura	ADJ
ejpam-1234	300	3	/	/	SYM
ejpam-1234	300	4	eur	eur	PROPN
ejpam-1234	300	5	.	.	PUNCT
ejpam-1234	301	1	j.	j.	PROPN
ejpam-1234	301	2	pure	pure	PROPN
ejpam-1234	301	3	appl	appl	PROPN
ejpam-1234	301	4	.	.	PROPN
ejpam-1234	301	5	math	math	PROPN
ejpam-1234	301	6	,	,	PUNCT
ejpam-1234	301	7	5	5	NUM
ejpam-1234	301	8	(	(	PUNCT
ejpam-1234	301	9	2012	2012	NUM
ejpam-1234	301	10	)	)	PUNCT
ejpam-1234	301	11	,	,	PUNCT
ejpam-1234	301	12	492	492	NUM
ejpam-1234	301	13	-	-	SYM
ejpam-1234	301	14	510	510	NUM
ejpam-1234	301	15	502	502	NUM
ejpam-1234	301	16	on	on	ADP
ejpam-1234	301	17	the	the	DET
ejpam-1234	301	18	other	other	ADJ
ejpam-1234	301	19	hand	hand	NOUN
ejpam-1234	301	20	,	,	PUNCT
ejpam-1234	301	21	the	the	DET
ejpam-1234	301	22	lehn	lehn	NOUN
ejpam-1234	301	23	-	-	PUNCT
ejpam-1234	301	24	sorger	sorger	NOUN
ejpam-1234	301	25	algebra	algebra	NOUN
ejpam-1234	301	26	associated	associate	VERB
ejpam-1234	301	27	to	to	ADP
ejpam-1234	301	28	h∗	h∗	PROPN
ejpam-1234	301	29	or	or	CCONJ
ejpam-1234	301	30	b	b	PROPN
ejpam-1234	301	31	(	(	PUNCT
ejpam-1234	301	32	[	[	X
ejpam-1234	301	33	x	x	X
ejpam-1234	301	34	/	/	SYM
ejpam-1234	301	35	g	g	NOUN
ejpam-1234	301	36	]	]	PUNCT
ejpam-1234	301	37	)	)	PUNCT
ejpam-1234	301	38	is	be	AUX
ejpam-1234	301	39	h∗or	h∗or	NUM
ejpam-1234	301	40	b([x	b([x	ADJ
ejpam-1234	301	41	/	/	SYM
ejpam-1234	301	42	g]){σi}=	g]){σi}=	PROPN
ejpam-1234	301	43	⊕	⊕	PROPN
ejpam-1234	301	44	σ∈σi	σ∈σi	PROPN
ejpam-1234	301	45	⊕	⊕	PROPN
ejpam-1234	301	46	ḡ∈ḡiσ	ḡ∈ḡiσ	PROPN
ejpam-1234	301	47	aḡ,σ	aḡ,σ	PROPN
ejpam-1234	301	48	,	,	PUNCT
ejpam-1234	301	49	aḡ,σ	aḡ,σ	PUNCT
ejpam-1234	301	50	:	:	PUNCT
ejpam-1234	301	51	=	=	SYM
ejpam-1234	301	52			PROPN
ejpam-1234	301	53			NOUN
ejpam-1234	301	54			NOUN
ejpam-1234	301	55	⊕	⊕	PROPN
ejpam-1234	301	56	g′∈ḡ	g′∈ḡ	PROPN
ejpam-1234	301	57	h∗((x	h∗((x	VERB
ejpam-1234	301	58	iσ)g	iσ)g	PROPN
ejpam-1234	301	59	′	′	NOUN
ejpam-1234	301	60	)	)	PUNCT
ejpam-1234	302	1			PROPN
ejpam-1234	302	2			NOUN
ejpam-1234	302	3			PUNCT
ejpam-1234	303	1	giσ	giσ	PROPN
ejpam-1234	303	2	.	.	PUNCT
ejpam-1234	304	1	proposition	proposition	NOUN
ejpam-1234	304	2	2	2	NUM
ejpam-1234	304	3	.	.	PUNCT
ejpam-1234	305	1	there	there	PRON
ejpam-1234	305	2	is	be	VERB
ejpam-1234	305	3	a	a	DET
ejpam-1234	305	4	canonical	canonical	ADJ
ejpam-1234	305	5	isomorphism	isomorphism	NOUN
ejpam-1234	305	6	of	of	ADP
ejpam-1234	305	7	graded	grade	VERB
ejpam-1234	305	8	σi	σi	PRON
ejpam-1234	305	9	-graded	-grade	VERB
ejpam-1234	305	10	σi	σi	PRON
ejpam-1234	305	11	-modules	-module	NOUN
ejpam-1234	305	12	which	which	PRON
ejpam-1234	305	13	preserves	preserve	VERB
ejpam-1234	305	14	the	the	DET
ejpam-1234	305	15	metric	metric	NOUN
ejpam-1234	305	16	:	:	PUNCT
ejpam-1234	305	17	φ	φ	PROPN
ejpam-1234	305	18	:	:	PUNCT
ejpam-1234	305	19	h∗or	h∗or	NUM
ejpam-1234	305	20	b([x	b([x	ADJ
ejpam-1234	305	21	/	/	SYM
ejpam-1234	305	22	g]){σi	g]){σi	NOUN
ejpam-1234	305	23	}	}	PUNCT
ejpam-1234	305	24	≃	≃	NOUN
ejpam-1234	305	25	−→h	−→h	PROPN
ejpam-1234	305	26	(	(	PUNCT
ejpam-1234	305	27	x	x	X
ejpam-1234	305	28	i	i	PRON
ejpam-1234	305	29	,	,	PUNCT
ejpam-1234	305	30	gi	gi	VERB
ejpam-1234	305	31	⋊σi	⋊σi	NOUN
ejpam-1234	305	32	)	)	PUNCT
ejpam-1234	305	33	gi	gi	NOUN
ejpam-1234	305	34	.	.	PUNCT
ejpam-1234	306	1	proof	proof	NOUN
ejpam-1234	306	2	.	.	PUNCT
ejpam-1234	307	1	choose	choose	VERB
ejpam-1234	307	2	{	{	PUNCT
ejpam-1234	307	3	ia	ia	NOUN
ejpam-1234	307	4	∈	∈	PROPN
ejpam-1234	307	5	a}a∈iσ	a}a∈iσ	ADV
ejpam-1234	307	6	.	.	PUNCT
ejpam-1234	308	1	consider	consider	VERB
ejpam-1234	308	2	the	the	DET
ejpam-1234	308	3	following	follow	VERB
ejpam-1234	308	4	isomorphisms	isomorphism	NOUN
ejpam-1234	308	5	:	:	PUNCT
ejpam-1234	308	6	h∗((x	h∗((x	NOUN
ejpam-1234	308	7	iσ)g)zgiσ	iσ)g)zgiσ	ADJ
ejpam-1234	308	8	(	(	PUNCT
ejpam-1234	308	9	g	g	NOUN
ejpam-1234	308	10	)	)	PUNCT
ejpam-1234	308	11	∼=aḡ,σ	∼=aḡ,σ	VERB
ejpam-1234	308	12	,	,	PUNCT
ejpam-1234	308	13	x	x	X
ejpam-1234	308	14	7→	7→	X
ejpam-1234	308	15	lx	lx	ADP
ejpam-1234	308	16	:	:	PUNCT
ejpam-1234	308	17	=	=	SYM
ejpam-1234	308	18	∑	∑	PUNCT
ejpam-1234	308	19	f∈giσ	f∈giσ	PROPN
ejpam-1234	308	20	ρf∗(x	ρf∗(x	NOUN
ejpam-1234	308	21	)	)	PUNCT
ejpam-1234	308	22	;	;	PUNCT
ejpam-1234	308	23	h∗((x	h∗((x	VERB
ejpam-1234	308	24	i)εgσ)zgi	i)εgσ)zgi	PROPN
ejpam-1234	308	25	(	(	PUNCT
ejpam-1234	308	26	εgσ	εgσ	NOUN
ejpam-1234	308	27	)	)	PUNCT
ejpam-1234	308	28	∼=hḡ,σ	∼=hḡ,σ	NOUN
ejpam-1234	308	29	,	,	PUNCT
ejpam-1234	308	30	v	v	ADP
ejpam-1234	308	31	7→	7→	NUM
ejpam-1234	308	32	fv	fv	X
ejpam-1234	308	33	:	:	PUNCT
ejpam-1234	308	34	=	=	SYM
ejpam-1234	308	35	∑	∑	PUNCT
ejpam-1234	308	36	f	f	PROPN
ejpam-1234	308	37	∈gi	∈gi	NOUN
ejpam-1234	308	38	ρf	ρf	PROPN
ejpam-1234	308	39	∗(v	∗(v	PROPN
ejpam-1234	308	40	)	)	PUNCT
ejpam-1234	308	41	.	.	PUNCT
ejpam-1234	309	1	from	from	ADP
ejpam-1234	309	2	lemma	lemma	PROPN
ejpam-1234	309	3	2	2	NUM
ejpam-1234	309	4	and	and	CCONJ
ejpam-1234	309	5	remark	remark	NOUN
ejpam-1234	309	6	4	4	NUM
ejpam-1234	309	7	,	,	PUNCT
ejpam-1234	309	8	we	we	PRON
ejpam-1234	309	9	also	also	ADV
ejpam-1234	309	10	have	have	AUX
ejpam-1234	309	11	zgiσ	zgiσ	PROPN
ejpam-1234	309	12	(	(	PUNCT
ejpam-1234	309	13	g	g	NOUN
ejpam-1234	309	14	)	)	PUNCT
ejpam-1234	309	15	=	=	SYM
ejpam-1234	309	16	∏	∏	NUM
ejpam-1234	309	17	a∈iσ	a∈iσ	NOUN
ejpam-1234	309	18	zg(ga	zg(ga	NOUN
ejpam-1234	309	19	)	)	PUNCT
ejpam-1234	309	20	∼=	∼=	PROPN
ejpam-1234	309	21	zgi	zgi	ADJ
ejpam-1234	309	22	(	(	PUNCT
ejpam-1234	309	23	εgσ	εgσ	NOUN
ejpam-1234	309	24	)	)	PUNCT
ejpam-1234	309	25	and	and	CCONJ
ejpam-1234	309	26	(	(	PUNCT
ejpam-1234	309	27	x	x	X
ejpam-1234	309	28	iσ)g	iσ)g	PROPN
ejpam-1234	309	29	=	=	SYM
ejpam-1234	309	30	∏	∏	PROPN
ejpam-1234	309	31	a∈iσ	a∈iσ	NOUN
ejpam-1234	309	32	x	x	PROPN
ejpam-1234	309	33	ga	ga	PROPN
ejpam-1234	309	34	∼=	∼=	PROPN
ejpam-1234	309	35	(	(	PUNCT
ejpam-1234	309	36	x	x	SYM
ejpam-1234	309	37	i)εgσ	i)εgσ	PROPN
ejpam-1234	309	38	,	,	PUNCT
ejpam-1234	309	39	which	which	PRON
ejpam-1234	309	40	imply	imply	VERB
ejpam-1234	309	41	h∗((x	h∗((x	VERB
ejpam-1234	309	42	iσ)g)zgiσ	iσ)g)zgiσ	ADJ
ejpam-1234	309	43	(	(	PUNCT
ejpam-1234	309	44	g	g	NOUN
ejpam-1234	309	45	)	)	PUNCT
ejpam-1234	309	46	∼=	∼=	PROPN
ejpam-1234	309	47	h∗((x	h∗((x	NOUN
ejpam-1234	309	48	i)εgσ)zgi	i)εgσ)zgi	ADJ
ejpam-1234	309	49	(	(	PUNCT
ejpam-1234	309	50	εgσ	εgσ	NOUN
ejpam-1234	309	51	)	)	PUNCT
ejpam-1234	309	52	where	where	SCONJ
ejpam-1234	309	53	(	(	PUNCT
ejpam-1234	309	54	x	x	SYM
ejpam-1234	309	55	7→	7→	NUM
ejpam-1234	309	56	∆x	∆x	NUM
ejpam-1234	309	57	)	)	PUNCT
ejpam-1234	309	58	.	.	PUNCT
ejpam-1234	310	1	define	define	VERB
ejpam-1234	310	2	φ	φ	NUM
ejpam-1234	310	3	by	by	ADP
ejpam-1234	310	4	φ(lx	φ(lx	NOUN
ejpam-1234	310	5	)	)	PUNCT
ejpam-1234	310	6	:	:	PUNCT
ejpam-1234	310	7	=	=	NOUN
ejpam-1234	310	8	f∆x	f∆x	PROPN
ejpam-1234	310	9	.	.	PUNCT
ejpam-1234	311	1	because	because	SCONJ
ejpam-1234	311	2	of	of	ADP
ejpam-1234	311	3	the	the	DET
ejpam-1234	311	4	summations	summation	NOUN
ejpam-1234	311	5	over	over	ADP
ejpam-1234	311	6	g	g	PROPN
ejpam-1234	311	7	iσ	iσ	ADV
ejpam-1234	311	8	and	and	CCONJ
ejpam-1234	311	9	gi	gi	INTJ
ejpam-1234	311	10	,	,	PUNCT
ejpam-1234	311	11	φ	φ	PROPN
ejpam-1234	311	12	is	be	AUX
ejpam-1234	311	13	independent	independent	ADJ
ejpam-1234	311	14	of	of	ADP
ejpam-1234	311	15	the	the	DET
ejpam-1234	311	16	choices	choice	NOUN
ejpam-1234	311	17	we	we	PRON
ejpam-1234	311	18	made	make	VERB
ejpam-1234	311	19	.	.	PUNCT
ejpam-1234	312	1	the	the	DET
ejpam-1234	312	2	σi	σi	PROPN
ejpam-1234	312	3	-equivariance	-equivariance	NOUN
ejpam-1234	312	4	is	be	AUX
ejpam-1234	312	5	clear	clear	ADJ
ejpam-1234	312	6	from	from	ADP
ejpam-1234	312	7	the	the	DET
ejpam-1234	312	8	commutative	commutative	ADJ
ejpam-1234	312	9	diagram	diagram	NOUN
ejpam-1234	312	10	∏	∏	PROPN
ejpam-1234	312	11	a∈iσ	a∈iσ	NOUN
ejpam-1234	312	12	x	x	PROPN
ejpam-1234	312	13	ga	ga	PROPN
ejpam-1234	312	14	∼=	∼=	PROPN
ejpam-1234	312	15	�	�	PROPN
ejpam-1234	312	16	�	�	PROPN
ejpam-1234	312	17	∼=	∼=	PART
ejpam-1234	312	18	//	//	NUM
ejpam-1234	312	19	∏	∏	PROPN
ejpam-1234	312	20	a∈iσ	a∈iσ	NOUN
ejpam-1234	312	21	∆a	∆a	PROPN
ejpam-1234	312	22	xga	xga	PROPN
ejpam-1234	312	23	∼=	∼=	PROPN
ejpam-1234	312	24	�	�	PROPN
ejpam-1234	312	25	�	�	PROPN
ejpam-1234	312	26	∏	∏	PROPN
ejpam-1234	312	27	τ(a)∈i	τ(a)∈i	NUM
ejpam-1234	312	28	τστ−1	τστ−1	NOUN
ejpam-1234	312	29	x	x	SYM
ejpam-1234	312	30	gτ(a	gτ(a	NOUN
ejpam-1234	312	31	)	)	PUNCT
ejpam-1234	312	32	∼=	∼=	PROPN
ejpam-1234	312	33	//	//	PUNCT
ejpam-1234	312	34	∏	∏	PROPN
ejpam-1234	312	35	τ(a)∈i	τ(a)∈i	NUM
ejpam-1234	312	36	τστ−1	τστ−1	X
ejpam-1234	312	37	∆	∆	PROPN
ejpam-1234	312	38	τ(a	τ(a	NOUN
ejpam-1234	312	39	)	)	PUNCT
ejpam-1234	312	40	x	x	SYM
ejpam-1234	312	41	gτ(a	gτ(a	NOUN
ejpam-1234	312	42	)	)	PUNCT
ejpam-1234	312	43	it	it	PRON
ejpam-1234	312	44	follows	follow	VERB
ejpam-1234	312	45	from	from	ADP
ejpam-1234	312	46	eq	eq	ADP
ejpam-1234	312	47	.	.	PUNCT
ejpam-1234	313	1	(	(	PUNCT
ejpam-1234	313	2	13	13	NUM
ejpam-1234	313	3	)	)	PUNCT
ejpam-1234	313	4	,	,	PUNCT
ejpam-1234	313	5	corollary	corollary	NOUN
ejpam-1234	313	6	1	1	NUM
ejpam-1234	313	7	and	and	CCONJ
ejpam-1234	313	8	eq	eq	NOUN
ejpam-1234	313	9	.	.	PUNCT
ejpam-1234	314	1	(	(	PUNCT
ejpam-1234	314	2	6	6	NUM
ejpam-1234	314	3	)	)	PUNCT
ejpam-1234	314	4	that	that	PRON
ejpam-1234	314	5	φ	φ	PROPN
ejpam-1234	314	6	preserves	preserve	VERB
ejpam-1234	314	7	the	the	DET
ejpam-1234	314	8	q	q	NOUN
ejpam-1234	314	9	-	-	PUNCT
ejpam-1234	314	10	grading	grade	VERB
ejpam-1234	314	11	.	.	PUNCT
ejpam-1234	315	1	since	since	SCONJ
ejpam-1234	315	2	the	the	DET
ejpam-1234	315	3	component	component	NOUN
ejpam-1234	315	4	of	of	ADP
ejpam-1234	315	5	h	h	NOUN
ejpam-1234	315	6	(	(	PUNCT
ejpam-1234	315	7	x	x	PROPN
ejpam-1234	315	8	i	i	PRON
ejpam-1234	315	9	,	,	PUNCT
ejpam-1234	315	10	gi	gi	VERB
ejpam-1234	315	11	⋊	⋊	NUM
ejpam-1234	315	12	σi	σi	NOUN
ejpam-1234	315	13	)	)	PUNCT
ejpam-1234	315	14	gi	gi	AUX
ejpam-1234	315	15	graded	grade	VERB
ejpam-1234	315	16	by	by	ADP
ejpam-1234	315	17	the	the	DET
ejpam-1234	315	18	identity	identity	NOUN
ejpam-1234	315	19	permutation	permutation	NOUN
ejpam-1234	315	20	(	(	PUNCT
ejpam-1234	315	21	the	the	DET
ejpam-1234	315	22	untwisted	untwisted	ADJ
ejpam-1234	315	23	sector	sector	NOUN
ejpam-1234	315	24	)	)	PUNCT
ejpam-1234	315	25	is	be	AUX
ejpam-1234	315	26	exactly	exactly	ADV
ejpam-1234	315	27	the	the	DET
ejpam-1234	315	28	frobenius	frobenius	NOUN
ejpam-1234	315	29	algebra	algebra	NOUN
ejpam-1234	315	30	h∗(x	h∗(x	NOUN
ejpam-1234	316	1	i	i	PRON
ejpam-1234	316	2	,	,	PUNCT
ejpam-1234	316	3	gi	gi	INTJ
ejpam-1234	316	4	)	)	PUNCT
ejpam-1234	316	5	g	g	NOUN
ejpam-1234	316	6	i	i	PRON
ejpam-1234	317	1	=	=	SYM
ejpam-1234	318	1	h∗	h∗	PROPN
ejpam-1234	318	2	or	or	CCONJ
ejpam-1234	318	3	b	b	PROPN
ejpam-1234	318	4	(	(	PUNCT
ejpam-1234	318	5	[	[	X
ejpam-1234	318	6	x	x	X
ejpam-1234	318	7	/	/	SYM
ejpam-1234	318	8	g])⊗i	g])⊗i	PROPN
ejpam-1234	318	9	,	,	PUNCT
ejpam-1234	318	10	this	this	PRON
ejpam-1234	318	11	yields	yield	VERB
ejpam-1234	318	12	the	the	DET
ejpam-1234	318	13	following	follow	VERB
ejpam-1234	318	14	proposition	proposition	NOUN
ejpam-1234	318	15	.	.	PUNCT
ejpam-1234	319	1	proposition	proposition	NOUN
ejpam-1234	319	2	3	3	NUM
ejpam-1234	319	3	.	.	PUNCT
ejpam-1234	320	1	the	the	DET
ejpam-1234	320	2	isomorphism	isomorphism	PROPN
ejpam-1234	320	3	φ	φ	PROPN
ejpam-1234	320	4	is	be	AUX
ejpam-1234	320	5	an	an	DET
ejpam-1234	320	6	isomorphism	isomorphism	NOUN
ejpam-1234	320	7	as	as	ADP
ejpam-1234	320	8	h∗	h∗	NOUN
ejpam-1234	320	9	or	or	CCONJ
ejpam-1234	320	10	b	b	PROPN
ejpam-1234	320	11	(	(	PUNCT
ejpam-1234	320	12	[	[	X
ejpam-1234	320	13	x	x	X
ejpam-1234	320	14	/	/	SYM
ejpam-1234	320	15	g])⊗i	g])⊗i	PROPN
ejpam-1234	320	16	-modules	-module	NOUN
ejpam-1234	320	17	.	.	PUNCT
ejpam-1234	321	1	in	in	ADP
ejpam-1234	321	2	particular	particular	ADJ
ejpam-1234	321	3	,	,	PUNCT
ejpam-1234	321	4	h	h	NOUN
ejpam-1234	321	5	(	(	PUNCT
ejpam-1234	321	6	x	x	PROPN
ejpam-1234	321	7	i	i	PRON
ejpam-1234	321	8	,	,	PUNCT
ejpam-1234	321	9	gi	gi	VERB
ejpam-1234	321	10	⋊σi	⋊σi	NOUN
ejpam-1234	321	11	)	)	PUNCT
ejpam-1234	321	12	gi	gi	PROPN
ejpam-1234	321	13	is	be	AUX
ejpam-1234	321	14	a	a	DET
ejpam-1234	321	15	special	special	ADJ
ejpam-1234	321	16	σi	σi	NOUN
ejpam-1234	321	17	-frobenius	-frobenius	PROPN
ejpam-1234	321	18	algebra	algebra	NOUN
ejpam-1234	321	19	.	.	PUNCT
ejpam-1234	322	1	furthermore	furthermore	ADV
ejpam-1234	322	2	,	,	PUNCT
ejpam-1234	322	3	φ	φ	PROPN
ejpam-1234	322	4	preserves	preserve	VERB
ejpam-1234	322	5	the	the	DET
ejpam-1234	322	6	metric	metric	NOUN
ejpam-1234	322	7	.	.	PUNCT
ejpam-1234	323	1	proof	proof	NOUN
ejpam-1234	323	2	.	.	PUNCT
ejpam-1234	324	1	we	we	PRON
ejpam-1234	324	2	will	will	AUX
ejpam-1234	324	3	show	show	VERB
ejpam-1234	324	4	that	that	SCONJ
ejpam-1234	324	5	the	the	DET
ejpam-1234	324	6	actions	action	NOUN
ejpam-1234	324	7	of	of	ADP
ejpam-1234	324	8	h∗	h∗	PROPN
ejpam-1234	324	9	or	or	CCONJ
ejpam-1234	324	10	b	b	PROPN
ejpam-1234	324	11	(	(	PUNCT
ejpam-1234	324	12	[	[	X
ejpam-1234	324	13	x	x	X
ejpam-1234	324	14	/	/	SYM
ejpam-1234	324	15	g])i	g])i	VERB
ejpam-1234	324	16	on	on	ADP
ejpam-1234	324	17	aḡ,σ	aḡ,σ	ADJ
ejpam-1234	324	18	and	and	CCONJ
ejpam-1234	324	19	on	on	ADP
ejpam-1234	324	20	hḡ,σ	hḡ,σ	NOUN
ejpam-1234	324	21	are	be	AUX
ejpam-1234	324	22	identified	identify	VERB
ejpam-1234	324	23	by	by	ADP
ejpam-1234	324	24	φ	φ	PROPN
ejpam-1234	324	25	.	.	PROPN
ejpam-1234	324	26	without	without	ADP
ejpam-1234	324	27	loss	loss	NOUN
ejpam-1234	324	28	of	of	ADP
ejpam-1234	324	29	generality	generality	NOUN
ejpam-1234	324	30	,	,	PUNCT
ejpam-1234	324	31	we	we	PRON
ejpam-1234	324	32	can	can	AUX
ejpam-1234	324	33	assume	assume	VERB
ejpam-1234	324	34	i	i	PRON
ejpam-1234	324	35	=	=	PUNCT
ejpam-1234	324	36	{	{	PUNCT
ejpam-1234	324	37	1	1	NUM
ejpam-1234	324	38	,	,	PUNCT
ejpam-1234	324	39	·	·	PUNCT
ejpam-1234	324	40	·	·	PUNCT
ejpam-1234	324	41	·	·	PUNCT
ejpam-1234	324	42	,	,	PUNCT
ejpam-1234	324	43	n	n	CCONJ
ejpam-1234	324	44	}	}	PUNCT
ejpam-1234	324	45	and	and	CCONJ
ejpam-1234	324	46	σ	σ	NUM
ejpam-1234	324	47	=	=	SYM
ejpam-1234	324	48	(	(	PUNCT
ejpam-1234	324	49	12	12	NUM
ejpam-1234	324	50	·	·	PUNCT
ejpam-1234	324	51	·	·	PUNCT
ejpam-1234	324	52	·	·	PUNCT
ejpam-1234	324	53	n	n	CCONJ
ejpam-1234	324	54	)	)	PUNCT
ejpam-1234	324	55	.	.	PUNCT
ejpam-1234	325	1	let	let	VERB
ejpam-1234	325	2	x	x	PRON
ejpam-1234	325	3	g	g	PROPN
ejpam-1234	325	4	∈	∈	PROPN
ejpam-1234	325	5	h∗(x	h∗(x	PROPN
ejpam-1234	325	6	g)zg(g	g)zg(g	NOUN
ejpam-1234	325	7	)	)	PUNCT
ejpam-1234	325	8	for	for	ADP
ejpam-1234	325	9	every	every	DET
ejpam-1234	325	10	g	g	PROPN
ejpam-1234	325	11	∈	∈	PROPN
ejpam-1234	325	12	g	g	NOUN
ejpam-1234	325	13	and	and	CCONJ
ejpam-1234	325	14	let	let	VERB
ejpam-1234	325	15	lxg	lxg	PROPN
ejpam-1234	325	16	:	:	PUNCT
ejpam-1234	325	17	=	=	SYM
ejpam-1234	325	18	∑	∑	PUNCT
ejpam-1234	325	19	k∈gρk(x	k∈gρk(x	PROPN
ejpam-1234	325	20	g	g	NOUN
ejpam-1234	325	21	)	)	PUNCT
ejpam-1234	325	22	∈	∈	PROPN
ejpam-1234	325	23	a	a	DET
ejpam-1234	325	24	ḡ,σ	ḡ,σ	VERB
ejpam-1234	325	25	and	and	CCONJ
ejpam-1234	325	26	φ(lxg	φ(lxg	NOUN
ejpam-1234	325	27	)	)	PUNCT
ejpam-1234	326	1	=	=	PUNCT
ejpam-1234	326	2	∑	∑	PUNCT
ejpam-1234	326	3	k∈gi	k∈gi	PROPN
ejpam-1234	326	4	ρk(∆xg	ρk(∆xg	PROPN
ejpam-1234	326	5	)	)	PUNCT
ejpam-1234	326	6	∈h	∈h	NOUN
ejpam-1234	326	7	ḡ,σ	ḡ,σ	VERB
ejpam-1234	326	8	.	.	PUNCT
ejpam-1234	327	1	we	we	PRON
ejpam-1234	327	2	need	need	VERB
ejpam-1234	327	3	to	to	PART
ejpam-1234	327	4	show	show	VERB
ejpam-1234	327	5	that	that	SCONJ
ejpam-1234	327	6	the	the	DET
ejpam-1234	327	7	lehn	lehn	ADJ
ejpam-1234	327	8	-	-	PUNCT
ejpam-1234	327	9	sorger	sorger	NOUN
ejpam-1234	327	10	product	product	NOUN
ejpam-1234	327	11	pls	pls	INTJ
ejpam-1234	327	12	:	:	PUNCT
ejpam-1234	327	13	=	=	SYM
ejpam-1234	327	14			PROPN
ejpam-1234	327	15			NOUN
ejpam-1234	327	16			PROPN
ejpam-1234	327	17	∑	∑	ADP
ejpam-1234	327	18	f1	f1	PROPN
ejpam-1234	327	19	,	,	PUNCT
ejpam-1234	327	20	·	·	PUNCT
ejpam-1234	327	21	·	·	PUNCT
ejpam-1234	327	22	·	·	PUNCT
ejpam-1234	327	23	,	,	PUNCT
ejpam-1234	327	24	fn∈g	fn∈g	PROPN
ejpam-1234	327	25	ρf1	ρf1	PROPN
ejpam-1234	327	26	(	(	PUNCT
ejpam-1234	327	27	xh1	xh1	PROPN
ejpam-1234	327	28	)	)	PUNCT
ejpam-1234	327	29	⊗	⊗	PROPN
ejpam-1234	327	30	·	·	PUNCT
ejpam-1234	327	31	·	·	PUNCT
ejpam-1234	327	32	·	·	PUNCT
ejpam-1234	327	33	⊗ρfn	⊗ρfn	NOUN
ejpam-1234	327	34	(	(	PUNCT
ejpam-1234	327	35	xhn	xhn	PROPN
ejpam-1234	327	36	)	)	PUNCT
ejpam-1234	327	37			PROPN
ejpam-1234	327	38			NOUN
ejpam-1234	327	39			PUNCT
ejpam-1234	327	40	·	·	PUNCT
ejpam-1234	327	41	∑	∑	PUNCT
ejpam-1234	327	42	k∈g	k∈g	VERB
ejpam-1234	327	43	ρk(x	ρk(x	PROPN
ejpam-1234	327	44	g	g	NOUN
ejpam-1234	327	45	)	)	PUNCT
ejpam-1234	327	46	!	!	PUNCT
ejpam-1234	328	1	tomoo	tomoo	VERB
ejpam-1234	328	2	matsumura	matsumura	ADJ
ejpam-1234	328	3	/	/	SYM
ejpam-1234	328	4	eur	eur	PROPN
ejpam-1234	328	5	.	.	PUNCT
ejpam-1234	329	1	j.	j.	PROPN
ejpam-1234	329	2	pure	pure	PROPN
ejpam-1234	329	3	appl	appl	PROPN
ejpam-1234	329	4	.	.	PROPN
ejpam-1234	329	5	math	math	PROPN
ejpam-1234	329	6	,	,	PUNCT
ejpam-1234	329	7	5	5	NUM
ejpam-1234	329	8	(	(	PUNCT
ejpam-1234	329	9	2012	2012	NUM
ejpam-1234	329	10	)	)	PUNCT
ejpam-1234	329	11	,	,	PUNCT
ejpam-1234	329	12	492	492	NUM
ejpam-1234	329	13	-	-	SYM
ejpam-1234	329	14	510	510	NUM
ejpam-1234	329	15	503	503	NUM
ejpam-1234	329	16	corresponds	correspond	NOUN
ejpam-1234	329	17	via	via	ADP
ejpam-1234	329	18	φ	φ	PROPN
ejpam-1234	329	19	to	to	ADP
ejpam-1234	329	20	the	the	DET
ejpam-1234	329	21	stringy	stringy	ADJ
ejpam-1234	329	22	product	product	NOUN
ejpam-1234	329	23	pst	pst	NOUN
ejpam-1234	329	24	:	:	PUNCT
ejpam-1234	329	25	=	=	SYM
ejpam-1234	329	26			PROPN
ejpam-1234	329	27			NOUN
ejpam-1234	329	28			PROPN
ejpam-1234	329	29	∑	∑	ADP
ejpam-1234	329	30	f1	f1	PROPN
ejpam-1234	329	31	,	,	PUNCT
ejpam-1234	329	32	·	·	PUNCT
ejpam-1234	329	33	·	·	PUNCT
ejpam-1234	329	34	·	·	PUNCT
ejpam-1234	329	35	,	,	PUNCT
ejpam-1234	329	36	fn∈g	fn∈g	PROPN
ejpam-1234	329	37	ρf1	ρf1	PROPN
ejpam-1234	329	38	(	(	PUNCT
ejpam-1234	329	39	xh1	xh1	PROPN
ejpam-1234	329	40	)	)	PUNCT
ejpam-1234	329	41	⊗	⊗	PROPN
ejpam-1234	329	42	·	·	PUNCT
ejpam-1234	329	43	·	·	PUNCT
ejpam-1234	329	44	·	·	PUNCT
ejpam-1234	329	45	⊗ρfn	⊗ρfn	NOUN
ejpam-1234	330	1	(	(	PUNCT
ejpam-1234	330	2	xhn	xhn	PROPN
ejpam-1234	330	3	)	)	PUNCT
ejpam-1234	330	4			PROPN
ejpam-1234	330	5			NOUN
ejpam-1234	330	6			PUNCT
ejpam-1234	330	7	·	·	PUNCT
ejpam-1234	330	8			VERB
ejpam-1234	330	9			NOUN
ejpam-1234	330	10	∑	∑	PUNCT
ejpam-1234	330	11	k∈gi	k∈gi	VERB
ejpam-1234	330	12	ρk(∆xg	ρk(∆xg	PROPN
ejpam-1234	330	13	)	)	PUNCT
ejpam-1234	330	14			PROPN
ejpam-1234	331	1			PUNCT
ejpam-1234	332	1	.	.	PUNCT
ejpam-1234	333	1	let	let	VERB
ejpam-1234	333	2	z	z	NOUN
ejpam-1234	333	3	:	:	PUNCT
ejpam-1234	333	4	=	=	SYM
ejpam-1234	333	5	x	x	SYM
ejpam-1234	333	6	g	g	NOUN
ejpam-1234	333	7	,	,	PUNCT
ejpam-1234	333	8	f1h1	f1h1	X
ejpam-1234	333	9	f	f	NOUN
ejpam-1234	333	10	−1	−1	NOUN
ejpam-1234	333	11	1	1	NUM
ejpam-1234	333	12	,	,	PUNCT
ejpam-1234	333	13	·	·	PUNCT
ejpam-1234	333	14	·	·	PUNCT
ejpam-1234	333	15	·	·	PUNCT
ejpam-1234	333	16	,	,	PUNCT
ejpam-1234	333	17	fnhn	fnhn	NOUN
ejpam-1234	333	18	f	f	PROPN
ejpam-1234	333	19	−1	−1	NOUN
ejpam-1234	333	20	n	n	PROPN
ejpam-1234	333	21	,	,	PUNCT
ejpam-1234	333	22	q	q	X
ejpam-1234	333	23	:	:	PUNCT
ejpam-1234	333	24	z	z	NOUN
ejpam-1234	333	25	,	,	PUNCT
ejpam-1234	333	26	→	→	SYM
ejpam-1234	333	27	x	x	SYM
ejpam-1234	333	28	fnhn	fnhn	NOUN
ejpam-1234	333	29	f	f	PROPN
ejpam-1234	333	30	−1	−1	NOUN
ejpam-1234	333	31	n	n	PROPN
ejpam-1234	333	32	·	·	PUNCT
ejpam-1234	333	33	·	·	PUNCT
ejpam-1234	333	34	·	·	PUNCT
ejpam-1234	333	35	f1h1	f1h1	PROPN
ejpam-1234	333	36	f	f	X
ejpam-1234	333	37	−1	−1	NOUN
ejpam-1234	333	38	1	1	NUM
ejpam-1234	333	39	g	g	NOUN
ejpam-1234	333	40	and	and	CCONJ
ejpam-1234	333	41	∆q	∆q	PROPN
ejpam-1234	333	42	:	:	PUNCT
ejpam-1234	333	43	∆z	∆z	PROPN
ejpam-1234	333	44	,	,	PUNCT
ejpam-1234	333	45	→∆	→∆	NOUN
ejpam-1234	333	46	x	x	PART
ejpam-1234	333	47	fnhn	fnhn	NOUN
ejpam-1234	333	48	f−1	f−1	PROPN
ejpam-1234	333	49	n	n	CCONJ
ejpam-1234	333	50	·	·	PUNCT
ejpam-1234	333	51	·	·	PUNCT
ejpam-1234	333	52	·	·	PUNCT
ejpam-1234	333	53	f1h1	f1h1	PROPN
ejpam-1234	333	54	f−1	f−1	PROPN
ejpam-1234	333	55	1	1	NUM
ejpam-1234	333	56	g	g	NOUN
ejpam-1234	333	57	.	.	PUNCT
ejpam-1234	334	1	then	then	ADV
ejpam-1234	334	2	pls	pls	PROPN
ejpam-1234	334	3	is	be	AUX
ejpam-1234	334	4	computed	compute	VERB
ejpam-1234	334	5	as	as	SCONJ
ejpam-1234	334	6	follows	follow	VERB
ejpam-1234	334	7	.	.	PUNCT
ejpam-1234	335	1	pls	pls	INTJ
ejpam-1234	335	2	=	=	PUNCT
ejpam-1234	335	3	∑	∑	PUNCT
ejpam-1234	335	4	f1	f1	PROPN
ejpam-1234	335	5	,	,	PUNCT
ejpam-1234	335	6	·	·	PUNCT
ejpam-1234	335	7	·	·	PUNCT
ejpam-1234	335	8	·	·	PUNCT
ejpam-1234	335	9	,	,	PUNCT
ejpam-1234	335	10	fn	fn	NOUN
ejpam-1234	335	11	,	,	PUNCT
ejpam-1234	335	12	k∈g	k∈g	NOUN
ejpam-1234	335	13	�	�	PROPN
ejpam-1234	335	14	ρf1	ρf1	PROPN
ejpam-1234	335	15	(	(	PUNCT
ejpam-1234	335	16	xh1	xh1	PROPN
ejpam-1234	335	17	)	)	PUNCT
ejpam-1234	335	18	·	·	PUNCT
ejpam-1234	335	19	·	·	PUNCT
ejpam-1234	335	20	·	·	PUNCT
ejpam-1234	335	21	·	·	PUNCT
ejpam-1234	336	1	·	·	PUNCT
ejpam-1234	336	2	ρfn	ρfn	NOUN
ejpam-1234	336	3	(	(	PUNCT
ejpam-1234	336	4	xhn	xhn	PROPN
ejpam-1234	336	5	)	)	PUNCT
ejpam-1234	336	6	·	·	PUNCT
ejpam-1234	336	7	ρk(x	ρk(x	NUM
ejpam-1234	336	8	g	g	NOUN
ejpam-1234	336	9	)	)	PUNCT
ejpam-1234	336	10	�	�	PROPN
ejpam-1234	336	11	=	=	PUNCT
ejpam-1234	336	12	∑	∑	PUNCT
ejpam-1234	336	13	k∈g	k∈g	VERB
ejpam-1234	336	14	ρk	ρk	ADP
ejpam-1234	336	15			PROPN
ejpam-1234	336	16			NOUN
ejpam-1234	336	17			PROPN
ejpam-1234	336	18	∑	∑	ADV
ejpam-1234	336	19	f1	f1	PROPN
ejpam-1234	336	20	,	,	PUNCT
ejpam-1234	336	21	·	·	PUNCT
ejpam-1234	336	22	·	·	PUNCT
ejpam-1234	336	23	·	·	PUNCT
ejpam-1234	336	24	,	,	PUNCT
ejpam-1234	336	25	fn∈g	fn∈g	PROPN
ejpam-1234	336	26	�	�	PROPN
ejpam-1234	336	27	ρfn	ρfn	NOUN
ejpam-1234	336	28	(	(	PUNCT
ejpam-1234	336	29	xhn	xhn	PROPN
ejpam-1234	336	30	)	)	PUNCT
ejpam-1234	336	31	·	·	PUNCT
ejpam-1234	336	32	·	·	PUNCT
ejpam-1234	336	33	·	·	PUNCT
ejpam-1234	336	34	·	·	PUNCT
ejpam-1234	336	35	·	·	PUNCT
ejpam-1234	336	36	ρf1	ρf1	PROPN
ejpam-1234	336	37	(	(	PUNCT
ejpam-1234	336	38	xh1	xh1	PROPN
ejpam-1234	336	39	)	)	PUNCT
ejpam-1234	336	40	·	·	PUNCT
ejpam-1234	337	1	x	x	SYM
ejpam-1234	337	2	g	g	PROPN
ejpam-1234	337	3	�	�	PROPN
ejpam-1234	337	4			PROPN
ejpam-1234	337	5			VERB
ejpam-1234	337	6			PUNCT
ejpam-1234	338	1	=	=	PUNCT
ejpam-1234	338	2	∑	∑	PUNCT
ejpam-1234	338	3	k∈g	k∈g	VERB
ejpam-1234	338	4	ρk	ρk	ADP
ejpam-1234	338	5			PROPN
ejpam-1234	338	6			NOUN
ejpam-1234	338	7			PROPN
ejpam-1234	338	8	∑	∑	ADV
ejpam-1234	338	9	f1	f1	PROPN
ejpam-1234	338	10	,	,	PUNCT
ejpam-1234	338	11	·	·	PUNCT
ejpam-1234	338	12	·	·	PUNCT
ejpam-1234	338	13	·	·	PUNCT
ejpam-1234	338	14	,	,	PUNCT
ejpam-1234	338	15	fn∈g	fn∈g	PROPN
ejpam-1234	338	16	q∗	q∗	PROPN
ejpam-1234	338	17	�	�	PROPN
ejpam-1234	338	18	ρfn	ρfn	NOUN
ejpam-1234	338	19	(	(	PUNCT
ejpam-1234	338	20	xhn	xhn	PROPN
ejpam-1234	338	21	)	)	PUNCT
ejpam-1234	338	22	|z	|z	PROPN
ejpam-1234	338	23	∪	∪	X
ejpam-1234	338	24	·	·	PUNCT
ejpam-1234	338	25	·	·	PUNCT
ejpam-1234	338	26	·	·	PUNCT
ejpam-1234	338	27	∪ρf1	∪ρf1	PROPN
ejpam-1234	338	28	(	(	PUNCT
ejpam-1234	338	29	xh1	xh1	PROPN
ejpam-1234	338	30	)	)	PUNCT
ejpam-1234	338	31	|z	|z	PROPN
ejpam-1234	338	32	∪	∪	PROPN
ejpam-1234	338	33	x	x	X
ejpam-1234	338	34	g	g	PROPN
ejpam-1234	338	35	|z	|z	PROPN
ejpam-1234	338	36	∪	∪	PROPN
ejpam-1234	338	37	c	c	PROPN
ejpam-1234	338	38	(	(	PUNCT
ejpam-1234	338	39	fnhn	fnhn	NOUN
ejpam-1234	338	40	f	f	PROPN
ejpam-1234	338	41	−1	−1	NOUN
ejpam-1234	338	42	n	n	PROPN
ejpam-1234	338	43	,	,	PUNCT
ejpam-1234	338	44	·	·	PUNCT
ejpam-1234	338	45	·	·	PUNCT
ejpam-1234	338	46	·	·	PUNCT
ejpam-1234	338	47	,	,	PUNCT
ejpam-1234	338	48	f1h1	f1h1	X
ejpam-1234	338	49	f	f	NOUN
ejpam-1234	338	50	−1	−1	NOUN
ejpam-1234	338	51	1	1	NUM
ejpam-1234	338	52	,	,	PUNCT
ejpam-1234	338	53	g	g	NOUN
ejpam-1234	338	54	)	)	PUNCT
ejpam-1234	338	55	�	�	PROPN
ejpam-1234	338	56			PROPN
ejpam-1234	338	57			VERB
ejpam-1234	338	58			PUNCT
ejpam-1234	339	1	where	where	SCONJ
ejpam-1234	339	2	the	the	DET
ejpam-1234	339	3	first	first	ADJ
ejpam-1234	339	4	equality	equality	NOUN
ejpam-1234	339	5	follows	follow	VERB
ejpam-1234	339	6	from	from	ADP
ejpam-1234	339	7	the	the	DET
ejpam-1234	339	8	definition	definition	NOUN
ejpam-1234	339	9	and	and	CCONJ
ejpam-1234	339	10	the	the	DET
ejpam-1234	339	11	fact	fact	NOUN
ejpam-1234	339	12	that	that	SCONJ
ejpam-1234	339	13	gd(1,σ	gd(1,σ	NOUN
ejpam-1234	339	14	)	)	PUNCT
ejpam-1234	340	1	=	=	SYM
ejpam-1234	340	2	0	0	NUM
ejpam-1234	340	3	,	,	PUNCT
ejpam-1234	340	4	the	the	DET
ejpam-1234	340	5	second	second	ADJ
ejpam-1234	340	6	equality	equality	NOUN
ejpam-1234	340	7	follows	follow	VERB
ejpam-1234	340	8	by	by	ADP
ejpam-1234	340	9	the	the	DET
ejpam-1234	340	10	g	g	NOUN
ejpam-1234	340	11	-	-	PUNCT
ejpam-1234	340	12	equivariance	equivariance	NOUN
ejpam-1234	340	13	and	and	CCONJ
ejpam-1234	340	14	the	the	DET
ejpam-1234	340	15	commutativity	commutativity	NOUN
ejpam-1234	340	16	of	of	ADP
ejpam-1234	340	17	the	the	DET
ejpam-1234	340	18	multiplication	multiplication	NOUN
ejpam-1234	340	19	in	in	ADP
ejpam-1234	340	20	h	h	PROPN
ejpam-1234	340	21	(	(	PUNCT
ejpam-1234	340	22	x	x	NOUN
ejpam-1234	340	23	,	,	PUNCT
ejpam-1234	340	24	g)g	g)g	NOUN
ejpam-1234	340	25	and	and	CCONJ
ejpam-1234	340	26	replacing	replace	VERB
ejpam-1234	340	27	k−1	k−1	PROPN
ejpam-1234	340	28	fi	fi	NOUN
ejpam-1234	340	29	by	by	ADP
ejpam-1234	340	30	fi	fi	NOUN
ejpam-1234	340	31	and	and	CCONJ
ejpam-1234	340	32	the	the	DET
ejpam-1234	340	33	third	third	ADJ
ejpam-1234	340	34	equality	equality	NOUN
ejpam-1234	340	35	follows	follow	VERB
ejpam-1234	340	36	from	from	ADP
ejpam-1234	340	37	lemma	lemma	PROPN
ejpam-1234	340	38	1	1	NUM
ejpam-1234	340	39	.	.	PUNCT
ejpam-1234	341	1	on	on	ADP
ejpam-1234	341	2	the	the	DET
ejpam-1234	341	3	other	other	ADJ
ejpam-1234	341	4	hand	hand	NOUN
ejpam-1234	341	5	,	,	PUNCT
ejpam-1234	341	6	pst	pst	NOUN
ejpam-1234	341	7	is	be	AUX
ejpam-1234	341	8	computed	compute	VERB
ejpam-1234	341	9	as	as	SCONJ
ejpam-1234	341	10	follows	follow	VERB
ejpam-1234	341	11	.	.	PUNCT
ejpam-1234	342	1	pst	pst	NOUN
ejpam-1234	342	2	=	=	SYM
ejpam-1234	342	3	∑	∑	PUNCT
ejpam-1234	342	4	k∈gi	k∈gi	PROPN
ejpam-1234	342	5	ρk	ρk	ADP
ejpam-1234	342	6			PROPN
ejpam-1234	342	7			NOUN
ejpam-1234	342	8			PROPN
ejpam-1234	342	9	∑	∑	ADV
ejpam-1234	342	10	f1	f1	PROPN
ejpam-1234	342	11	,	,	PUNCT
ejpam-1234	342	12	·	·	PUNCT
ejpam-1234	342	13	·	·	PUNCT
ejpam-1234	342	14	·	·	PUNCT
ejpam-1234	342	15	,	,	PUNCT
ejpam-1234	342	16	fn∈g	fn∈g	PROPN
ejpam-1234	342	17	�	�	PROPN
ejpam-1234	342	18	ρf1	ρf1	PROPN
ejpam-1234	342	19	(	(	PUNCT
ejpam-1234	342	20	xh1	xh1	PROPN
ejpam-1234	342	21	)	)	PUNCT
ejpam-1234	343	1	⊗	⊗	PROPN
ejpam-1234	344	1	·	·	PUNCT
ejpam-1234	344	2	·	·	PUNCT
ejpam-1234	344	3	·	·	PUNCT
ejpam-1234	344	4	⊗ρfn	⊗ρfn	NOUN
ejpam-1234	344	5	(	(	PUNCT
ejpam-1234	344	6	xhn	xhn	PROPN
ejpam-1234	344	7	)	)	PUNCT
ejpam-1234	344	8	�	�	PROPN
ejpam-1234	344	9	·	·	NUM
ejpam-1234	344	10	∆xg	∆xg	NOUN
ejpam-1234	344	11			NOUN
ejpam-1234	344	12			VERB
ejpam-1234	344	13			PUNCT
ejpam-1234	345	1	=	=	PUNCT
ejpam-1234	345	2	∑	∑	PUNCT
ejpam-1234	345	3	k∈gi	k∈gi	VERB
ejpam-1234	345	4	ρk	ρk	ADP
ejpam-1234	345	5			PROPN
ejpam-1234	345	6			NOUN
ejpam-1234	345	7			PROPN
ejpam-1234	345	8	∑	∑	ADV
ejpam-1234	345	9	f1	f1	PROPN
ejpam-1234	345	10	,	,	PUNCT
ejpam-1234	345	11	·	·	PUNCT
ejpam-1234	345	12	·	·	PUNCT
ejpam-1234	345	13	·	·	PUNCT
ejpam-1234	345	14	,	,	PUNCT
ejpam-1234	345	15	fn∈g	fn∈g	PROPN
ejpam-1234	345	16	∆q∗	∆q∗	VERB
ejpam-1234	345	17	�	�	PROPN
ejpam-1234	345	18	ρf1	ρf1	PROPN
ejpam-1234	345	19	(	(	PUNCT
ejpam-1234	345	20	xh1	xh1	PROPN
ejpam-1234	345	21	)	)	PUNCT
ejpam-1234	345	22	⊗	⊗	PROPN
ejpam-1234	345	23	·	·	PUNCT
ejpam-1234	345	24	·	·	PUNCT
ejpam-1234	345	25	·	·	PUNCT
ejpam-1234	346	1	⊗ρfn	⊗ρfn	NOUN
ejpam-1234	346	2	(	(	PUNCT
ejpam-1234	346	3	xhn	xhn	PROPN
ejpam-1234	346	4	)	)	PUNCT
ejpam-1234	346	5	�	�	PROPN
ejpam-1234	346	6	�	�	PROPN
ejpam-1234	346	7	∆z	∆z	PROPN
ejpam-1234	346	8	∪∆xg	∪∆xg	VERB
ejpam-1234	346	9	|∆z	|∆z	PROPN
ejpam-1234	346	10	∪∆∗c	∪∆∗c	X
ejpam-1234	346	11	(	(	PUNCT
ejpam-1234	346	12	fnhn	fnhn	NOUN
ejpam-1234	346	13	f	f	PROPN
ejpam-1234	346	14	−1	−1	NOUN
ejpam-1234	346	15	n	n	PROPN
ejpam-1234	346	16	,	,	PUNCT
ejpam-1234	346	17	·	·	PUNCT
ejpam-1234	346	18	·	·	PUNCT
ejpam-1234	346	19	·	·	PUNCT
ejpam-1234	346	20	,	,	PUNCT
ejpam-1234	346	21	f1h1	f1h1	X
ejpam-1234	346	22	f	f	NOUN
ejpam-1234	346	23	−1	−1	NOUN
ejpam-1234	346	24	1	1	NUM
ejpam-1234	346	25	,	,	PUNCT
ejpam-1234	346	26	g	g	NOUN
ejpam-1234	346	27	)	)	PUNCT
ejpam-1234	346	28			PROPN
ejpam-1234	346	29			NOUN
ejpam-1234	346	30			PUNCT
ejpam-1234	347	1			PROPN
ejpam-1234	347	2			VERB
ejpam-1234	347	3			PUNCT
ejpam-1234	348	1	where	where	SCONJ
ejpam-1234	348	2	the	the	DET
ejpam-1234	348	3	second	second	ADJ
ejpam-1234	348	4	equality	equality	NOUN
ejpam-1234	348	5	follows	follow	VERB
ejpam-1234	348	6	from	from	ADP
ejpam-1234	348	7	lemma	lemma	PROPN
ejpam-1234	348	8	3	3	NUM
ejpam-1234	348	9	.	.	PUNCT
ejpam-1234	349	1	now	now	ADV
ejpam-1234	349	2	it	it	PRON
ejpam-1234	349	3	is	be	AUX
ejpam-1234	349	4	clear	clear	ADJ
ejpam-1234	349	5	that	that	SCONJ
ejpam-1234	349	6	φ(pls	φ(pls	NOUN
ejpam-1234	349	7	)	)	PUNCT
ejpam-1234	349	8	=	=	PUNCT
ejpam-1234	349	9	pst	pst	NOUN
ejpam-1234	349	10	.	.	PUNCT
ejpam-1234	350	1	since	since	SCONJ
ejpam-1234	350	2	the	the	DET
ejpam-1234	350	3	metric	metric	NOUN
ejpam-1234	350	4	of	of	ADP
ejpam-1234	350	5	a	a	DET
ejpam-1234	350	6	special	special	ADJ
ejpam-1234	350	7	g	g	NOUN
ejpam-1234	350	8	-	-	PUNCT
ejpam-1234	350	9	frobenius	frobenius	NOUN
ejpam-1234	350	10	algebra	algebra	NOUN
ejpam-1234	350	11	is	be	AUX
ejpam-1234	350	12	completely	completely	ADV
ejpam-1234	350	13	determined	determine	VERB
ejpam-1234	350	14	by	by	ADP
ejpam-1234	350	15	the	the	DET
ejpam-1234	350	16	frobenius	frobenius	NOUN
ejpam-1234	350	17	algebra	algebra	NOUN
ejpam-1234	350	18	structure	structure	NOUN
ejpam-1234	350	19	on	on	ADP
ejpam-1234	350	20	the	the	DET
ejpam-1234	350	21	untwisted	untwist	VERB
ejpam-1234	350	22	sector	sector	NOUN
ejpam-1234	350	23	and	and	CCONJ
ejpam-1234	350	24	its	its	PRON
ejpam-1234	350	25	action	action	NOUN
ejpam-1234	350	26	(	(	PUNCT
ejpam-1234	350	27	see	see	VERB
ejpam-1234	350	28	[	[	PUNCT
ejpam-1234	350	29	theorem	theorem	ADJ
ejpam-1234	350	30	4.1	4.1	NUM
ejpam-1234	350	31	,	,	PUNCT
ejpam-1234	350	32	12	12	NUM
ejpam-1234	350	33	]	]	PUNCT
ejpam-1234	350	34	or	or	CCONJ
ejpam-1234	350	35	appendix	appendix	NOUN
ejpam-1234	350	36	)	)	PUNCT
ejpam-1234	350	37	,	,	PUNCT
ejpam-1234	350	38	the	the	DET
ejpam-1234	350	39	isomorphism	isomorphism	NOUN
ejpam-1234	350	40	also	also	ADV
ejpam-1234	350	41	preserves	preserve	VERB
ejpam-1234	350	42	the	the	DET
ejpam-1234	350	43	metric	metric	NOUN
ejpam-1234	350	44	.	.	PUNCT
ejpam-1234	351	1	so	so	ADV
ejpam-1234	351	2	far	far	ADV
ejpam-1234	351	3	,	,	PUNCT
ejpam-1234	351	4	we	we	PRON
ejpam-1234	351	5	have	have	AUX
ejpam-1234	351	6	proved	prove	VERB
ejpam-1234	351	7	that	that	SCONJ
ejpam-1234	351	8	φ	φ	PROPN
ejpam-1234	351	9	is	be	AUX
ejpam-1234	351	10	a	a	DET
ejpam-1234	351	11	g	g	NOUN
ejpam-1234	351	12	-	-	PUNCT
ejpam-1234	351	13	equivariant	equivariant	ADJ
ejpam-1234	351	14	isomorphism	isomorphism	NOUN
ejpam-1234	351	15	of	of	ADP
ejpam-1234	351	16	special	special	ADJ
ejpam-1234	351	17	σi	σi	PROPN
ejpam-1234	351	18	-reconstruction	-reconstruction	PROPN
ejpam-1234	351	19	data	datum	NOUN
ejpam-1234	351	20	.	.	PUNCT
ejpam-1234	352	1	thus	thus	ADV
ejpam-1234	352	2	,	,	PUNCT
ejpam-1234	352	3	by	by	ADP
ejpam-1234	352	4	theorem	theorem	VERB
ejpam-1234	352	5	4.1	4.1	NUM
ejpam-1234	352	6	of	of	ADP
ejpam-1234	352	7	[	[	X
ejpam-1234	352	8	12	12	NUM
ejpam-1234	352	9	]	]	PUNCT
ejpam-1234	352	10	,	,	PUNCT
ejpam-1234	352	11	if	if	SCONJ
ejpam-1234	352	12	the	the	DET
ejpam-1234	352	13	associated	associate	VERB
ejpam-1234	352	14	graded	grade	VERB
ejpam-1234	352	15	cocycles	cocycle	NOUN
ejpam-1234	352	16	coincide	coincide	VERB
ejpam-1234	352	17	,	,	PUNCT
ejpam-1234	352	18	then	then	ADV
ejpam-1234	352	19	φ	φ	PROPN
ejpam-1234	352	20	is	be	AUX
ejpam-1234	352	21	a	a	DET
ejpam-1234	352	22	g	g	NOUN
ejpam-1234	352	23	-	-	PUNCT
ejpam-1234	352	24	frobenius	frobenius	NOUN
ejpam-1234	352	25	algebra	algebra	NOUN
ejpam-1234	352	26	isomorphism	isomorphism	NOUN
ejpam-1234	352	27	.	.	PUNCT
ejpam-1234	353	1	from	from	ADP
ejpam-1234	353	2	theorem	theorem	ADJ
ejpam-1234	353	3	6.5	6.5	NUM
ejpam-1234	353	4	of	of	ADP
ejpam-1234	353	5	[	[	X
ejpam-1234	353	6	13	13	NUM
ejpam-1234	353	7	]	]	PUNCT
ejpam-1234	353	8	and	and	CCONJ
ejpam-1234	353	9	the	the	DET
ejpam-1234	353	10	fact	fact	NOUN
ejpam-1234	353	11	that	that	SCONJ
ejpam-1234	353	12	the	the	DET
ejpam-1234	353	13	graded	grade	VERB
ejpam-1234	353	14	cocycle	cocycle	NOUN
ejpam-1234	353	15	of	of	ADP
ejpam-1234	353	16	a	a	DET
ejpam-1234	353	17	lehn	lehn	ADJ
ejpam-1234	353	18	-	-	PUNCT
ejpam-1234	353	19	sorger	sorger	NOUN
ejpam-1234	353	20	’s	’s	PART
ejpam-1234	353	21	algebra	algebra	NOUN
ejpam-1234	353	22	is	be	AUX
ejpam-1234	353	23	normalized	normalize	VERB
ejpam-1234	353	24	[	[	PUNCT
ejpam-1234	353	25	13	13	NUM
ejpam-1234	353	26	,	,	PUNCT
ejpam-1234	353	27	p.77	p.77	NOUN
ejpam-1234	353	28	,	,	PUNCT
ejpam-1234	353	29	]	]	PUNCT
ejpam-1234	353	30	,	,	PUNCT
ejpam-1234	353	31	it	it	PRON
ejpam-1234	353	32	suffices	suffice	VERB
ejpam-1234	353	33	to	to	PART
ejpam-1234	353	34	show	show	VERB
ejpam-1234	353	35	:	:	PUNCT
ejpam-1234	353	36	proposition	proposition	NOUN
ejpam-1234	353	37	4	4	NUM
ejpam-1234	353	38	.	.	PUNCT
ejpam-1234	354	1	let	let	VERB
ejpam-1234	354	2	1σ	1σ	NOUN
ejpam-1234	354	3	be	be	AUX
ejpam-1234	354	4	the	the	DET
ejpam-1234	354	5	identity	identity	NOUN
ejpam-1234	354	6	of	of	ADP
ejpam-1234	354	7	the	the	DET
ejpam-1234	354	8	frobenius	frobenius	NOUN
ejpam-1234	354	9	algebra	algebra	PROPN
ejpam-1234	354	10	hor	hor	PROPN
ejpam-1234	354	11	b([x	b([x	PROPN
ejpam-1234	354	12	/	/	SYM
ejpam-1234	354	13	g	g	NOUN
ejpam-1234	354	14	]	]	PUNCT
ejpam-1234	354	15	)	)	PUNCT
ejpam-1234	354	16	⊗iσ	⊗iσ	NOUN
ejpam-1234	354	17	.	.	PUNCT
ejpam-1234	355	1	the	the	DET
ejpam-1234	355	2	graded	grade	VERB
ejpam-1234	355	3	cocycle	cocycle	NOUN
ejpam-1234	355	4	defined	define	VERB
ejpam-1234	355	5	by	by	ADP
ejpam-1234	355	6	the	the	DET
ejpam-1234	355	7	special	special	ADJ
ejpam-1234	355	8	σi	σi	PROPN
ejpam-1234	355	9	-frobenius	-frobenius	ADJ
ejpam-1234	355	10	algebra	algebra	NOUN
ejpam-1234	355	11	structure	structure	NOUN
ejpam-1234	355	12	on	on	ADP
ejpam-1234	355	13	h(x	h(x	PROPN
ejpam-1234	355	14	i	i	PRON
ejpam-1234	355	15	,	,	PUNCT
ejpam-1234	355	16	gi	gi	VERB
ejpam-1234	355	17	⋊σi	⋊σi	NOUN
ejpam-1234	355	18	)	)	PUNCT
ejpam-1234	355	19	gi	gi	VERB
ejpam-1234	355	20	with	with	ADP
ejpam-1234	355	21	the	the	DET
ejpam-1234	355	22	cyclic	cyclic	ADJ
ejpam-1234	355	23	generators	generator	NOUN
ejpam-1234	355	24	{	{	PUNCT
ejpam-1234	355	25	φ(1σ	φ(1σ	NUM
ejpam-1234	355	26	)	)	PUNCT
ejpam-1234	355	27	}	}	PUNCT
ejpam-1234	355	28	is	be	AUX
ejpam-1234	355	29	normalized	normalize	VERB
ejpam-1234	355	30	.	.	PUNCT
ejpam-1234	356	1	proof	proof	NOUN
ejpam-1234	356	2	.	.	PUNCT
ejpam-1234	357	1	the	the	DET
ejpam-1234	357	2	graded	grade	VERB
ejpam-1234	357	3	cocycle	cocycle	NOUN
ejpam-1234	357	4	γ	γ	X
ejpam-1234	357	5	is	be	AUX
ejpam-1234	357	6	defined	define	VERB
ejpam-1234	357	7	by	by	ADP
ejpam-1234	357	8	φ(1σ	φ(1σ	NOUN
ejpam-1234	357	9	)	)	PUNCT
ejpam-1234	357	10	·	·	SYM
ejpam-1234	357	11	φ(1τ	φ(1τ	NOUN
ejpam-1234	357	12	)	)	PUNCT
ejpam-1234	357	13	=	=	SYM
ejpam-1234	357	14	γσ	γσ	PROPN
ejpam-1234	357	15	,	,	PUNCT
ejpam-1234	357	16	τφ(1στ	τφ(1στ	PROPN
ejpam-1234	357	17	)	)	PUNCT
ejpam-1234	357	18	.	.	PUNCT
ejpam-1234	358	1	if	if	SCONJ
ejpam-1234	358	2	1σ	1σ	PROPN
ejpam-1234	358	3	is	be	AUX
ejpam-1234	358	4	the	the	DET
ejpam-1234	358	5	identity	identity	NOUN
ejpam-1234	358	6	element	element	NOUN
ejpam-1234	358	7	of	of	ADP
ejpam-1234	358	8	the	the	DET
ejpam-1234	358	9	ordinary	ordinary	ADJ
ejpam-1234	358	10	cohomology	cohomology	NOUN
ejpam-1234	358	11	ring	ring	NOUN
ejpam-1234	358	12	h∗((x	h∗((x	NOUN
ejpam-1234	358	13	i)σ	i)σ	NOUN
ejpam-1234	358	14	)	)	PUNCT
ejpam-1234	358	15	,	,	PUNCT
ejpam-1234	358	16	then	then	ADV
ejpam-1234	358	17	φ(1σ	φ(1σ	NUM
ejpam-1234	358	18	)	)	PUNCT
ejpam-1234	358	19	=	=	SYM
ejpam-1234	358	20	1	1	NUM
ejpam-1234	358	21	|giσ	|giσ	VERB
ejpam-1234	358	22	|	|	ADV
ejpam-1234	358	23	∑	∑	PROPN
ejpam-1234	358	24	f	f	PROPN
ejpam-1234	358	25	∈gi	∈gi	NOUN
ejpam-1234	358	26	ρ	ρ	PROPN
ejpam-1234	358	27	f	f	PROPN
ejpam-1234	358	28	�	�	PROPN
ejpam-1234	358	29	1σ	1σ	PROPN
ejpam-1234	358	30	�	�	PROPN
ejpam-1234	358	31	.	.	PUNCT
ejpam-1234	359	1	tomoo	tomoo	VERB
ejpam-1234	359	2	matsumura	matsumura	ADJ
ejpam-1234	359	3	/	/	SYM
ejpam-1234	359	4	eur	eur	PROPN
ejpam-1234	359	5	.	.	PUNCT
ejpam-1234	360	1	j.	j.	PROPN
ejpam-1234	360	2	pure	pure	PROPN
ejpam-1234	360	3	appl	appl	PROPN
ejpam-1234	360	4	.	.	PROPN
ejpam-1234	360	5	math	math	PROPN
ejpam-1234	360	6	,	,	PUNCT
ejpam-1234	360	7	5	5	NUM
ejpam-1234	360	8	(	(	PUNCT
ejpam-1234	360	9	2012	2012	NUM
ejpam-1234	360	10	)	)	PUNCT
ejpam-1234	360	11	,	,	PUNCT
ejpam-1234	360	12	492	492	NUM
ejpam-1234	360	13	-	-	SYM
ejpam-1234	360	14	510	510	NUM
ejpam-1234	360	15	504	504	NUM
ejpam-1234	360	16	let	let	VERB
ejpam-1234	360	17	σ	σ	NOUN
ejpam-1234	360	18	,	,	PUNCT
ejpam-1234	360	19	τ	τ	PROPN
ejpam-1234	360	20	be	be	VERB
ejpam-1234	360	21	transversal	transversal	ADJ
ejpam-1234	360	22	and	and	CCONJ
ejpam-1234	360	23	|τ|	|τ|	ADP
ejpam-1234	360	24	=	=	ADJ
ejpam-1234	360	25	1	1	X
ejpam-1234	360	26	.	.	NOUN
ejpam-1234	360	27	without	without	ADP
ejpam-1234	360	28	loss	loss	NOUN
ejpam-1234	360	29	of	of	ADP
ejpam-1234	360	30	generality	generality	NOUN
ejpam-1234	360	31	,	,	PUNCT
ejpam-1234	360	32	we	we	PRON
ejpam-1234	360	33	can	can	AUX
ejpam-1234	360	34	assume	assume	VERB
ejpam-1234	360	35	iσ	iσ	ADP
ejpam-1234	360	36	,	,	PUNCT
ejpam-1234	360	37	τ	τ	PROPN
ejpam-1234	360	38	=	=	PUNCT
ejpam-1234	360	39	{	{	PUNCT
ejpam-1234	360	40	i	i	NOUN
ejpam-1234	360	41	}	}	PUNCT
ejpam-1234	360	42	and	and	CCONJ
ejpam-1234	360	43	therefore	therefore	ADV
ejpam-1234	360	44	,	,	PUNCT
ejpam-1234	360	45	let	let	VERB
ejpam-1234	360	46	τ	τ	X
ejpam-1234	360	47	=	=	PUNCT
ejpam-1234	360	48	(	(	PUNCT
ejpam-1234	360	49	i	i	NOUN
ejpam-1234	360	50	j	j	PROPN
ejpam-1234	360	51	)	)	PUNCT
ejpam-1234	360	52	and	and	CCONJ
ejpam-1234	360	53	iσ	iσ	ADV
ejpam-1234	360	54	=	=	PUNCT
ejpam-1234	360	55	{	{	PUNCT
ejpam-1234	360	56	a	a	DET
ejpam-1234	360	57	,	,	PUNCT
ejpam-1234	360	58	b	b	NOUN
ejpam-1234	360	59	}	}	PUNCT
ejpam-1234	360	60	where	where	SCONJ
ejpam-1234	360	61	i	i	PRON
ejpam-1234	360	62	∈	∈	VERB
ejpam-1234	360	63	a	a	PRON
ejpam-1234	360	64	and	and	CCONJ
ejpam-1234	360	65	j	j	PROPN
ejpam-1234	360	66	∈	∈	PROPN
ejpam-1234	360	67	b.	b.	PROPN
ejpam-1234	361	1	we	we	PRON
ejpam-1234	361	2	compute	compute	VERB
ejpam-1234	361	3	φ(1σ	φ(1σ	NUM
ejpam-1234	361	4	)	)	PUNCT
ejpam-1234	361	5	·	·	SYM
ejpam-1234	361	6	φ(1τ	φ(1τ	NOUN
ejpam-1234	361	7	)	)	PUNCT
ejpam-1234	361	8	=	=	SYM
ejpam-1234	361	9			PROPN
ejpam-1234	361	10			NOUN
ejpam-1234	361	11			NOUN
ejpam-1234	361	12	1	1	NUM
ejpam-1234	361	13	|giσ	|giσ	VERB
ejpam-1234	361	14	|	|	ADV
ejpam-1234	361	15	∑	∑	PROPN
ejpam-1234	361	16	f	f	PROPN
ejpam-1234	361	17	∈gi	∈gi	NOUN
ejpam-1234	361	18	ρf	ρf	PROPN
ejpam-1234	361	19	�	�	PROPN
ejpam-1234	361	20	1σ	1σ	PROPN
ejpam-1234	361	21	�	�	PROPN
ejpam-1234	361	22			PROPN
ejpam-1234	361	23			NOUN
ejpam-1234	361	24			PUNCT
ejpam-1234	361	25	·	·	PUNCT
ejpam-1234	361	26			PROPN
ejpam-1234	361	27			NOUN
ejpam-1234	361	28			NOUN
ejpam-1234	361	29	1	1	NUM
ejpam-1234	361	30	|giτ	|giτ	ADP
ejpam-1234	361	31	|	|	ADV
ejpam-1234	361	32	∑	∑	ADV
ejpam-1234	361	33	g∈gi	g∈gi	NOUN
ejpam-1234	361	34	ρg	ρg	PROPN
ejpam-1234	361	35	�	�	PROPN
ejpam-1234	361	36	1τ	1τ	NUM
ejpam-1234	361	37	�	�	PROPN
ejpam-1234	361	38			PROPN
ejpam-1234	361	39			VERB
ejpam-1234	361	40			PUNCT
ejpam-1234	362	1	=	=	SYM
ejpam-1234	362	2	1	1	NUM
ejpam-1234	362	3	|g||iσ|+|iτ|	|g||iσ|+|iτ|	NOUN
ejpam-1234	362	4	∑	∑	PUNCT
ejpam-1234	362	5	f	f	PROPN
ejpam-1234	362	6	∈gi	∈gi	NOUN
ejpam-1234	362	7	ρf	ρf	PART
ejpam-1234	362	8			VERB
ejpam-1234	362	9			NOUN
ejpam-1234	362	10			NOUN
ejpam-1234	362	11	∑	∑	ADP
ejpam-1234	362	12	g∈gi	g∈gi	NOUN
ejpam-1234	362	13	1σ	1σ	NOUN
ejpam-1234	362	14	·	·	SYM
ejpam-1234	362	15	ρg(1τ	ρg(1τ	NUM
ejpam-1234	362	16	)	)	PUNCT
ejpam-1234	362	17			NOUN
ejpam-1234	362	18			VERB
ejpam-1234	362	19			PUNCT
ejpam-1234	363	1	=	=	SYM
ejpam-1234	363	2	1	1	NUM
ejpam-1234	363	3	|g|n+1	|g|n+1	PROPN
ejpam-1234	363	4	∑	∑	PROPN
ejpam-1234	363	5	f	f	PROPN
ejpam-1234	363	6	∈gi	∈gi	NOUN
ejpam-1234	363	7	ρf	ρf	PART
ejpam-1234	363	8			VERB
ejpam-1234	363	9			NOUN
ejpam-1234	363	10			NOUN
ejpam-1234	363	11			NOUN
ejpam-1234	363	12	|g|iτ	|g|iτ	VERB
ejpam-1234	363	13	∑	∑	PUNCT
ejpam-1234	363	14	g∈gi/	g∈gi/	VERB
ejpam-1234	363	15	�	�	PROPN
ejpam-1234	363	16	∏	∏	PROPN
ejpam-1234	364	1	c∈iτ	c∈iτ	NOUN
ejpam-1234	365	1	∆c	∆c	PROPN
ejpam-1234	365	2	g	g	PROPN
ejpam-1234	365	3	�	�	PROPN
ejpam-1234	365	4	1σ	1σ	PROPN
ejpam-1234	365	5	·	·	SYM
ejpam-1234	365	6	ρg(1τ	ρg(1τ	NUM
ejpam-1234	365	7	)	)	PUNCT
ejpam-1234	365	8			PROPN
ejpam-1234	365	9			NOUN
ejpam-1234	365	10			VERB
ejpam-1234	365	11			PUNCT
ejpam-1234	366	1	=	=	PUNCT
ejpam-1234	366	2	|g|n−1	|g|n−1	X
ejpam-1234	366	3	|g|n+1	|g|n+1	NOUN
ejpam-1234	366	4	∑	∑	PROPN
ejpam-1234	366	5	f	f	PROPN
ejpam-1234	366	6	∈gi	∈gi	NOUN
ejpam-1234	366	7	ρf	ρf	PART
ejpam-1234	366	8			VERB
ejpam-1234	366	9			NOUN
ejpam-1234	366	10			NOUN
ejpam-1234	366	11	∑	∑	PUNCT
ejpam-1234	366	12	g∈∆a	g∈∆a	PROPN
ejpam-1234	366	13	g	g	PROPN
ejpam-1234	366	14	×∆b	×∆b	PROPN
ejpam-1234	366	15	g	g	PROPN
ejpam-1234	366	16	/∆g	/∆g	SYM
ejpam-1234	366	17	ρg(1σ	ρg(1σ	PROPN
ejpam-1234	366	18	·	·	SYM
ejpam-1234	366	19	1τ	1τ	NUM
ejpam-1234	366	20	)	)	PUNCT
ejpam-1234	366	21			PROPN
ejpam-1234	366	22			VERB
ejpam-1234	366	23			PUNCT
ejpam-1234	367	1	=	=	SYM
ejpam-1234	367	2	1	1	NUM
ejpam-1234	367	3	|g|	|g|	PROPN
ejpam-1234	367	4	∑	∑	PROPN
ejpam-1234	367	5	f	f	PROPN
ejpam-1234	367	6	∈gi	∈gi	NOUN
ejpam-1234	367	7	ρf	ρf	PROPN
ejpam-1234	367	8	�	�	PROPN
ejpam-1234	367	9	1στ	1στ	PROPN
ejpam-1234	367	10	�	�	PROPN
ejpam-1234	367	11	=	=	PUNCT
ejpam-1234	367	12	φ(1στ	φ(1στ	NOUN
ejpam-1234	367	13	)	)	PUNCT
ejpam-1234	367	14	where	where	SCONJ
ejpam-1234	367	15	the	the	DET
ejpam-1234	367	16	fourth	fourth	ADJ
ejpam-1234	367	17	equality	equality	NOUN
ejpam-1234	367	18	follows	follow	VERB
ejpam-1234	367	19	from	from	ADP
ejpam-1234	367	20	gi/	gi/	NOUN
ejpam-1234	367	21	�	�	PROPN
ejpam-1234	367	22	∏	∏	PROPN
ejpam-1234	368	1	c∈iτ	c∈iτ	NOUN
ejpam-1234	368	2	∆c	∆c	PROPN
ejpam-1234	368	3	g	g	PROPN
ejpam-1234	368	4	�	�	PROPN
ejpam-1234	368	5	∼=∆a	∼=∆a	VERB
ejpam-1234	368	6	g	g	PROPN
ejpam-1234	368	7	×∆b	×∆b	X
ejpam-1234	368	8	g	g	PROPN
ejpam-1234	368	9	/∆g	/∆g	PUNCT
ejpam-1234	368	10	and	and	CCONJ
ejpam-1234	368	11	the	the	DET
ejpam-1234	368	12	gi	gi	NOUN
ejpam-1234	368	13	-equivariance	-equivariance	NOUN
ejpam-1234	368	14	of	of	ADP
ejpam-1234	368	15	the	the	DET
ejpam-1234	368	16	stringy	stringy	ADJ
ejpam-1234	368	17	product	product	NOUN
ejpam-1234	368	18	.	.	PUNCT
ejpam-1234	369	1	the	the	DET
ejpam-1234	369	2	last	last	ADJ
ejpam-1234	369	3	equality	equality	NOUN
ejpam-1234	369	4	follows	follow	VERB
ejpam-1234	369	5	from	from	ADP
ejpam-1234	369	6	1σ	1σ	PROPN
ejpam-1234	369	7	·	·	PUNCT
ejpam-1234	369	8	1τ	1τ	NUM
ejpam-1234	369	9	=	=	SYM
ejpam-1234	369	10	1στ	1στ	NOUN
ejpam-1234	369	11	which	which	PRON
ejpam-1234	369	12	holds	hold	VERB
ejpam-1234	369	13	because	because	SCONJ
ejpam-1234	369	14	of	of	ADP
ejpam-1234	369	15	transversality	transversality	NOUN
ejpam-1234	369	16	.	.	PUNCT
ejpam-1234	370	1	thus	thus	ADV
ejpam-1234	370	2	γσ	γσ	ADP
ejpam-1234	370	3	,	,	PUNCT
ejpam-1234	370	4	τ	τ	PROPN
ejpam-1234	370	5	=	=	SYM
ejpam-1234	370	6	1	1	X
ejpam-1234	370	7	.	.	PUNCT
ejpam-1234	370	8	theorem	theorem	NOUN
ejpam-1234	370	9	4	4	NUM
ejpam-1234	370	10	.	.	PUNCT
ejpam-1234	371	1	the	the	DET
ejpam-1234	371	2	canonical	canonical	ADJ
ejpam-1234	371	3	isomorphism	isomorphism	PROPN
ejpam-1234	371	4	φ	φ	PROPN
ejpam-1234	371	5	is	be	AUX
ejpam-1234	371	6	an	an	DET
ejpam-1234	371	7	isomorphism	isomorphism	NOUN
ejpam-1234	371	8	of	of	ADP
ejpam-1234	371	9	σi	σi	PROPN
ejpam-1234	371	10	-frobenius	-frobenius	PROPN
ejpam-1234	371	11	algebras	algebra	NOUN
ejpam-1234	371	12	.	.	PUNCT
ejpam-1234	372	1	proof	proof	NOUN
ejpam-1234	372	2	.	.	PUNCT
ejpam-1234	373	1	since	since	SCONJ
ejpam-1234	373	2	the	the	DET
ejpam-1234	373	3	lehn	lehn	NOUN
ejpam-1234	373	4	-	-	PUNCT
ejpam-1234	373	5	sorger	sorger	NOUN
ejpam-1234	373	6	algebra	algebra	NOUN
ejpam-1234	373	7	is	be	AUX
ejpam-1234	373	8	always	always	ADV
ejpam-1234	373	9	normalized	normalize	VERB
ejpam-1234	373	10	(	(	PUNCT
ejpam-1234	373	11	see	see	VERB
ejpam-1234	373	12	appendix	appendix	NOUN
ejpam-1234	373	13	)	)	PUNCT
ejpam-1234	373	14	,	,	PUNCT
ejpam-1234	373	15	propositions	proposition	NOUN
ejpam-1234	373	16	2	2	NUM
ejpam-1234	373	17	,	,	PUNCT
ejpam-1234	373	18	3	3	NUM
ejpam-1234	373	19	and	and	CCONJ
ejpam-1234	373	20	4	4	NUM
ejpam-1234	373	21	imply	imply	VERB
ejpam-1234	373	22	that	that	SCONJ
ejpam-1234	373	23	φ	φ	PROPN
ejpam-1234	373	24	is	be	AUX
ejpam-1234	373	25	an	an	DET
ejpam-1234	373	26	isomorphism	isomorphism	NOUN
ejpam-1234	373	27	of	of	ADP
ejpam-1234	373	28	normalized	normalize	VERB
ejpam-1234	373	29	special	special	ADJ
ejpam-1234	373	30	σi	σi	PROPN
ejpam-1234	373	31	-reconstruction	-reconstruction	PROPN
ejpam-1234	373	32	data	datum	NOUN
ejpam-1234	373	33	.	.	PUNCT
ejpam-1234	374	1	therefore	therefore	ADV
ejpam-1234	374	2	by	by	ADP
ejpam-1234	374	3	theorem	theorem	NOUN
ejpam-1234	374	4	4.1	4.1	NUM
ejpam-1234	374	5	of	of	ADP
ejpam-1234	374	6	[	[	X
ejpam-1234	374	7	12	12	NUM
ejpam-1234	374	8	]	]	PUNCT
ejpam-1234	374	9	and	and	CCONJ
ejpam-1234	374	10	theorem	theorem	VERB
ejpam-1234	374	11	6.5	6.5	NUM
ejpam-1234	374	12	of	of	ADP
ejpam-1234	374	13	[	[	X
ejpam-1234	374	14	13	13	NUM
ejpam-1234	374	15	]	]	PUNCT
ejpam-1234	374	16	,	,	PUNCT
ejpam-1234	374	17	we	we	PRON
ejpam-1234	374	18	can	can	AUX
ejpam-1234	374	19	conclude	conclude	VERB
ejpam-1234	374	20	that	that	SCONJ
ejpam-1234	374	21	φ	φ	PROPN
ejpam-1234	374	22	preserves	preserve	VERB
ejpam-1234	374	23	the	the	DET
ejpam-1234	374	24	σi	σi	PROPN
ejpam-1234	374	25	-frobenius	-frobenius	PROPN
ejpam-1234	374	26	algebra	algebra	NOUN
ejpam-1234	374	27	structures	structure	NOUN
ejpam-1234	374	28	.	.	PUNCT
ejpam-1234	375	1	5	5	X
ejpam-1234	375	2	.	.	PUNCT
ejpam-1234	375	3	hilbert	hilbert	NOUN
ejpam-1234	375	4	schemes	scheme	NOUN
ejpam-1234	375	5	and	and	CCONJ
ejpam-1234	375	6	wreath	wreath	NOUN
ejpam-1234	375	7	products	product	NOUN
ejpam-1234	375	8	orbifolds	orbifold	VERB
ejpam-1234	375	9	in	in	ADP
ejpam-1234	375	10	this	this	DET
ejpam-1234	375	11	section	section	NOUN
ejpam-1234	375	12	,	,	PUNCT
ejpam-1234	375	13	we	we	PRON
ejpam-1234	375	14	will	will	AUX
ejpam-1234	375	15	relate	relate	VERB
ejpam-1234	375	16	the	the	DET
ejpam-1234	375	17	wreath	wreath	NOUN
ejpam-1234	375	18	product	product	NOUN
ejpam-1234	375	19	orbifold	orbifold	NOUN
ejpam-1234	375	20	associated	associate	VERB
ejpam-1234	375	21	to	to	ADP
ejpam-1234	375	22	a	a	DET
ejpam-1234	375	23	g	g	NOUN
ejpam-1234	375	24	-	-	PUNCT
ejpam-1234	375	25	variety	variety	NOUN
ejpam-1234	375	26	x	x	NOUN
ejpam-1234	375	27	to	to	ADP
ejpam-1234	375	28	the	the	DET
ejpam-1234	375	29	hilbert	hilbert	NOUN
ejpam-1234	375	30	scheme	scheme	NOUN
ejpam-1234	375	31	of	of	ADP
ejpam-1234	375	32	n	n	NOUN
ejpam-1234	375	33	-	-	PUNCT
ejpam-1234	375	34	points	point	NOUN
ejpam-1234	375	35	on	on	ADP
ejpam-1234	375	36	y	y	PROPN
ejpam-1234	375	37	when	when	SCONJ
ejpam-1234	375	38	y	y	PROPN
ejpam-1234	375	39	is	be	AUX
ejpam-1234	375	40	a	a	DET
ejpam-1234	375	41	crepant	crepant	ADJ
ejpam-1234	375	42	resolution	resolution	NOUN
ejpam-1234	375	43	of	of	ADP
ejpam-1234	375	44	x	x	PROPN
ejpam-1234	375	45	/	/	SYM
ejpam-1234	375	46	g.	g.	NOUN
ejpam-1234	375	47	throughout	throughout	ADP
ejpam-1234	375	48	the	the	DET
ejpam-1234	375	49	section	section	NOUN
ejpam-1234	375	50	,	,	PUNCT
ejpam-1234	375	51	all	all	DET
ejpam-1234	375	52	vector	vector	NOUN
ejpam-1234	375	53	spaces	space	NOUN
ejpam-1234	375	54	are	be	AUX
ejpam-1234	375	55	over	over	ADP
ejpam-1234	375	56	c	c	PROPN
ejpam-1234	376	1	and	and	CCONJ
ejpam-1234	376	2	we	we	PRON
ejpam-1234	376	3	will	will	AUX
ejpam-1234	376	4	work	work	VERB
ejpam-1234	376	5	in	in	ADP
ejpam-1234	376	6	the	the	DET
ejpam-1234	376	7	algebraic	algebraic	ADJ
ejpam-1234	376	8	category	category	NOUN
ejpam-1234	376	9	.	.	PUNCT
ejpam-1234	377	1	definition	definition	NOUN
ejpam-1234	377	2	6	6	NUM
ejpam-1234	377	3	.	.	PUNCT
ejpam-1234	378	1	let	let	VERB
ejpam-1234	378	2	w	w	NOUN
ejpam-1234	378	3	be	be	AUX
ejpam-1234	378	4	a	a	DET
ejpam-1234	378	5	normal	normal	ADJ
ejpam-1234	378	6	variety	variety	NOUN
ejpam-1234	378	7	over	over	ADP
ejpam-1234	378	8	c	c	PROPN
ejpam-1234	378	9	and	and	CCONJ
ejpam-1234	378	10	let	let	VERB
ejpam-1234	378	11	l	l	NOUN
ejpam-1234	378	12	be	be	AUX
ejpam-1234	378	13	a	a	DET
ejpam-1234	378	14	rank	rank	NOUN
ejpam-1234	378	15	1	1	NUM
ejpam-1234	378	16	,	,	PUNCT
ejpam-1234	378	17	torsion	torsion	NOUN
ejpam-1234	378	18	free	free	ADJ
ejpam-1234	378	19	,	,	PUNCT
ejpam-1234	378	20	coherent	coherent	ADJ
ejpam-1234	378	21	sheaf	sheaf	NOUN
ejpam-1234	378	22	of	of	ADP
ejpam-1234	378	23	ow	ow	INTJ
ejpam-1234	378	24	-module	-module	NOUN
ejpam-1234	378	25	over	over	ADP
ejpam-1234	378	26	w.	w.	PROPN
ejpam-1234	378	27	l	l	PROPN
ejpam-1234	378	28	is	be	AUX
ejpam-1234	378	29	called	call	VERB
ejpam-1234	378	30	divisorial	divisorial	ADJ
ejpam-1234	378	31	[	[	X
ejpam-1234	378	32	20	20	NUM
ejpam-1234	378	33	]	]	PUNCT
ejpam-1234	378	34	if	if	SCONJ
ejpam-1234	378	35	and	and	CCONJ
ejpam-1234	378	36	only	only	ADV
ejpam-1234	378	37	if	if	SCONJ
ejpam-1234	378	38	any	any	DET
ejpam-1234	378	39	torsion	torsion	NOUN
ejpam-1234	378	40	free	free	ADJ
ejpam-1234	378	41	coherent	coherent	ADJ
ejpam-1234	378	42	sheaf	sheaf	NOUN
ejpam-1234	378	43	of	of	ADP
ejpam-1234	378	44	ow	ow	PROPN
ejpam-1234	378	45	-module	-module	PROPN
ejpam-1234	378	46	,	,	PUNCT
ejpam-1234	378	47	m	m	VERB
ejpam-1234	378	48	,	,	PUNCT
ejpam-1234	378	49	such	such	ADJ
ejpam-1234	378	50	that	that	SCONJ
ejpam-1234	378	51	l	l	NOUN
ejpam-1234	378	52	⊂m	⊂m	PROPN
ejpam-1234	378	53	and	and	CCONJ
ejpam-1234	378	54	supp(m	supp(m	NOUN
ejpam-1234	378	55	/l	/l	PUNCT
ejpam-1234	378	56	)	)	PUNCT
ejpam-1234	378	57	has	have	VERB
ejpam-1234	378	58	codimension	codimension	NOUN
ejpam-1234	378	59	≥	≥	NOUN
ejpam-1234	378	60	2	2	NUM
ejpam-1234	378	61	,	,	PUNCT
ejpam-1234	378	62	coincides	coincide	VERB
ejpam-1234	378	63	with	with	ADP
ejpam-1234	378	64	l	l	PROPN
ejpam-1234	378	65	.	.	PUNCT
ejpam-1234	379	1	remark	remark	NOUN
ejpam-1234	379	2	6	6	NUM
ejpam-1234	379	3	.	.	PUNCT
ejpam-1234	380	1	let	let	VERB
ejpam-1234	380	2	l	l	NOUN
ejpam-1234	380	3	be	be	AUX
ejpam-1234	380	4	divisorial	divisorial	ADJ
ejpam-1234	380	5	.	.	PUNCT
ejpam-1234	381	1	if	if	SCONJ
ejpam-1234	381	2	w	w	NOUN
ejpam-1234	381	3	0	0	NUM
ejpam-1234	381	4	⊂w	⊂w	PROPN
ejpam-1234	381	5	is	be	AUX
ejpam-1234	381	6	a	a	DET
ejpam-1234	381	7	non	non	ADJ
ejpam-1234	381	8	-	-	ADJ
ejpam-1234	381	9	singular	singular	ADJ
ejpam-1234	381	10	open	open	ADJ
ejpam-1234	381	11	subvariety	subvariety	NOUN
ejpam-1234	381	12	such	such	ADJ
ejpam-1234	381	13	that	that	SCONJ
ejpam-1234	381	14	w\w	w\w	PROPN
ejpam-1234	381	15	0	0	PROPN
ejpam-1234	381	16	has	have	VERB
ejpam-1234	381	17	codimension	codimension	NOUN
ejpam-1234	381	18	≥	≥	NOUN
ejpam-1234	381	19	2	2	NUM
ejpam-1234	381	20	,	,	PUNCT
ejpam-1234	381	21	then	then	ADV
ejpam-1234	381	22	l	l	PROPN
ejpam-1234	381	23	|x	|x	PROPN
ejpam-1234	381	24	0	0	NUM
ejpam-1234	381	25	is	be	AUX
ejpam-1234	381	26	invertible	invertible	ADJ
ejpam-1234	381	27	and	and	CCONJ
ejpam-1234	381	28	l	l	NOUN
ejpam-1234	381	29	=	=	SYM
ejpam-1234	381	30	j∗(l	j∗(l	PROPN
ejpam-1234	381	31	|x	|x	NOUN
ejpam-1234	381	32	0	0	NUM
ejpam-1234	381	33	)	)	PUNCT
ejpam-1234	382	1	[	[	X
ejpam-1234	382	2	20	20	NUM
ejpam-1234	382	3	]	]	PUNCT
ejpam-1234	382	4	,	,	PUNCT
ejpam-1234	382	5	where	where	SCONJ
ejpam-1234	382	6	j	j	NOUN
ejpam-1234	382	7	:	:	PUNCT
ejpam-1234	382	8	w	w	NOUN
ejpam-1234	382	9	0	0	NUM
ejpam-1234	382	10	,	,	PUNCT
ejpam-1234	382	11	→	→	SYM
ejpam-1234	382	12	w	w	ADP
ejpam-1234	382	13	tomoo	tomoo	VERB
ejpam-1234	382	14	matsumura	matsumura	ADJ
ejpam-1234	382	15	/	/	SYM
ejpam-1234	382	16	eur	eur	PROPN
ejpam-1234	382	17	.	.	PUNCT
ejpam-1234	383	1	j.	j.	PROPN
ejpam-1234	383	2	pure	pure	PROPN
ejpam-1234	383	3	appl	appl	PROPN
ejpam-1234	383	4	.	.	PROPN
ejpam-1234	383	5	math	math	PROPN
ejpam-1234	383	6	,	,	PUNCT
ejpam-1234	383	7	5	5	NUM
ejpam-1234	383	8	(	(	PUNCT
ejpam-1234	383	9	2012	2012	NUM
ejpam-1234	383	10	)	)	PUNCT
ejpam-1234	383	11	,	,	PUNCT
ejpam-1234	383	12	492	492	NUM
ejpam-1234	383	13	-	-	SYM
ejpam-1234	383	14	510	510	NUM
ejpam-1234	383	15	505	505	NUM
ejpam-1234	383	16	denotes	denote	NOUN
ejpam-1234	383	17	the	the	DET
ejpam-1234	383	18	canonical	canonical	ADJ
ejpam-1234	383	19	inclusion	inclusion	NOUN
ejpam-1234	383	20	.	.	PUNCT
ejpam-1234	384	1	let	let	VERB
ejpam-1234	384	2	kw	kw	INTJ
ejpam-1234	384	3	be	be	AUX
ejpam-1234	384	4	the	the	DET
ejpam-1234	384	5	canonical	canonical	ADJ
ejpam-1234	384	6	divisor	divisor	NOUN
ejpam-1234	384	7	of	of	ADP
ejpam-1234	384	8	w.	w.	NOUN
ejpam-1234	384	9	by	by	ADP
ejpam-1234	384	10	proposition	proposition	NOUN
ejpam-1234	384	11	(	(	PUNCT
ejpam-1234	384	12	7	7	NUM
ejpam-1234	384	13	)	)	PUNCT
ejpam-1234	384	14	in	in	ADP
ejpam-1234	384	15	[	[	X
ejpam-1234	384	16	20	20	NUM
ejpam-1234	384	17	]	]	PUNCT
ejpam-1234	384	18	,	,	PUNCT
ejpam-1234	384	19	the	the	DET
ejpam-1234	384	20	canonical	canonical	ADJ
ejpam-1234	384	21	sheaf	sheaf	NOUN
ejpam-1234	384	22	ωw	ωw	NOUN
ejpam-1234	384	23	:	:	PUNCT
ejpam-1234	384	24	=	=	SYM
ejpam-1234	384	25	o(kw	o(kw	NOUN
ejpam-1234	384	26	)	)	PUNCT
ejpam-1234	384	27	of	of	ADP
ejpam-1234	384	28	w	w	PROPN
ejpam-1234	384	29	is	be	AUX
ejpam-1234	384	30	divisorial	divisorial	ADJ
ejpam-1234	384	31	.	.	PUNCT
ejpam-1234	385	1	hence	hence	ADV
ejpam-1234	385	2	,	,	PUNCT
ejpam-1234	385	3	we	we	PRON
ejpam-1234	385	4	have	have	VERB
ejpam-1234	385	5	ωw	ωw	NUM
ejpam-1234	385	6	=	=	SYM
ejpam-1234	385	7	j∗ωw0	j∗ωw0	PROPN
ejpam-1234	385	8	since	since	SCONJ
ejpam-1234	385	9	ωw	ωw	PRON
ejpam-1234	385	10	|w0	|w0	NOUN
ejpam-1234	385	11	=	=	NOUN
ejpam-1234	385	12	ωw	ωw	NOUN
ejpam-1234	385	13	0	0	NUM
ejpam-1234	385	14	.	.	PUNCT
ejpam-1234	386	1	definition	definition	NOUN
ejpam-1234	386	2	7	7	NUM
ejpam-1234	386	3	.	.	PUNCT
ejpam-1234	387	1	let	let	VERB
ejpam-1234	387	2	w	w	NOUN
ejpam-1234	387	3	and	and	CCONJ
ejpam-1234	387	4	y	y	PROPN
ejpam-1234	387	5	be	be	AUX
ejpam-1234	387	6	normal	normal	ADJ
ejpam-1234	387	7	varieties	variety	NOUN
ejpam-1234	387	8	.	.	PUNCT
ejpam-1234	388	1	a	a	DET
ejpam-1234	388	2	birational	birational	ADJ
ejpam-1234	388	3	morphism	morphism	NOUN
ejpam-1234	388	4	π	π	NOUN
ejpam-1234	388	5	:	:	PUNCT
ejpam-1234	388	6	y	y	PROPN
ejpam-1234	388	7	→	→	PUNCT
ejpam-1234	388	8	w	w	PROPN
ejpam-1234	388	9	is	be	AUX
ejpam-1234	388	10	crepant	crepant	ADJ
ejpam-1234	388	11	if	if	SCONJ
ejpam-1234	388	12	ωy	ωy	PROPN
ejpam-1234	388	13	∼=	∼=	VERB
ejpam-1234	388	14	π∗ωw	π∗ωw	NOUN
ejpam-1234	388	15	.	.	PUNCT
ejpam-1234	389	1	a	a	DET
ejpam-1234	389	2	normal	normal	ADJ
ejpam-1234	389	3	variety	variety	NOUN
ejpam-1234	389	4	w	w	NOUN
ejpam-1234	389	5	is	be	AUX
ejpam-1234	389	6	gorenstein	gorenstein	ADJ
ejpam-1234	389	7	if	if	SCONJ
ejpam-1234	390	1	and	and	CCONJ
ejpam-1234	390	2	only	only	ADV
ejpam-1234	390	3	if	if	SCONJ
ejpam-1234	390	4	all	all	PRON
ejpam-1234	390	5	of	of	ADP
ejpam-1234	390	6	the	the	DET
ejpam-1234	390	7	local	local	ADJ
ejpam-1234	390	8	rings	ring	NOUN
ejpam-1234	390	9	are	be	AUX
ejpam-1234	390	10	cohen	cohen	NOUN
ejpam-1234	390	11	-	-	PUNCT
ejpam-1234	390	12	macaulay	macaulay	PROPN
ejpam-1234	390	13	and	and	CCONJ
ejpam-1234	390	14	kw	kw	PROPN
ejpam-1234	390	15	is	be	AUX
ejpam-1234	390	16	cartier	carti	ADJ
ejpam-1234	390	17	.	.	PUNCT
ejpam-1234	391	1	lemma	lemma	PROPN
ejpam-1234	391	2	5	5	X
ejpam-1234	391	3	.	.	PUNCT
ejpam-1234	392	1	let	let	VERB
ejpam-1234	392	2	w	w	NOUN
ejpam-1234	392	3	and	and	CCONJ
ejpam-1234	392	4	y	y	PROPN
ejpam-1234	392	5	be	be	AUX
ejpam-1234	392	6	gorenstein	gorenstein	ADJ
ejpam-1234	392	7	varieties	variety	NOUN
ejpam-1234	392	8	.	.	PUNCT
ejpam-1234	393	1	if	if	SCONJ
ejpam-1234	393	2	π	π	X
ejpam-1234	393	3	:	:	PUNCT
ejpam-1234	393	4	y	y	PROPN
ejpam-1234	393	5	→	→	PUNCT
ejpam-1234	393	6	w	w	NOUN
ejpam-1234	393	7	is	be	AUX
ejpam-1234	393	8	birational	birational	ADJ
ejpam-1234	393	9	,	,	PUNCT
ejpam-1234	393	10	then	then	ADV
ejpam-1234	393	11	π∗kx	π∗kx	PROPN
ejpam-1234	393	12	is	be	AUX
ejpam-1234	393	13	divisorial	divisorial	ADJ
ejpam-1234	393	14	.	.	PUNCT
ejpam-1234	394	1	proof	proof	NOUN
ejpam-1234	394	2	.	.	PUNCT
ejpam-1234	395	1	let	let	VERB
ejpam-1234	395	2	dim	dim	ADJ
ejpam-1234	395	3	w	w	NOUN
ejpam-1234	395	4	=	=	PUNCT
ejpam-1234	395	5	dim	dim	ADJ
ejpam-1234	395	6	y	y	NOUN
ejpam-1234	395	7	=	=	SYM
ejpam-1234	395	8	n.	n.	PROPN
ejpam-1234	395	9	since	since	SCONJ
ejpam-1234	395	10	kw	kw	PROPN
ejpam-1234	395	11	is	be	AUX
ejpam-1234	395	12	cartier	carti	ADJ
ejpam-1234	395	13	,	,	PUNCT
ejpam-1234	395	14	π∗kw	π∗kw	PROPN
ejpam-1234	395	15	is	be	AUX
ejpam-1234	395	16	also	also	ADV
ejpam-1234	395	17	cartier	cartier	ADJ
ejpam-1234	395	18	.	.	PUNCT
ejpam-1234	396	1	hence	hence	ADV
ejpam-1234	396	2	,	,	PUNCT
ejpam-1234	396	3	π∗ωw	π∗ωw	PROPN
ejpam-1234	396	4	is	be	AUX
ejpam-1234	396	5	torsion	torsion	NOUN
ejpam-1234	396	6	-	-	PUNCT
ejpam-1234	396	7	free	free	ADJ
ejpam-1234	396	8	and	and	CCONJ
ejpam-1234	396	9	of	of	ADP
ejpam-1234	396	10	rank	rank	NOUN
ejpam-1234	396	11	1	1	NUM
ejpam-1234	396	12	.	.	PUNCT
ejpam-1234	397	1	let	let	VERB
ejpam-1234	397	2	m	m	PRON
ejpam-1234	397	3	be	be	AUX
ejpam-1234	397	4	a	a	DET
ejpam-1234	397	5	torsion	torsion	NOUN
ejpam-1234	397	6	-	-	PUNCT
ejpam-1234	397	7	free	free	ADJ
ejpam-1234	397	8	sheaf	sheaf	NOUN
ejpam-1234	397	9	such	such	ADJ
ejpam-1234	397	10	that	that	SCONJ
ejpam-1234	397	11	π∗ωw	π∗ωw	PROPN
ejpam-1234	397	12	⊂	⊂	X
ejpam-1234	397	13	m	m	PROPN
ejpam-1234	397	14	and	and	CCONJ
ejpam-1234	397	15	the	the	DET
ejpam-1234	397	16	dimension	dimension	NOUN
ejpam-1234	397	17	of	of	ADP
ejpam-1234	397	18	suppm	suppm	PROPN
ejpam-1234	397	19	/π∗ωw	/π∗ωw	PROPN
ejpam-1234	397	20	is	be	AUX
ejpam-1234	397	21	at	at	ADP
ejpam-1234	397	22	most	most	ADJ
ejpam-1234	397	23	n−2	n−2	PROPN
ejpam-1234	397	24	.	.	PUNCT
ejpam-1234	398	1	let	let	VERB
ejpam-1234	398	2	l	l	NOUN
ejpam-1234	398	3	:	:	PUNCT
ejpam-1234	398	4	=	=	SYM
ejpam-1234	398	5	ky−π	ky−π	NOUN
ejpam-1234	398	6	∗kw	∗kw	PUNCT
ejpam-1234	398	7	.	.	PUNCT
ejpam-1234	399	1	l	l	NOUN
ejpam-1234	399	2	is	be	AUX
ejpam-1234	399	3	cartier	cartier	ADJ
ejpam-1234	399	4	and	and	CCONJ
ejpam-1234	399	5	l	l	NOUN
ejpam-1234	399	6	:	:	PUNCT
ejpam-1234	399	7	=	=	PUNCT
ejpam-1234	399	8	o(l	o(l	PROPN
ejpam-1234	399	9	)	)	PUNCT
ejpam-1234	399	10	is	be	AUX
ejpam-1234	399	11	an	an	DET
ejpam-1234	399	12	invertible	invertible	ADJ
ejpam-1234	399	13	sheaf	sheaf	NOUN
ejpam-1234	399	14	.	.	PUNCT
ejpam-1234	400	1	it	it	PRON
ejpam-1234	400	2	follows	follow	VERB
ejpam-1234	400	3	that	that	SCONJ
ejpam-1234	400	4	π∗ωw	π∗ωw	PROPN
ejpam-1234	400	5	⊗l	⊗l	ADJ
ejpam-1234	400	6	∼=ωy	∼=ωy	ADJ
ejpam-1234	400	7	⊂m	⊂m	PROPN
ejpam-1234	400	8	⊗l	⊗l	NOUN
ejpam-1234	400	9	and	and	CCONJ
ejpam-1234	400	10	dim(supp((m	dim(supp((m	NOUN
ejpam-1234	400	11	⊗l	⊗l	ADJ
ejpam-1234	400	12	)	)	PUNCT
ejpam-1234	400	13	/ωy	/ωy	NUM
ejpam-1234	400	14	)	)	PUNCT
ejpam-1234	400	15	)	)	PUNCT
ejpam-1234	400	16	≤	≤	NUM
ejpam-1234	400	17	dim(suppm	dim(suppm	VERB
ejpam-1234	400	18	/π∗ωw	/π∗ωw	INTJ
ejpam-1234	400	19	)	)	PUNCT
ejpam-1234	400	20	≤	≤	NUM
ejpam-1234	400	21	n−	n−	NOUN
ejpam-1234	400	22	2	2	NUM
ejpam-1234	400	23	.	.	PUNCT
ejpam-1234	401	1	since	since	SCONJ
ejpam-1234	401	2	hn−1((m	hn−1((m	NUM
ejpam-1234	401	3	⊗l	⊗l	NOUN
ejpam-1234	401	4	)	)	PUNCT
ejpam-1234	401	5	/ωy	/ωy	PUNCT
ejpam-1234	401	6	)	)	PUNCT
ejpam-1234	401	7	=	=	SYM
ejpam-1234	401	8	0	0	NUM
ejpam-1234	401	9	,	,	PUNCT
ejpam-1234	401	10	we	we	PRON
ejpam-1234	401	11	have	have	VERB
ejpam-1234	401	12	hn(m	hn(m	ADV
ejpam-1234	401	13	⊗l	⊗l	ADJ
ejpam-1234	401	14	)	)	PUNCT
ejpam-1234	402	1	∼=	∼=	PROPN
ejpam-1234	402	2	hn(ωy	hn(ωy	NOUN
ejpam-1234	402	3	)	)	PUNCT
ejpam-1234	403	1	∼=	∼=	NOUN
ejpam-1234	403	2	c	c	NOUN
ejpam-1234	403	3	by	by	ADP
ejpam-1234	403	4	serre	serre	X
ejpam-1234	403	5	duality	duality	NOUN
ejpam-1234	403	6	.	.	PUNCT
ejpam-1234	404	1	hence	hence	ADV
ejpam-1234	404	2	,	,	PUNCT
ejpam-1234	404	3	there	there	PRON
ejpam-1234	404	4	exists	exist	VERB
ejpam-1234	404	5	an	an	DET
ejpam-1234	404	6	element	element	NOUN
ejpam-1234	404	7	in	in	ADP
ejpam-1234	404	8	hom(m	hom(m	PROPN
ejpam-1234	404	9	⊗l	⊗l	NOUN
ejpam-1234	404	10	,	,	PUNCT
ejpam-1234	404	11	ωy	ωy	PROPN
ejpam-1234	404	12	)	)	PUNCT
ejpam-1234	404	13	which	which	PRON
ejpam-1234	404	14	gives	give	VERB
ejpam-1234	404	15	a	a	DET
ejpam-1234	404	16	splitting	splitting	NOUN
ejpam-1234	404	17	of	of	ADP
ejpam-1234	404	18	the	the	DET
ejpam-1234	404	19	short	short	ADJ
ejpam-1234	404	20	exact	exact	ADJ
ejpam-1234	404	21	sequence	sequence	NOUN
ejpam-1234	404	22	0→ωy	0→ωy	NOUN
ejpam-1234	404	23	→m	→m	PUNCT
ejpam-1234	404	24	⊗l	⊗l	NOUN
ejpam-1234	404	25	→	→	SYM
ejpam-1234	404	26	(	(	PUNCT
ejpam-1234	404	27	m	m	NOUN
ejpam-1234	404	28	⊗l	⊗l	ADJ
ejpam-1234	404	29	)	)	PUNCT
ejpam-1234	404	30	/ωy	/ωy	PUNCT
ejpam-1234	405	1	→	→	X
ejpam-1234	405	2	0	0	X
ejpam-1234	405	3	.	.	PUNCT
ejpam-1234	406	1	however	however	ADV
ejpam-1234	406	2	,	,	PUNCT
ejpam-1234	406	3	since	since	SCONJ
ejpam-1234	406	4	m	m	PROPN
ejpam-1234	406	5	⊗l	⊗l	PROPN
ejpam-1234	406	6	is	be	AUX
ejpam-1234	406	7	torsion	torsion	NOUN
ejpam-1234	406	8	-	-	PUNCT
ejpam-1234	406	9	free	free	ADJ
ejpam-1234	406	10	,	,	PUNCT
ejpam-1234	406	11	(	(	PUNCT
ejpam-1234	406	12	m	m	NOUN
ejpam-1234	406	13	⊗l	⊗l	ADJ
ejpam-1234	406	14	)	)	PUNCT
ejpam-1234	406	15	/ωy	/ωy	PUNCT
ejpam-1234	407	1	=	=	NOUN
ejpam-1234	407	2	0	0	X
ejpam-1234	407	3	.	.	PUNCT
ejpam-1234	407	4	theorem	theorem	NOUN
ejpam-1234	407	5	5	5	NUM
ejpam-1234	407	6	.	.	PUNCT
ejpam-1234	408	1	let	let	AUX
ejpam-1234	408	2	w	w	NOUN
ejpam-1234	408	3	and	and	CCONJ
ejpam-1234	408	4	y	y	PROPN
ejpam-1234	408	5	be	be	AUX
ejpam-1234	408	6	normal	normal	ADJ
ejpam-1234	408	7	varieties	variety	NOUN
ejpam-1234	408	8	with	with	ADP
ejpam-1234	408	9	dimension	dimension	NOUN
ejpam-1234	408	10	≥	≥	NOUN
ejpam-1234	408	11	2	2	NUM
ejpam-1234	408	12	.	.	PUNCT
ejpam-1234	408	13	suppose	suppose	VERB
ejpam-1234	408	14	that	that	SCONJ
ejpam-1234	408	15	w\w	w\w	PROPN
ejpam-1234	408	16	0	0	PROPN
ejpam-1234	408	17	has	have	VERB
ejpam-1234	408	18	codimension	codimension	NOUN
ejpam-1234	408	19	≥	≥	NOUN
ejpam-1234	408	20	2	2	NUM
ejpam-1234	408	21	and	and	CCONJ
ejpam-1234	408	22	that	that	SCONJ
ejpam-1234	408	23	y	y	PROPN
ejpam-1234	408	24	n	n	CCONJ
ejpam-1234	408	25	/	/	SYM
ejpam-1234	408	26	σn	σn	PROPN
ejpam-1234	408	27	and	and	CCONJ
ejpam-1234	408	28	w	w	PROPN
ejpam-1234	408	29	n	n	CCONJ
ejpam-1234	408	30	/	/	SYM
ejpam-1234	408	31	σn	σn	NOUN
ejpam-1234	408	32	are	be	AUX
ejpam-1234	408	33	gorenstein	gorenstein	ADJ
ejpam-1234	408	34	.	.	PUNCT
ejpam-1234	409	1	if	if	SCONJ
ejpam-1234	409	2	π	π	X
ejpam-1234	409	3	:	:	PUNCT
ejpam-1234	409	4	y	y	PROPN
ejpam-1234	409	5	→	→	PUNCT
ejpam-1234	409	6	w	w	PROPN
ejpam-1234	409	7	is	be	AUX
ejpam-1234	409	8	a	a	DET
ejpam-1234	409	9	crepant	crepant	ADJ
ejpam-1234	409	10	resolution	resolution	NOUN
ejpam-1234	409	11	,	,	PUNCT
ejpam-1234	409	12	then	then	ADV
ejpam-1234	409	13	the	the	DET
ejpam-1234	409	14	induced	induced	ADJ
ejpam-1234	409	15	map	map	NOUN
ejpam-1234	409	16	π̃	π̃	PROPN
ejpam-1234	409	17	:	:	PUNCT
ejpam-1234	409	18	y	y	PROPN
ejpam-1234	409	19	n	n	CCONJ
ejpam-1234	409	20	/	/	SYM
ejpam-1234	409	21	σn→w	σn→w	PROPN
ejpam-1234	409	22	n	n	CCONJ
ejpam-1234	409	23	/	/	SYM
ejpam-1234	409	24	σn	σn	PROPN
ejpam-1234	409	25	is	be	AUX
ejpam-1234	409	26	crepant	crepant	ADJ
ejpam-1234	409	27	.	.	PUNCT
ejpam-1234	410	1	proof	proof	NOUN
ejpam-1234	410	2	.	.	PUNCT
ejpam-1234	411	1	the	the	DET
ejpam-1234	411	2	smooth	smooth	ADJ
ejpam-1234	411	3	locus	locus	NOUN
ejpam-1234	411	4	of	of	ADP
ejpam-1234	411	5	w	w	PROPN
ejpam-1234	411	6	n	n	CCONJ
ejpam-1234	411	7	/	/	SYM
ejpam-1234	411	8	σn	σn	NOUN
ejpam-1234	411	9	is	be	AUX
ejpam-1234	411	10	equal	equal	ADJ
ejpam-1234	411	11	to	to	ADP
ejpam-1234	411	12	(	(	PUNCT
ejpam-1234	411	13	w	w	NOUN
ejpam-1234	411	14	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	411	15	)	)	PUNCT
ejpam-1234	411	16	/σn	/σn	PUNCT
ejpam-1234	411	17	where	where	SCONJ
ejpam-1234	411	18	∆⋆w	∆⋆w	PROPN
ejpam-1234	411	19	is	be	AUX
ejpam-1234	411	20	the	the	DET
ejpam-1234	411	21	set	set	NOUN
ejpam-1234	411	22	of	of	ADP
ejpam-1234	411	23	points	point	NOUN
ejpam-1234	411	24	in	in	ADP
ejpam-1234	411	25	w	w	NOUN
ejpam-1234	411	26	n	n	NOUN
ejpam-1234	411	27	with	with	ADP
ejpam-1234	411	28	non	non	ADJ
ejpam-1234	411	29	-	-	ADJ
ejpam-1234	411	30	trivial	trivial	ADJ
ejpam-1234	411	31	isotropy	isotropy	NOUN
ejpam-1234	411	32	.	.	PUNCT
ejpam-1234	412	1	let	let	VERB
ejpam-1234	412	2	dy	dy	NOUN
ejpam-1234	412	3	:	:	PUNCT
ejpam-1234	412	4	=	=	SYM
ejpam-1234	412	5	π−1(∆⋆w	π−1(∆⋆w	NOUN
ejpam-1234	412	6	)	)	PUNCT
ejpam-1234	412	7	.	.	PUNCT
ejpam-1234	413	1	let	let	VERB
ejpam-1234	413	2	π̄	π̄	VERB
ejpam-1234	413	3	:	:	PUNCT
ejpam-1234	413	4	y	y	PROPN
ejpam-1234	413	5	n\dy	n\dy	PROPN
ejpam-1234	413	6	→	→	SYM
ejpam-1234	413	7	w	w	X
ejpam-1234	413	8	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	413	9	be	be	VERB
ejpam-1234	413	10	the	the	DET
ejpam-1234	413	11	map	map	NOUN
ejpam-1234	413	12	π×n	π×n	PROPN
ejpam-1234	413	13	restricted	restrict	VERB
ejpam-1234	413	14	to	to	ADP
ejpam-1234	413	15	y	y	PROPN
ejpam-1234	413	16	n\dy	n\dy	PROPN
ejpam-1234	413	17	.	.	PUNCT
ejpam-1234	414	1	since	since	SCONJ
ejpam-1234	414	2	π×n	π×n	PROPN
ejpam-1234	414	3	:	:	PUNCT
ejpam-1234	414	4	y	y	PROPN
ejpam-1234	414	5	n	n	PROPN
ejpam-1234	414	6	→	→	SYM
ejpam-1234	414	7	w	w	NOUN
ejpam-1234	414	8	n	n	PROPN
ejpam-1234	414	9	is	be	AUX
ejpam-1234	414	10	crepant	crepant	ADJ
ejpam-1234	414	11	,	,	PUNCT
ejpam-1234	414	12	ky	ky	PROPN
ejpam-1234	414	13	n	n	PROPN
ejpam-1234	414	14	=	=	SYM
ejpam-1234	415	1	(	(	PUNCT
ejpam-1234	415	2	π×n)∗kw	π×n)∗kw	PROPN
ejpam-1234	415	3	n	n	X
ejpam-1234	415	4	.	.	PUNCT
ejpam-1234	416	1	consider	consider	VERB
ejpam-1234	416	2	the	the	DET
ejpam-1234	416	3	commutative	commutative	ADJ
ejpam-1234	416	4	diagram	diagram	NOUN
ejpam-1234	416	5	y	y	PROPN
ejpam-1234	416	6	n	n	PROPN
ejpam-1234	416	7	←−−−	←−−−	PROPN
ejpam-1234	416	8	y	y	PROPN
ejpam-1234	416	9	n\dy	n\dy	PROPN
ejpam-1234	416	10	π×n	π×n	PROPN
ejpam-1234	416	11			NOUN
ejpam-1234	416	12			NOUN
ejpam-1234	416	13	y	y	PROPN
ejpam-1234	416	14	π̄	π̄	VERB
ejpam-1234	416	15			PROPN
ejpam-1234	416	16			PROPN
ejpam-1234	417	1	y	y	PROPN
ejpam-1234	417	2	w	w	PROPN
ejpam-1234	417	3	n	n	PROPN
ejpam-1234	417	4	←−−−	←−−−	PROPN
ejpam-1234	417	5	w	w	NOUN
ejpam-1234	417	6	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	417	7	where	where	SCONJ
ejpam-1234	417	8	the	the	DET
ejpam-1234	417	9	horizontal	horizontal	ADJ
ejpam-1234	417	10	arrows	arrow	NOUN
ejpam-1234	417	11	are	be	AUX
ejpam-1234	417	12	the	the	DET
ejpam-1234	417	13	obvious	obvious	ADJ
ejpam-1234	417	14	inclusions	inclusion	NOUN
ejpam-1234	417	15	.	.	PUNCT
ejpam-1234	418	1	we	we	PRON
ejpam-1234	418	2	have	have	VERB
ejpam-1234	418	3	ky	ky	PROPN
ejpam-1234	418	4	n\dy	n\dy	PROPN
ejpam-1234	418	5	=	=	SYM
ejpam-1234	418	6	ky	ky	PROPN
ejpam-1234	418	7	n	n	CCONJ
ejpam-1234	418	8	|y	|y	ADJ
ejpam-1234	418	9	n\dy	n\dy	ADJ
ejpam-1234	418	10	=	=	SYM
ejpam-1234	418	11	�	�	PROPN
ejpam-1234	418	12	(	(	PUNCT
ejpam-1234	418	13	π×n)∗kw	π×n)∗kw	PROPN
ejpam-1234	418	14	n	n	CCONJ
ejpam-1234	418	15	�	�	PROPN
ejpam-1234	418	16	|y	|y	NOUN
ejpam-1234	418	17	n\dy	n\dy	ADJ
ejpam-1234	418	18	=	=	SYM
ejpam-1234	418	19	π̄∗(kwn	π̄∗(kwn	PROPN
ejpam-1234	418	20	|w	|w	ADJ
ejpam-1234	418	21	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	418	22	)	)	PUNCT
ejpam-1234	419	1	=	=	SYM
ejpam-1234	419	2	π̄∗kw	π̄∗kw	ADJ
ejpam-1234	419	3	n\∆⋆w	n\∆⋆w	INTJ
ejpam-1234	419	4	.	.	PUNCT
ejpam-1234	420	1	(	(	PUNCT
ejpam-1234	420	2	12	12	NUM
ejpam-1234	420	3	)	)	PUNCT
ejpam-1234	420	4	consider	consider	VERB
ejpam-1234	420	5	the	the	DET
ejpam-1234	420	6	following	follow	VERB
ejpam-1234	420	7	commutative	commutative	ADJ
ejpam-1234	420	8	diagram	diagram	PROPN
ejpam-1234	420	9	y	y	PROPN
ejpam-1234	420	10	n\dy	n\dy	PROPN
ejpam-1234	420	11	q	q	PROPN
ejpam-1234	420	12	−−−→	−−−→	PROPN
ejpam-1234	420	13	(	(	PUNCT
ejpam-1234	420	14	y	y	PROPN
ejpam-1234	420	15	n\dy	n\dy	PROPN
ejpam-1234	420	16	)	)	PUNCT
ejpam-1234	420	17	/σn	/σn	PUNCT
ejpam-1234	421	1	π̄	π̄	VERB
ejpam-1234	421	2			PROPN
ejpam-1234	421	3			PROPN
ejpam-1234	422	1	y	y	PROPN
ejpam-1234	422	2	π̃′	π̃′	PROPN
ejpam-1234	422	3			PROPN
ejpam-1234	422	4			PROPN
ejpam-1234	422	5	y	y	PROPN
ejpam-1234	422	6	w	w	PROPN
ejpam-1234	422	7	n\∆⋆w	n\∆⋆w	PROPN
ejpam-1234	422	8	q′	q′	NUM
ejpam-1234	422	9	−−−→	−−−→	PROPN
ejpam-1234	422	10	(	(	PUNCT
ejpam-1234	422	11	w	w	NOUN
ejpam-1234	422	12	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	422	13	)	)	PUNCT
ejpam-1234	422	14	/σn	/σn	PRON
ejpam-1234	423	1	tomoo	tomoo	VERB
ejpam-1234	423	2	matsumura	matsumura	ADV
ejpam-1234	423	3	/	/	SYM
ejpam-1234	423	4	eur	eur	PROPN
ejpam-1234	423	5	.	.	PUNCT
ejpam-1234	424	1	j.	j.	PROPN
ejpam-1234	424	2	pure	pure	PROPN
ejpam-1234	424	3	appl	appl	PROPN
ejpam-1234	424	4	.	.	PROPN
ejpam-1234	424	5	math	math	PROPN
ejpam-1234	424	6	,	,	PUNCT
ejpam-1234	424	7	5	5	NUM
ejpam-1234	424	8	(	(	PUNCT
ejpam-1234	424	9	2012	2012	NUM
ejpam-1234	424	10	)	)	PUNCT
ejpam-1234	424	11	,	,	PUNCT
ejpam-1234	424	12	492	492	NUM
ejpam-1234	424	13	-	-	SYM
ejpam-1234	424	14	510	510	NUM
ejpam-1234	424	15	506	506	NUM
ejpam-1234	424	16	where	where	SCONJ
ejpam-1234	424	17	q	q	NOUN
ejpam-1234	424	18	and	and	CCONJ
ejpam-1234	424	19	q′	q′	NOUN
ejpam-1234	424	20	are	be	AUX
ejpam-1234	424	21	the	the	DET
ejpam-1234	424	22	canonical	canonical	ADJ
ejpam-1234	424	23	projections	projection	NOUN
ejpam-1234	424	24	.	.	PUNCT
ejpam-1234	425	1	since	since	SCONJ
ejpam-1234	425	2	the	the	DET
ejpam-1234	425	3	actions	action	NOUN
ejpam-1234	425	4	of	of	ADP
ejpam-1234	425	5	σi	σi	PRON
ejpam-1234	425	6	on	on	ADP
ejpam-1234	425	7	y	y	PROPN
ejpam-1234	425	8	n\dy	n\dy	PROPN
ejpam-1234	425	9	and	and	CCONJ
ejpam-1234	425	10	w	w	PROPN
ejpam-1234	425	11	n\∆⋆w	n\∆⋆w	NOUN
ejpam-1234	425	12	are	be	AUX
ejpam-1234	425	13	free	free	ADJ
ejpam-1234	425	14	,	,	PUNCT
ejpam-1234	425	15	equation	equation	NOUN
ejpam-1234	425	16	(	(	PUNCT
ejpam-1234	425	17	12	12	NUM
ejpam-1234	425	18	)	)	PUNCT
ejpam-1234	425	19	implies	imply	VERB
ejpam-1234	425	20	that	that	SCONJ
ejpam-1234	425	21	k(y	k(y	PROPN
ejpam-1234	425	22	n\dy	n\dy	ADV
ejpam-1234	425	23	)	)	PUNCT
ejpam-1234	425	24	/σn	/σn	PUNCT
ejpam-1234	426	1	=	=	PUNCT
ejpam-1234	426	2	π̃′∗k(w	π̃′∗k(w	PUNCT
ejpam-1234	426	3	n\∆⋆	n\∆⋆	PROPN
ejpam-1234	426	4	w	w	PROPN
ejpam-1234	426	5	)	)	PUNCT
ejpam-1234	426	6	/σn	/σn	PUNCT
ejpam-1234	426	7	.	.	PUNCT
ejpam-1234	427	1	hence	hence	ADV
ejpam-1234	427	2	ky	ky	PROPN
ejpam-1234	427	3	n	n	CCONJ
ejpam-1234	427	4	/	/	SYM
ejpam-1234	427	5	σn	σn	PROPN
ejpam-1234	427	6	|(y	|(y	NUM
ejpam-1234	427	7	n\dy	n\dy	ADJ
ejpam-1234	427	8	)	)	PUNCT
ejpam-1234	427	9	/σn	/σn	PUNCT
ejpam-1234	428	1	=	=	PUNCT
ejpam-1234	428	2	�	�	PROPN
ejpam-1234	428	3	π̃∗kw	π̃∗kw	PROPN
ejpam-1234	428	4	n	n	CCONJ
ejpam-1234	428	5	/	/	SYM
ejpam-1234	428	6	σn	σn	PROPN
ejpam-1234	428	7	�	�	PROPN
ejpam-1234	428	8	|(y	|(y	NUM
ejpam-1234	428	9	n\dy	n\dy	PROPN
ejpam-1234	428	10	)	)	PUNCT
ejpam-1234	428	11	/σn	/σn	PUNCT
ejpam-1234	428	12	.	.	PUNCT
ejpam-1234	429	1	since	since	SCONJ
ejpam-1234	429	2	both	both	PRON
ejpam-1234	429	3	ky	ky	PROPN
ejpam-1234	429	4	n	n	CCONJ
ejpam-1234	429	5	/	/	SYM
ejpam-1234	429	6	σn	σn	PROPN
ejpam-1234	429	7	and	and	CCONJ
ejpam-1234	429	8	π̃∗kw	π̃∗kw	PROPN
ejpam-1234	429	9	n	n	CCONJ
ejpam-1234	429	10	/	/	SYM
ejpam-1234	429	11	σn	σn	NOUN
ejpam-1234	429	12	are	be	AUX
ejpam-1234	429	13	divisorial	divisorial	ADJ
ejpam-1234	429	14	(	(	PUNCT
ejpam-1234	429	15	remark	remark	NOUN
ejpam-1234	429	16	6	6	NUM
ejpam-1234	429	17	,	,	PUNCT
ejpam-1234	429	18	lemma	lemma	PROPN
ejpam-1234	429	19	5	5	NUM
ejpam-1234	429	20	)	)	PUNCT
ejpam-1234	429	21	,	,	PUNCT
ejpam-1234	429	22	we	we	PRON
ejpam-1234	429	23	obtain	obtain	VERB
ejpam-1234	429	24	ky	ky	PROPN
ejpam-1234	429	25	n	n	CCONJ
ejpam-1234	429	26	/	/	SYM
ejpam-1234	429	27	σn	σn	NOUN
ejpam-1234	429	28	=	=	PUNCT
ejpam-1234	429	29	π̃∗kw	π̃∗kw	NOUN
ejpam-1234	429	30	n	n	CCONJ
ejpam-1234	429	31	/	/	SYM
ejpam-1234	429	32	σn	σn	PROPN
ejpam-1234	429	33	.	.	PUNCT
ejpam-1234	430	1	remark	remark	PROPN
ejpam-1234	430	2	7	7	NUM
ejpam-1234	430	3	.	.	PUNCT
ejpam-1234	431	1	for	for	ADP
ejpam-1234	431	2	a	a	DET
ejpam-1234	431	3	non	non	ADJ
ejpam-1234	431	4	-	-	ADJ
ejpam-1234	431	5	singular	singular	ADJ
ejpam-1234	431	6	variety	variety	NOUN
ejpam-1234	431	7	x	x	NOUN
ejpam-1234	431	8	with	with	ADP
ejpam-1234	431	9	an	an	DET
ejpam-1234	431	10	action	action	NOUN
ejpam-1234	431	11	of	of	ADP
ejpam-1234	431	12	a	a	DET
ejpam-1234	431	13	finite	finite	ADJ
ejpam-1234	431	14	group	group	NOUN
ejpam-1234	431	15	g	g	PROPN
ejpam-1234	431	16	,	,	PUNCT
ejpam-1234	431	17	the	the	DET
ejpam-1234	431	18	variety	variety	NOUN
ejpam-1234	431	19	x	x	NOUN
ejpam-1234	431	20	/	/	SYM
ejpam-1234	431	21	g	g	PROPN
ejpam-1234	431	22	is	be	AUX
ejpam-1234	431	23	gorenstein	gorenstein	ADJ
ejpam-1234	431	24	if	if	SCONJ
ejpam-1234	431	25	and	and	CCONJ
ejpam-1234	431	26	only	only	ADV
ejpam-1234	431	27	if	if	SCONJ
ejpam-1234	431	28	the	the	DET
ejpam-1234	431	29	age	age	NOUN
ejpam-1234	431	30	of	of	ADP
ejpam-1234	431	31	α	α	NOUN
ejpam-1234	431	32	on	on	ADP
ejpam-1234	431	33	any	any	DET
ejpam-1234	431	34	connected	connected	ADJ
ejpam-1234	431	35	component	component	NOUN
ejpam-1234	431	36	is	be	AUX
ejpam-1234	431	37	an	an	DET
ejpam-1234	431	38	integer	integer	NOUN
ejpam-1234	431	39	for	for	ADP
ejpam-1234	431	40	all	all	DET
ejpam-1234	431	41	α	α	PRON
ejpam-1234	431	42	∈	∈	NOUN
ejpam-1234	431	43	g.	g.	NOUN
ejpam-1234	431	44	see	see	VERB
ejpam-1234	431	45	remark	remark	NOUN
ejpam-1234	431	46	(	(	PUNCT
ejpam-1234	431	47	3.2	3.2	NUM
ejpam-1234	431	48	)	)	PUNCT
ejpam-1234	431	49	in	in	ADP
ejpam-1234	431	50	[	[	X
ejpam-1234	431	51	20	20	NUM
ejpam-1234	431	52	]	]	PUNCT
ejpam-1234	431	53	.	.	PUNCT
ejpam-1234	432	1	if	if	SCONJ
ejpam-1234	432	2	dim	dim	ADJ
ejpam-1234	432	3	x	x	VERB
ejpam-1234	432	4	is	be	AUX
ejpam-1234	432	5	even	even	ADV
ejpam-1234	432	6	and	and	CCONJ
ejpam-1234	432	7	x	x	NOUN
ejpam-1234	432	8	/	/	SYM
ejpam-1234	432	9	g	g	PROPN
ejpam-1234	432	10	is	be	AUX
ejpam-1234	432	11	gorenstein	gorenstein	ADJ
ejpam-1234	432	12	,	,	PUNCT
ejpam-1234	432	13	by	by	ADP
ejpam-1234	432	14	corollary	corollary	ADJ
ejpam-1234	432	15	1	1	NUM
ejpam-1234	432	16	,	,	PUNCT
ejpam-1234	432	17	x	x	NOUN
ejpam-1234	432	18	n	n	CCONJ
ejpam-1234	432	19	/	/	SYM
ejpam-1234	432	20	gn	gn	PROPN
ejpam-1234	432	21	⋊σn	⋊σn	PROPN
ejpam-1234	432	22	is	be	AUX
ejpam-1234	432	23	gorenstein	gorenstein	ADJ
ejpam-1234	432	24	.	.	PUNCT
ejpam-1234	433	1	in	in	ADP
ejpam-1234	433	2	particular	particular	ADJ
ejpam-1234	433	3	,	,	PUNCT
ejpam-1234	433	4	for	for	ADP
ejpam-1234	433	5	a	a	DET
ejpam-1234	433	6	non	non	ADJ
ejpam-1234	433	7	-	-	ADJ
ejpam-1234	433	8	singular	singular	ADJ
ejpam-1234	433	9	variety	variety	NOUN
ejpam-1234	433	10	y	y	PROPN
ejpam-1234	433	11	with	with	ADP
ejpam-1234	433	12	even	even	ADV
ejpam-1234	433	13	(	(	PUNCT
ejpam-1234	433	14	complex	complex	ADJ
ejpam-1234	433	15	)	)	PUNCT
ejpam-1234	433	16	dimension	dimension	NOUN
ejpam-1234	433	17	,	,	PUNCT
ejpam-1234	433	18	the	the	DET
ejpam-1234	433	19	age	age	NOUN
ejpam-1234	433	20	of	of	ADP
ejpam-1234	433	21	the	the	DET
ejpam-1234	433	22	symmetric	symmetric	ADJ
ejpam-1234	433	23	product	product	NOUN
ejpam-1234	433	24	y	y	PROPN
ejpam-1234	433	25	n	n	CCONJ
ejpam-1234	433	26	/	/	SYM
ejpam-1234	433	27	σn	σn	PROPN
ejpam-1234	433	28	is	be	AUX
ejpam-1234	433	29	always	always	ADV
ejpam-1234	433	30	an	an	DET
ejpam-1234	433	31	integer	integer	NOUN
ejpam-1234	433	32	so	so	SCONJ
ejpam-1234	433	33	that	that	SCONJ
ejpam-1234	433	34	y	y	PROPN
ejpam-1234	433	35	n	n	CCONJ
ejpam-1234	433	36	/	/	SYM
ejpam-1234	433	37	σn	σn	PROPN
ejpam-1234	433	38	is	be	AUX
ejpam-1234	433	39	gorenstein	gorenstein	ADJ
ejpam-1234	433	40	.	.	PUNCT
ejpam-1234	434	1	if	if	SCONJ
ejpam-1234	434	2	y	y	PROPN
ejpam-1234	434	3	is	be	AUX
ejpam-1234	434	4	a	a	DET
ejpam-1234	434	5	smooth	smooth	ADJ
ejpam-1234	434	6	projective	projective	ADJ
ejpam-1234	434	7	surface	surface	NOUN
ejpam-1234	434	8	,	,	PUNCT
ejpam-1234	434	9	then	then	ADV
ejpam-1234	434	10	the	the	DET
ejpam-1234	434	11	hilbert	hilbert	PROPN
ejpam-1234	434	12	-	-	PUNCT
ejpam-1234	434	13	chow	chow	PROPN
ejpam-1234	434	14	morphism	morphism	NOUN
ejpam-1234	434	15	y	y	PROPN
ejpam-1234	434	16	[	[	X
ejpam-1234	434	17	n	n	X
ejpam-1234	434	18	]	]	PUNCT
ejpam-1234	434	19	→	→	SYM
ejpam-1234	434	20	y	y	PROPN
ejpam-1234	434	21	n	n	CCONJ
ejpam-1234	434	22	/	/	SYM
ejpam-1234	434	23	σn	σn	PROPN
ejpam-1234	434	24	is	be	AUX
ejpam-1234	434	25	a	a	DET
ejpam-1234	434	26	resolution	resolution	NOUN
ejpam-1234	434	27	of	of	ADP
ejpam-1234	434	28	singularities	singularity	NOUN
ejpam-1234	434	29	[	[	X
ejpam-1234	434	30	8	8	NUM
ejpam-1234	434	31	]	]	PUNCT
ejpam-1234	434	32	,	,	PUNCT
ejpam-1234	434	33	which	which	PRON
ejpam-1234	434	34	is	be	AUX
ejpam-1234	434	35	also	also	ADV
ejpam-1234	434	36	crepant	crepant	ADJ
ejpam-1234	434	37	[	[	X
ejpam-1234	434	38	1	1	NUM
ejpam-1234	434	39	]	]	PUNCT
ejpam-1234	434	40	.	.	PUNCT
ejpam-1234	435	1	hence	hence	ADV
ejpam-1234	435	2	,	,	PUNCT
ejpam-1234	435	3	together	together	ADV
ejpam-1234	435	4	with	with	ADP
ejpam-1234	435	5	theorem	theorem	ADJ
ejpam-1234	435	6	5	5	NUM
ejpam-1234	435	7	and	and	CCONJ
ejpam-1234	435	8	remark	remark	NOUN
ejpam-1234	435	9	7	7	NUM
ejpam-1234	435	10	,	,	PUNCT
ejpam-1234	435	11	we	we	PRON
ejpam-1234	435	12	obtain	obtain	VERB
ejpam-1234	435	13	the	the	DET
ejpam-1234	435	14	following	follow	VERB
ejpam-1234	435	15	statement	statement	NOUN
ejpam-1234	435	16	conjectured	conjecture	VERB
ejpam-1234	435	17	on	on	ADP
ejpam-1234	435	18	p.20	p.20	X
ejpam-1234	435	19	of	of	ADP
ejpam-1234	435	20	[	[	X
ejpam-1234	435	21	25	25	NUM
ejpam-1234	435	22	]	]	PUNCT
ejpam-1234	435	23	:	:	PUNCT
ejpam-1234	435	24	corollary	corollary	ADJ
ejpam-1234	435	25	2	2	X
ejpam-1234	435	26	.	.	PUNCT
ejpam-1234	436	1	let	let	VERB
ejpam-1234	436	2	x	x	PRON
ejpam-1234	436	3	be	be	AUX
ejpam-1234	436	4	a	a	DET
ejpam-1234	436	5	smooth	smooth	ADJ
ejpam-1234	436	6	projective	projective	ADJ
ejpam-1234	436	7	surface	surface	NOUN
ejpam-1234	436	8	with	with	ADP
ejpam-1234	436	9	an	an	DET
ejpam-1234	436	10	action	action	NOUN
ejpam-1234	436	11	of	of	ADP
ejpam-1234	436	12	a	a	DET
ejpam-1234	436	13	finite	finite	ADJ
ejpam-1234	436	14	group	group	NOUN
ejpam-1234	436	15	g.	g.	PROPN
ejpam-1234	436	16	suppose	suppose	VERB
ejpam-1234	436	17	that	that	SCONJ
ejpam-1234	436	18	x	x	X
ejpam-1234	436	19	/	/	SYM
ejpam-1234	436	20	g	g	PROPN
ejpam-1234	436	21	is	be	AUX
ejpam-1234	436	22	gorenstein	gorenstein	ADJ
ejpam-1234	436	23	.	.	PUNCT
ejpam-1234	437	1	if	if	SCONJ
ejpam-1234	437	2	π	π	X
ejpam-1234	437	3	:	:	PUNCT
ejpam-1234	437	4	y	y	PROPN
ejpam-1234	437	5	→	→	SYM
ejpam-1234	437	6	x	x	X
ejpam-1234	437	7	/	/	SYM
ejpam-1234	437	8	g	g	PROPN
ejpam-1234	437	9	is	be	AUX
ejpam-1234	437	10	a	a	DET
ejpam-1234	437	11	crepant	crepant	ADJ
ejpam-1234	437	12	resolution	resolution	NOUN
ejpam-1234	437	13	,	,	PUNCT
ejpam-1234	437	14	then	then	ADV
ejpam-1234	437	15	y	y	PROPN
ejpam-1234	437	16	[	[	X
ejpam-1234	437	17	n]→w	n]→w	PRON
ejpam-1234	437	18	n	n	CCONJ
ejpam-1234	437	19	/	/	SYM
ejpam-1234	437	20	σn	σn	PROPN
ejpam-1234	437	21	is	be	AUX
ejpam-1234	437	22	a	a	DET
ejpam-1234	437	23	crepant	crepant	ADJ
ejpam-1234	437	24	resolution	resolution	NOUN
ejpam-1234	437	25	.	.	PUNCT
ejpam-1234	438	1	together	together	ADV
ejpam-1234	438	2	with	with	ADP
ejpam-1234	438	3	theorem	theorem	NOUN
ejpam-1234	438	4	4	4	NUM
ejpam-1234	438	5	,	,	PUNCT
ejpam-1234	438	6	we	we	PRON
ejpam-1234	438	7	obtain	obtain	VERB
ejpam-1234	438	8	the	the	DET
ejpam-1234	438	9	following	follow	VERB
ejpam-1234	438	10	result	result	NOUN
ejpam-1234	438	11	.	.	PUNCT
ejpam-1234	439	1	theorem	theorem	ADJ
ejpam-1234	439	2	6	6	NUM
ejpam-1234	439	3	.	.	PUNCT
ejpam-1234	440	1	let	let	VERB
ejpam-1234	440	2	y	y	PRON
ejpam-1234	440	3	be	be	AUX
ejpam-1234	440	4	a	a	DET
ejpam-1234	440	5	smooth	smooth	ADJ
ejpam-1234	440	6	projective	projective	ADJ
ejpam-1234	440	7	surface	surface	NOUN
ejpam-1234	440	8	with	with	ADP
ejpam-1234	440	9	trivial	trivial	ADJ
ejpam-1234	440	10	canonical	canonical	ADJ
ejpam-1234	440	11	class	class	NOUN
ejpam-1234	440	12	.	.	PUNCT
ejpam-1234	441	1	let	let	VERB
ejpam-1234	441	2	x	x	PRON
ejpam-1234	441	3	be	be	AUX
ejpam-1234	441	4	a	a	DET
ejpam-1234	441	5	smooth	smooth	ADJ
ejpam-1234	441	6	projective	projective	ADJ
ejpam-1234	441	7	surface	surface	NOUN
ejpam-1234	441	8	with	with	ADP
ejpam-1234	441	9	an	an	DET
ejpam-1234	441	10	action	action	NOUN
ejpam-1234	441	11	of	of	ADP
ejpam-1234	441	12	g	g	NOUN
ejpam-1234	441	13	such	such	ADJ
ejpam-1234	441	14	that	that	SCONJ
ejpam-1234	441	15	x	x	X
ejpam-1234	441	16	/	/	SYM
ejpam-1234	441	17	g	g	PROPN
ejpam-1234	441	18	is	be	AUX
ejpam-1234	441	19	gorenstein	gorenstein	ADJ
ejpam-1234	441	20	.	.	PUNCT
ejpam-1234	442	1	suppose	suppose	VERB
ejpam-1234	442	2	that	that	SCONJ
ejpam-1234	442	3	π	π	PRON
ejpam-1234	442	4	:	:	PUNCT
ejpam-1234	442	5	y	y	PROPN
ejpam-1234	442	6	→	→	SYM
ejpam-1234	442	7	x	x	X
ejpam-1234	442	8	/	/	SYM
ejpam-1234	442	9	g	g	PROPN
ejpam-1234	442	10	is	be	AUX
ejpam-1234	442	11	a	a	DET
ejpam-1234	442	12	crepant	crepant	ADJ
ejpam-1234	442	13	resolution	resolution	NOUN
ejpam-1234	442	14	and	and	CCONJ
ejpam-1234	442	15	that	that	SCONJ
ejpam-1234	442	16	h∗(y	h∗(y	PROPN
ejpam-1234	442	17	)	)	PUNCT
ejpam-1234	442	18	∼=	∼=	PROPN
ejpam-1234	442	19	h∗	h∗	NOUN
ejpam-1234	442	20	or	or	CCONJ
ejpam-1234	442	21	b	b	PROPN
ejpam-1234	442	22	(	(	PUNCT
ejpam-1234	442	23	[	[	X
ejpam-1234	442	24	x	x	X
ejpam-1234	442	25	/	/	SYM
ejpam-1234	442	26	g	g	NOUN
ejpam-1234	442	27	]	]	PUNCT
ejpam-1234	442	28	)	)	PUNCT
ejpam-1234	442	29	as	as	ADP
ejpam-1234	442	30	frobenius	frobenius	NOUN
ejpam-1234	442	31	algebras	algebra	NOUN
ejpam-1234	442	32	,	,	PUNCT
ejpam-1234	442	33	then	then	ADV
ejpam-1234	442	34	y	y	PROPN
ejpam-1234	443	1	[	[	X
ejpam-1234	443	2	n]→	n]→	X
ejpam-1234	443	3	x	x	SYM
ejpam-1234	443	4	n	n	CCONJ
ejpam-1234	443	5	/	/	SYM
ejpam-1234	443	6	σn	σn	PROPN
ejpam-1234	443	7	is	be	AUX
ejpam-1234	443	8	a	a	DET
ejpam-1234	443	9	hyper	hyper	ADJ
ejpam-1234	443	10	-	-	ADJ
ejpam-1234	443	11	kähler	kähler	NOUN
ejpam-1234	443	12	resolution	resolution	NOUN
ejpam-1234	443	13	and	and	CCONJ
ejpam-1234	443	14	h∗(y	h∗(y	PROPN
ejpam-1234	443	15	[	[	X
ejpam-1234	443	16	n	n	X
ejpam-1234	443	17	]	]	PUNCT
ejpam-1234	443	18	)	)	PUNCT
ejpam-1234	443	19	is	be	AUX
ejpam-1234	443	20	isomorphic	isomorphic	ADJ
ejpam-1234	443	21	as	as	ADP
ejpam-1234	443	22	a	a	DET
ejpam-1234	443	23	ring	ring	NOUN
ejpam-1234	443	24	to	to	ADP
ejpam-1234	443	25	h∗	h∗	PROPN
ejpam-1234	443	26	or	or	CCONJ
ejpam-1234	443	27	b	b	PROPN
ejpam-1234	443	28	(	(	PUNCT
ejpam-1234	443	29	[	[	X
ejpam-1234	443	30	x	x	X
ejpam-1234	443	31	n	n	CCONJ
ejpam-1234	443	32	/	/	SYM
ejpam-1234	443	33	gn	gn	PROPN
ejpam-1234	443	34	⋊σn	⋊σn	PROPN
ejpam-1234	443	35	]	]	PUNCT
ejpam-1234	443	36	)	)	PUNCT
ejpam-1234	443	37	.	.	PUNCT
ejpam-1234	444	1	proof	proof	NOUN
ejpam-1234	444	2	.	.	PUNCT
ejpam-1234	445	1	we	we	PRON
ejpam-1234	445	2	have	have	VERB
ejpam-1234	445	3	h	h	NOUN
ejpam-1234	445	4	(	(	PUNCT
ejpam-1234	445	5	y	y	PROPN
ejpam-1234	445	6	n	n	CCONJ
ejpam-1234	445	7	,	,	PUNCT
ejpam-1234	445	8	σn	σn	NOUN
ejpam-1234	445	9	)	)	PUNCT
ejpam-1234	445	10	∼=	∼=	PROPN
ejpam-1234	445	11	h∗(y	h∗(y	NOUN
ejpam-1234	445	12	)	)	PUNCT
ejpam-1234	445	13	{	{	PUNCT
ejpam-1234	445	14	σn	σn	NOUN
ejpam-1234	445	15	}	}	PUNCT
ejpam-1234	445	16	∼=	∼=	PROPN
ejpam-1234	445	17	h∗	h∗	NOUN
ejpam-1234	445	18	or	or	CCONJ
ejpam-1234	445	19	b	b	NOUN
ejpam-1234	445	20	(	(	PUNCT
ejpam-1234	445	21	[	[	X
ejpam-1234	445	22	x	x	X
ejpam-1234	445	23	/	/	SYM
ejpam-1234	445	24	g]){σn	g]){σn	NOUN
ejpam-1234	445	25	}	}	PUNCT
ejpam-1234	445	26	∼=h	∼=h	NOUN
ejpam-1234	445	27	(	(	PUNCT
ejpam-1234	445	28	x	x	NOUN
ejpam-1234	445	29	n	n	CCONJ
ejpam-1234	445	30	,	,	PUNCT
ejpam-1234	445	31	gn⋊σn	gn⋊σn	PROPN
ejpam-1234	445	32	)	)	PUNCT
ejpam-1234	446	1	gn	gn	PROPN
ejpam-1234	446	2	where	where	SCONJ
ejpam-1234	446	3	the	the	DET
ejpam-1234	446	4	first	first	ADJ
ejpam-1234	446	5	equality	equality	NOUN
ejpam-1234	446	6	is	be	AUX
ejpam-1234	446	7	due	due	ADJ
ejpam-1234	446	8	to	to	ADP
ejpam-1234	446	9	[	[	X
ejpam-1234	446	10	7	7	NUM
ejpam-1234	446	11	]	]	PUNCT
ejpam-1234	446	12	and	and	CCONJ
ejpam-1234	446	13	the	the	DET
ejpam-1234	446	14	third	third	NOUN
ejpam-1234	446	15	is	be	AUX
ejpam-1234	446	16	theorem	theorem	VERB
ejpam-1234	446	17	4	4	NUM
ejpam-1234	446	18	.	.	PUNCT
ejpam-1234	447	1	since	since	SCONJ
ejpam-1234	447	2	h∗(y	h∗(y	PROPN
ejpam-1234	447	3	[	[	X
ejpam-1234	447	4	n	n	X
ejpam-1234	447	5	]	]	PUNCT
ejpam-1234	447	6	)	)	PUNCT
ejpam-1234	447	7	∼=	∼=	PROPN
ejpam-1234	447	8	h∗(y	h∗(y	NOUN
ejpam-1234	447	9	)	)	PUNCT
ejpam-1234	447	10	{	{	PUNCT
ejpam-1234	447	11	σn	σn	NOUN
ejpam-1234	447	12	}	}	PUNCT
ejpam-1234	447	13	σn	σn	NOUN
ejpam-1234	447	14	[	[	X
ejpam-1234	447	15	14	14	NUM
ejpam-1234	447	16	]	]	PUNCT
ejpam-1234	447	17	,	,	PUNCT
ejpam-1234	447	18	we	we	PRON
ejpam-1234	447	19	obtain	obtain	VERB
ejpam-1234	447	20	the	the	DET
ejpam-1234	447	21	theorem	theorem	NOUN
ejpam-1234	447	22	by	by	ADP
ejpam-1234	447	23	taking	take	VERB
ejpam-1234	447	24	σn	σn	NOUN
ejpam-1234	447	25	-	-	PUNCT
ejpam-1234	447	26	invariants	invariant	NOUN
ejpam-1234	447	27	everywhere	everywhere	ADV
ejpam-1234	447	28	in	in	ADP
ejpam-1234	447	29	the	the	DET
ejpam-1234	447	30	above	above	ADJ
ejpam-1234	447	31	equality	equality	NOUN
ejpam-1234	447	32	.	.	PUNCT
ejpam-1234	448	1	theorem	theorem	NOUN
ejpam-1234	448	2	6	6	NUM
ejpam-1234	448	3	is	be	AUX
ejpam-1234	448	4	a	a	DET
ejpam-1234	448	5	special	special	ADJ
ejpam-1234	448	6	case	case	NOUN
ejpam-1234	448	7	of	of	ADP
ejpam-1234	448	8	the	the	DET
ejpam-1234	448	9	following	follow	VERB
ejpam-1234	448	10	conjecture	conjecture	NOUN
ejpam-1234	448	11	due	due	ADP
ejpam-1234	448	12	to	to	ADP
ejpam-1234	448	13	ruan	ruan	NOUN
ejpam-1234	448	14	[	[	X
ejpam-1234	448	15	22	22	NUM
ejpam-1234	448	16	]	]	PUNCT
ejpam-1234	448	17	.	.	PUNCT
ejpam-1234	449	1	conjecture	conjecture	NOUN
ejpam-1234	449	2	1	1	NUM
ejpam-1234	449	3	(	(	PUNCT
ejpam-1234	449	4	cohomological	cohomological	ADJ
ejpam-1234	449	5	hyper	hyper	ADJ
ejpam-1234	449	6	-	-	ADJ
ejpam-1234	449	7	kähler	kähler	NOUN
ejpam-1234	449	8	resolution	resolution	NOUN
ejpam-1234	449	9	conjecture	conjecture	NOUN
ejpam-1234	449	10	)	)	PUNCT
ejpam-1234	449	11	.	.	PUNCT
ejpam-1234	450	1	suppose	suppose	VERB
ejpam-1234	450	2	that	that	SCONJ
ejpam-1234	450	3	y	y	PROPN
ejpam-1234	450	4	→	→	PUNCT
ejpam-1234	450	5	x	x	PUNCT
ejpam-1234	450	6	be	be	AUX
ejpam-1234	450	7	a	a	DET
ejpam-1234	450	8	hyper	hyper	ADJ
ejpam-1234	450	9	-	-	ADJ
ejpam-1234	450	10	kähler	kähler	ADJ
ejpam-1234	450	11	resolution	resolution	NOUN
ejpam-1234	450	12	of	of	ADP
ejpam-1234	450	13	the	the	DET
ejpam-1234	450	14	coarse	coarse	ADJ
ejpam-1234	450	15	moduli	moduli	NOUN
ejpam-1234	450	16	space	space	NOUN
ejpam-1234	450	17	x	x	ADJ
ejpam-1234	450	18	of	of	ADP
ejpam-1234	450	19	an	an	DET
ejpam-1234	450	20	orbifoldx	orbifoldx	ADJ
ejpam-1234	450	21	.	.	PUNCT
ejpam-1234	451	1	the	the	DET
ejpam-1234	451	2	ordinary	ordinary	ADJ
ejpam-1234	451	3	cohomology	cohomology	NOUN
ejpam-1234	451	4	ring	ring	NOUN
ejpam-1234	451	5	h∗(y	h∗(y	PROPN
ejpam-1234	451	6	)	)	PUNCT
ejpam-1234	451	7	of	of	ADP
ejpam-1234	451	8	y	y	PROPN
ejpam-1234	451	9	is	be	AUX
ejpam-1234	451	10	isomorphic	isomorphic	ADJ
ejpam-1234	451	11	to	to	ADP
ejpam-1234	451	12	the	the	DET
ejpam-1234	451	13	chen	chen	PROPN
ejpam-1234	451	14	-	-	PUNCT
ejpam-1234	451	15	ruan	ruan	PROPN
ejpam-1234	451	16	orbifold	orbifold	PROPN
ejpam-1234	451	17	cohomology	cohomology	NOUN
ejpam-1234	451	18	ring	ring	PROPN
ejpam-1234	451	19	h∗	h∗	PROPN
ejpam-1234	451	20	or	or	CCONJ
ejpam-1234	451	21	b	b	PROPN
ejpam-1234	451	22	(	(	PUNCT
ejpam-1234	451	23	x	x	NOUN
ejpam-1234	451	24	)	)	PUNCT
ejpam-1234	451	25	of	of	ADP
ejpam-1234	451	26	x	x	SYM
ejpam-1234	451	27	.	.	PUNCT
ejpam-1234	451	28	remark	remark	PROPN
ejpam-1234	451	29	8	8	NUM
ejpam-1234	451	30	.	.	PUNCT
ejpam-1234	452	1	the	the	DET
ejpam-1234	452	2	conjecture	conjecture	NOUN
ejpam-1234	452	3	in	in	ADP
ejpam-1234	452	4	the	the	DET
ejpam-1234	452	5	special	special	ADJ
ejpam-1234	452	6	case	case	NOUN
ejpam-1234	452	7	of	of	ADP
ejpam-1234	452	8	wreath	wreath	NOUN
ejpam-1234	452	9	product	product	NOUN
ejpam-1234	452	10	orbifolds	orbifold	VERB
ejpam-1234	452	11	has	have	AUX
ejpam-1234	452	12	been	be	AUX
ejpam-1234	452	13	verified	verify	VERB
ejpam-1234	452	14	when	when	SCONJ
ejpam-1234	452	15	x	x	PROPN
ejpam-1234	452	16	=	=	SYM
ejpam-1234	452	17	c2	c2	PROPN
ejpam-1234	452	18	and	and	CCONJ
ejpam-1234	452	19	g	g	PROPN
ejpam-1234	452	20	is	be	AUX
ejpam-1234	452	21	a	a	DET
ejpam-1234	452	22	finite	finite	ADJ
ejpam-1234	452	23	subgroup	subgroup	NOUN
ejpam-1234	452	24	of	of	ADP
ejpam-1234	452	25	sl2(c	sl2(c	PROPN
ejpam-1234	452	26	)	)	PUNCT
ejpam-1234	452	27	in	in	ADP
ejpam-1234	452	28	[	[	X
ejpam-1234	452	29	6	6	NUM
ejpam-1234	452	30	]	]	PUNCT
ejpam-1234	452	31	.	.	PUNCT
ejpam-1234	453	1	in	in	ADP
ejpam-1234	453	2	particular	particular	ADJ
ejpam-1234	453	3	,	,	PUNCT
ejpam-1234	453	4	an	an	DET
ejpam-1234	453	5	explicit	explicit	ADJ
ejpam-1234	453	6	ring	ring	NOUN
ejpam-1234	453	7	isomorphism	isomorphism	NOUN
ejpam-1234	453	8	between	between	ADP
ejpam-1234	453	9	h∗(y	h∗(y	PROPN
ejpam-1234	453	10	[	[	X
ejpam-1234	453	11	n	n	X
ejpam-1234	453	12	]	]	PUNCT
ejpam-1234	453	13	)	)	PUNCT
ejpam-1234	453	14	and	and	CCONJ
ejpam-1234	453	15	h∗	h∗	PROPN
ejpam-1234	453	16	or	or	CCONJ
ejpam-1234	453	17	b	b	PROPN
ejpam-1234	453	18	(	(	PUNCT
ejpam-1234	453	19	[	[	X
ejpam-1234	453	20	x	x	X
ejpam-1234	453	21	n	n	CCONJ
ejpam-1234	453	22	/	/	SYM
ejpam-1234	453	23	gn	gn	PROPN
ejpam-1234	453	24	⋊σn	⋊σn	PROPN
ejpam-1234	453	25	]	]	PUNCT
ejpam-1234	453	26	)	)	PUNCT
ejpam-1234	453	27	has	have	AUX
ejpam-1234	453	28	been	be	AUX
ejpam-1234	453	29	established	establish	VERB
ejpam-1234	453	30	when	when	SCONJ
ejpam-1234	453	31	x	x	PROPN
ejpam-1234	453	32	=	=	SYM
ejpam-1234	453	33	c2	c2	PROPN
ejpam-1234	453	34	and	and	CCONJ
ejpam-1234	453	35	g	g	PROPN
ejpam-1234	453	36	is	be	AUX
ejpam-1234	453	37	a	a	DET
ejpam-1234	453	38	finite	finite	ADJ
ejpam-1234	453	39	cyclic	cyclic	ADJ
ejpam-1234	453	40	subgroup	subgroup	NOUN
ejpam-1234	453	41	of	of	ADP
ejpam-1234	453	42	sl2(c	sl2(c	PROPN
ejpam-1234	453	43	)	)	PUNCT
ejpam-1234	453	44	by	by	ADP
ejpam-1234	453	45	using	use	VERB
ejpam-1234	453	46	fock	fock	ADJ
ejpam-1234	453	47	space	space	NOUN
ejpam-1234	453	48	methods	method	NOUN
ejpam-1234	453	49	in	in	ADP
ejpam-1234	453	50	[	[	X
ejpam-1234	453	51	19	19	NUM
ejpam-1234	453	52	]	]	PUNCT
ejpam-1234	453	53	.	.	PUNCT
ejpam-1234	454	1	remark	remark	PROPN
ejpam-1234	454	2	9	9	NUM
ejpam-1234	454	3	.	.	PUNCT
ejpam-1234	455	1	in	in	ADP
ejpam-1234	455	2	theorem	theorem	NOUN
ejpam-1234	455	3	6	6	NUM
ejpam-1234	455	4	,	,	PUNCT
ejpam-1234	455	5	the	the	DET
ejpam-1234	455	6	claim	claim	NOUN
ejpam-1234	455	7	still	still	ADV
ejpam-1234	455	8	holds	hold	VERB
ejpam-1234	455	9	if	if	SCONJ
ejpam-1234	455	10	we	we	PRON
ejpam-1234	455	11	replace	replace	VERB
ejpam-1234	455	12	the	the	DET
ejpam-1234	455	13	ordinary	ordinary	ADJ
ejpam-1234	455	14	cohomology	cohomology	NOUN
ejpam-1234	455	15	and	and	CCONJ
ejpam-1234	455	16	orbifold	orbifold	ADJ
ejpam-1234	455	17	cohomology	cohomology	NOUN
ejpam-1234	455	18	by	by	ADP
ejpam-1234	455	19	ordinary	ordinary	ADJ
ejpam-1234	455	20	k	k	NOUN
ejpam-1234	455	21	-	-	NOUN
ejpam-1234	455	22	theory	theory	NOUN
ejpam-1234	455	23	and	and	CCONJ
ejpam-1234	455	24	orbifold	orbifold	ADJ
ejpam-1234	455	25	k	k	NOUN
ejpam-1234	455	26	-	-	NOUN
ejpam-1234	455	27	theory	theory	NOUN
ejpam-1234	455	28	respectively	respectively	ADV
ejpam-1234	455	29	by	by	ADP
ejpam-1234	455	30	the	the	DET
ejpam-1234	455	31	results	result	NOUN
ejpam-1234	455	32	in	in	ADP
ejpam-1234	455	33	[	[	X
ejpam-1234	455	34	10	10	NUM
ejpam-1234	455	35	]	]	PUNCT
ejpam-1234	455	36	.	.	PUNCT
ejpam-1234	456	1	references	reference	NOUN
ejpam-1234	456	2	507	507	NUM
ejpam-1234	456	3	acknowledgements	acknowledgement	NOUN
ejpam-1234	456	4	the	the	DET
ejpam-1234	456	5	author	author	NOUN
ejpam-1234	456	6	is	be	AUX
ejpam-1234	456	7	greatly	greatly	ADV
ejpam-1234	456	8	indebted	indebted	ADJ
ejpam-1234	456	9	to	to	ADP
ejpam-1234	456	10	his	his	PRON
ejpam-1234	456	11	thesis	thesis	NOUN
ejpam-1234	456	12	advisor	advisor	PROPN
ejpam-1234	456	13	takashi	takashi	PROPN
ejpam-1234	456	14	kimura	kimura	PROPN
ejpam-1234	456	15	,	,	PUNCT
ejpam-1234	456	16	who	who	PRON
ejpam-1234	456	17	has	have	AUX
ejpam-1234	456	18	provided	provide	VERB
ejpam-1234	456	19	constant	constant	ADJ
ejpam-1234	456	20	guidance	guidance	NOUN
ejpam-1234	456	21	throughout	throughout	ADP
ejpam-1234	456	22	the	the	DET
ejpam-1234	456	23	course	course	NOUN
ejpam-1234	456	24	of	of	ADP
ejpam-1234	456	25	this	this	DET
ejpam-1234	456	26	project	project	NOUN
ejpam-1234	456	27	.	.	PUNCT
ejpam-1234	457	1	the	the	DET
ejpam-1234	457	2	author	author	NOUN
ejpam-1234	457	3	would	would	AUX
ejpam-1234	457	4	like	like	VERB
ejpam-1234	457	5	to	to	PART
ejpam-1234	457	6	thank	thank	VERB
ejpam-1234	457	7	r.	r.	PROPN
ejpam-1234	457	8	kaufmann	kaufmann	PROPN
ejpam-1234	457	9	to	to	PART
ejpam-1234	457	10	point	point	VERB
ejpam-1234	457	11	out	out	ADP
ejpam-1234	457	12	his	his	PRON
ejpam-1234	457	13	papers	paper	NOUN
ejpam-1234	457	14	to	to	PART
ejpam-1234	457	15	improve	improve	VERB
ejpam-1234	457	16	significantly	significantly	ADV
ejpam-1234	457	17	from	from	ADP
ejpam-1234	457	18	my	my	PRON
ejpam-1234	457	19	thesis	thesis	NOUN
ejpam-1234	457	20	[	[	X
ejpam-1234	457	21	17	17	NUM
ejpam-1234	457	22	]	]	PUNCT
ejpam-1234	457	23	.	.	PUNCT
ejpam-1234	458	1	it	it	PRON
ejpam-1234	458	2	is	be	AUX
ejpam-1234	458	3	also	also	ADV
ejpam-1234	458	4	pleasure	pleasure	ADJ
ejpam-1234	458	5	to	to	PART
ejpam-1234	458	6	thank	thank	VERB
ejpam-1234	458	7	d.	d.	PROPN
ejpam-1234	458	8	abramovich	abramovich	PROPN
ejpam-1234	458	9	,	,	PUNCT
ejpam-1234	458	10	a.	a.	NOUN
ejpam-1234	458	11	craw	craw	PROPN
ejpam-1234	458	12	,	,	PUNCT
ejpam-1234	458	13	b.	b.	PROPN
ejpam-1234	458	14	fantechi	fantechi	PROPN
ejpam-1234	458	15	,	,	PUNCT
ejpam-1234	458	16	s.	s.	PROPN
ejpam-1234	458	17	okada	okada	PROPN
ejpam-1234	458	18	,	,	PUNCT
ejpam-1234	458	19	f.	f.	PROPN
ejpam-1234	458	20	perroni	perroni	PROPN
ejpam-1234	458	21	,	,	PUNCT
ejpam-1234	458	22	w.	w.	PROPN
ejpam-1234	458	23	wang	wang	PROPN
ejpam-1234	458	24	for	for	ADP
ejpam-1234	458	25	important	important	ADJ
ejpam-1234	458	26	advice	advice	NOUN
ejpam-1234	458	27	and	and	CCONJ
ejpam-1234	458	28	useful	useful	ADJ
ejpam-1234	458	29	conversations	conversation	NOUN
ejpam-1234	458	30	.	.	PUNCT
ejpam-1234	459	1	the	the	DET
ejpam-1234	459	2	author	author	NOUN
ejpam-1234	459	3	is	be	AUX
ejpam-1234	459	4	supported	support	VERB
ejpam-1234	459	5	by	by	ADP
ejpam-1234	459	6	the	the	DET
ejpam-1234	459	7	national	national	PROPN
ejpam-1234	459	8	research	research	PROPN
ejpam-1234	459	9	foundation	foundation	PROPN
ejpam-1234	459	10	of	of	ADP
ejpam-1234	459	11	korea	korea	PROPN
ejpam-1234	459	12	(	(	PUNCT
ejpam-1234	459	13	nrf	nrf	NOUN
ejpam-1234	459	14	)	)	PUNCT
ejpam-1234	459	15	grants	grant	NOUN
ejpam-1234	459	16	funded	fund	VERB
ejpam-1234	459	17	by	by	ADP
ejpam-1234	459	18	the	the	DET
ejpam-1234	459	19	korea	korea	PROPN
ejpam-1234	459	20	government	government	NOUN
ejpam-1234	459	21	(	(	PUNCT
ejpam-1234	459	22	mest	mest	NOUN
ejpam-1234	459	23	)	)	PUNCT
ejpam-1234	459	24	(	(	PUNCT
ejpam-1234	459	25	no	no	INTJ
ejpam-1234	459	26	.	.	NOUN
ejpam-1234	459	27	2012	2012	NUM
ejpam-1234	459	28	-	-	SYM
ejpam-1234	459	29	0000795	0000795	NUM
ejpam-1234	459	30	,	,	PUNCT
ejpam-1234	459	31	2011	2011	NUM
ejpam-1234	459	32	-	-	SYM
ejpam-1234	459	33	0001181	0001181	NUM
ejpam-1234	459	34	)	)	PUNCT
ejpam-1234	459	35	.	.	PUNCT
ejpam-1234	460	1	he	he	PRON
ejpam-1234	460	2	also	also	ADV
ejpam-1234	460	3	would	would	AUX
ejpam-1234	460	4	like	like	VERB
ejpam-1234	460	5	to	to	PART
ejpam-1234	460	6	express	express	VERB
ejpam-1234	460	7	his	his	PRON
ejpam-1234	460	8	gratitude	gratitude	NOUN
ejpam-1234	460	9	to	to	ADP
ejpam-1234	460	10	the	the	DET
ejpam-1234	460	11	algebraic	algebraic	ADJ
ejpam-1234	460	12	structure	structure	NOUN
ejpam-1234	460	13	and	and	CCONJ
ejpam-1234	460	14	its	its	PRON
ejpam-1234	460	15	application	application	NOUN
ejpam-1234	460	16	research	research	NOUN
ejpam-1234	460	17	institute	institute	NOUN
ejpam-1234	460	18	at	at	ADP
ejpam-1234	460	19	kaist	kaist	NOUN
ejpam-1234	460	20	for	for	ADP
ejpam-1234	460	21	providing	provide	VERB
ejpam-1234	460	22	him	he	PRON
ejpam-1234	460	23	an	an	DET
ejpam-1234	460	24	excellent	excellent	ADJ
ejpam-1234	460	25	research	research	NOUN
ejpam-1234	460	26	environment	environment	NOUN
ejpam-1234	460	27	in	in	ADP
ejpam-1234	460	28	2011	2011	NUM
ejpam-1234	460	29	-	-	SYM
ejpam-1234	460	30	2012	2012	NUM
ejpam-1234	460	31	.	.	PUNCT
ejpam-1234	461	1	references	reference	NOUN
ejpam-1234	461	2	[	[	X
ejpam-1234	461	3	1	1	NUM
ejpam-1234	461	4	]	]	PUNCT
ejpam-1234	461	5	a.	a.	NOUN
ejpam-1234	461	6	beauville	beauville	NOUN
ejpam-1234	461	7	.	.	PUNCT
ejpam-1234	462	1	variétés	variétés	PROPN
ejpam-1234	462	2	kähleriennes	kählerienne	NOUN
ejpam-1234	462	3	do	do	AUX
ejpam-1234	462	4	nt	not	PART
ejpam-1234	462	5	la	la	VERB
ejpam-1234	462	6	première	première	PROPN
ejpam-1234	462	7	classe	classe	PROPN
ejpam-1234	462	8	de	de	PROPN
ejpam-1234	462	9	chern	chern	PROPN
ejpam-1234	462	10	est	est	X
ejpam-1234	462	11	nulle	nulle	X
ejpam-1234	462	12	.	.	PUNCT
ejpam-1234	463	1	j.	j.	PROPN
ejpam-1234	463	2	differential	differential	PROPN
ejpam-1234	463	3	geom	geom	PROPN
ejpam-1234	463	4	.	.	PROPN
ejpam-1234	463	5	,	,	PUNCT
ejpam-1234	463	6	18(4):755–782	18(4):755–782	PROPN
ejpam-1234	463	7	(	(	PUNCT
ejpam-1234	463	8	1984	1984	NUM
ejpam-1234	463	9	)	)	PUNCT
ejpam-1234	463	10	,	,	PUNCT
ejpam-1234	463	11	1983	1983	NUM
ejpam-1234	463	12	.	.	PUNCT
ejpam-1234	464	1	[	[	X
ejpam-1234	464	2	2	2	NUM
ejpam-1234	464	3	]	]	PUNCT
ejpam-1234	464	4	l.	l.	PROPN
ejpam-1234	464	5	a.	a.	PROPN
ejpam-1234	464	6	borisov	borisov	PROPN
ejpam-1234	464	7	,	,	PUNCT
ejpam-1234	464	8	l.	l.	PROPN
ejpam-1234	464	9	chen	chen	PROPN
ejpam-1234	464	10	,	,	PUNCT
ejpam-1234	464	11	and	and	CCONJ
ejpam-1234	464	12	g.	g.	PROPN
ejpam-1234	464	13	g.	g.	PROPN
ejpam-1234	464	14	smith	smith	PROPN
ejpam-1234	464	15	.	.	PUNCT
ejpam-1234	465	1	the	the	DET
ejpam-1234	465	2	orbifold	orbifold	PROPN
ejpam-1234	465	3	chow	chow	PROPN
ejpam-1234	465	4	ring	ring	NOUN
ejpam-1234	465	5	of	of	ADP
ejpam-1234	465	6	toric	toric	ADJ
ejpam-1234	465	7	deligne	deligne	ADJ
ejpam-1234	465	8	-	-	PUNCT
ejpam-1234	465	9	mumford	mumford	NOUN
ejpam-1234	465	10	stacks	stack	NOUN
ejpam-1234	465	11	.	.	PUNCT
ejpam-1234	466	1	j.	j.	PROPN
ejpam-1234	466	2	amer	amer	PROPN
ejpam-1234	466	3	.	.	PROPN
ejpam-1234	466	4	math	math	PROPN
ejpam-1234	466	5	.	.	PUNCT
ejpam-1234	467	1	soc	soc	PROPN
ejpam-1234	467	2	.	.	PUNCT
ejpam-1234	467	3	,	,	PUNCT
ejpam-1234	468	1	18(1):193–215	18(1):193–215	PROPN
ejpam-1234	468	2	(	(	PUNCT
ejpam-1234	468	3	electronic	electronic	ADJ
ejpam-1234	468	4	)	)	PUNCT
ejpam-1234	468	5	,	,	PUNCT
ejpam-1234	468	6	2005	2005	NUM
ejpam-1234	468	7	.	.	PUNCT
ejpam-1234	469	1	[	[	X
ejpam-1234	469	2	3	3	X
ejpam-1234	469	3	]	]	X
ejpam-1234	469	4	j.	j.	PROPN
ejpam-1234	469	5	bryan	bryan	PROPN
ejpam-1234	469	6	and	and	CCONJ
ejpam-1234	469	7	t.	t.	PROPN
ejpam-1234	469	8	graber	graber	PROPN
ejpam-1234	469	9	.	.	PUNCT
ejpam-1234	470	1	the	the	DET
ejpam-1234	470	2	crepant	crepant	PROPN
ejpam-1234	470	3	resolution	resolution	NOUN
ejpam-1234	470	4	conjecture	conjecture	NOUN
ejpam-1234	470	5	.	.	PUNCT
ejpam-1234	471	1	in	in	ADP
ejpam-1234	471	2	algebraic	algebraic	PROPN
ejpam-1234	471	3	geometry	geometry	NOUN
ejpam-1234	471	4	—	—	PUNCT
ejpam-1234	471	5	seattle	seattle	PROPN
ejpam-1234	471	6	2005	2005	NUM
ejpam-1234	471	7	.	.	PUNCT
ejpam-1234	472	1	part	part	NOUN
ejpam-1234	472	2	1	1	NUM
ejpam-1234	472	3	,	,	PUNCT
ejpam-1234	472	4	volume	volume	NOUN
ejpam-1234	472	5	80	80	NUM
ejpam-1234	472	6	of	of	ADP
ejpam-1234	472	7	proc	proc	PROPN
ejpam-1234	472	8	.	.	PUNCT
ejpam-1234	473	1	sympos	sympos	PROPN
ejpam-1234	473	2	.	.	PUNCT
ejpam-1234	474	1	pure	pure	ADJ
ejpam-1234	474	2	math	math	NOUN
ejpam-1234	474	3	.	.	PUNCT
ejpam-1234	475	1	,	,	PUNCT
ejpam-1234	475	2	pages	page	NOUN
ejpam-1234	475	3	23–42	23–42	NUM
ejpam-1234	475	4	.	.	PROPN
ejpam-1234	475	5	amer	amer	PROPN
ejpam-1234	475	6	.	.	PUNCT
ejpam-1234	476	1	math	math	PROPN
ejpam-1234	476	2	.	.	PUNCT
ejpam-1234	477	1	soc	soc	PROPN
ejpam-1234	477	2	.	.	PUNCT
ejpam-1234	477	3	,	,	PUNCT
ejpam-1234	477	4	providence	providence	NOUN
ejpam-1234	477	5	,	,	PUNCT
ejpam-1234	477	6	ri	ri	NOUN
ejpam-1234	477	7	,	,	PUNCT
ejpam-1234	477	8	2009	2009	NUM
ejpam-1234	477	9	.	.	PUNCT
ejpam-1234	478	1	[	[	X
ejpam-1234	478	2	4	4	X
ejpam-1234	478	3	]	]	PUNCT
ejpam-1234	478	4	w.	w.	PROPN
ejpam-1234	478	5	chen	chen	PROPN
ejpam-1234	478	6	and	and	CCONJ
ejpam-1234	478	7	y.	y.	PROPN
ejpam-1234	478	8	ruan	ruan	PROPN
ejpam-1234	478	9	.	.	PUNCT
ejpam-1234	479	1	a	a	DET
ejpam-1234	479	2	new	new	ADJ
ejpam-1234	479	3	cohomology	cohomology	NOUN
ejpam-1234	479	4	theory	theory	NOUN
ejpam-1234	479	5	of	of	ADP
ejpam-1234	479	6	orbifold	orbifold	PROPN
ejpam-1234	479	7	.	.	PUNCT
ejpam-1234	480	1	comm	comm	NOUN
ejpam-1234	480	2	.	.	PUNCT
ejpam-1234	480	3	math	math	NOUN
ejpam-1234	480	4	.	.	PUNCT
ejpam-1234	481	1	phys	phy	NOUN
ejpam-1234	481	2	.	.	PUNCT
ejpam-1234	481	3	,	,	PUNCT
ejpam-1234	481	4	248(1):1–31	248(1):1–31	NUM
ejpam-1234	481	5	,	,	PUNCT
ejpam-1234	481	6	2004	2004	NUM
ejpam-1234	481	7	.	.	PUNCT
ejpam-1234	482	1	[	[	X
ejpam-1234	482	2	5	5	X
ejpam-1234	482	3	]	]	X
ejpam-1234	482	4	d.	d.	PROPN
ejpam-1234	482	5	edidin	edidin	PROPN
ejpam-1234	482	6	,	,	PUNCT
ejpam-1234	482	7	t.	t.	PROPN
ejpam-1234	482	8	j.	j.	PROPN
ejpam-1234	482	9	jarvis	jarvis	PROPN
ejpam-1234	482	10	,	,	PUNCT
ejpam-1234	482	11	and	and	CCONJ
ejpam-1234	482	12	t.	t.	PROPN
ejpam-1234	482	13	kimura	kimura	NOUN
ejpam-1234	482	14	.	.	PUNCT
ejpam-1234	483	1	logarithmic	logarithmic	ADJ
ejpam-1234	483	2	trace	trace	NOUN
ejpam-1234	483	3	and	and	CCONJ
ejpam-1234	483	4	orbifold	orbifold	ADJ
ejpam-1234	483	5	products	product	NOUN
ejpam-1234	483	6	.	.	PUNCT
ejpam-1234	484	1	duke	duke	PROPN
ejpam-1234	484	2	math	math	PROPN
ejpam-1234	484	3	.	.	PUNCT
ejpam-1234	485	1	j.	j.	PROPN
ejpam-1234	485	2	,	,	PUNCT
ejpam-1234	485	3	153(3):427–473	153(3):427–473	NUM
ejpam-1234	485	4	,	,	PUNCT
ejpam-1234	485	5	2010	2010	NUM
ejpam-1234	485	6	.	.	PUNCT
ejpam-1234	486	1	[	[	X
ejpam-1234	486	2	6	6	NUM
ejpam-1234	486	3	]	]	PUNCT
ejpam-1234	486	4	p.	p.	NOUN
ejpam-1234	486	5	etingof	etingof	NOUN
ejpam-1234	486	6	and	and	CCONJ
ejpam-1234	486	7	v.	v.	ADP
ejpam-1234	486	8	ginzburg	ginzburg	NOUN
ejpam-1234	486	9	.	.	PUNCT
ejpam-1234	487	1	symplectic	symplectic	ADJ
ejpam-1234	487	2	reflection	reflection	NOUN
ejpam-1234	487	3	algebras	algebras	PROPN
ejpam-1234	487	4	,	,	PUNCT
ejpam-1234	487	5	calogero	calogero	PROPN
ejpam-1234	487	6	-	-	PUNCT
ejpam-1234	487	7	moser	moser	PROPN
ejpam-1234	487	8	space	space	NOUN
ejpam-1234	487	9	,	,	PUNCT
ejpam-1234	487	10	and	and	CCONJ
ejpam-1234	487	11	deformed	deform	VERB
ejpam-1234	487	12	harish	harish	PROPN
ejpam-1234	487	13	-	-	PUNCT
ejpam-1234	487	14	chandra	chandra	PROPN
ejpam-1234	487	15	homomorphism	homomorphism	PROPN
ejpam-1234	487	16	.	.	PUNCT
ejpam-1234	488	1	invent	invent	NOUN
ejpam-1234	488	2	.	.	PUNCT
ejpam-1234	489	1	math	math	NOUN
ejpam-1234	489	2	.	.	PUNCT
ejpam-1234	489	3	,	,	PUNCT
ejpam-1234	489	4	147(2):243–348	147(2):243–348	NUM
ejpam-1234	489	5	,	,	PUNCT
ejpam-1234	489	6	2002	2002	NUM
ejpam-1234	489	7	.	.	PUNCT
ejpam-1234	490	1	[	[	X
ejpam-1234	490	2	7	7	X
ejpam-1234	490	3	]	]	X
ejpam-1234	490	4	b.	b.	PROPN
ejpam-1234	490	5	fantechi	fantechi	PROPN
ejpam-1234	490	6	and	and	CCONJ
ejpam-1234	490	7	l.	l.	PROPN
ejpam-1234	490	8	göttsche	göttsche	PROPN
ejpam-1234	490	9	.	.	PUNCT
ejpam-1234	491	1	orbifold	orbifold	PROPN
ejpam-1234	491	2	cohomology	cohomology	NOUN
ejpam-1234	491	3	for	for	ADP
ejpam-1234	491	4	global	global	ADJ
ejpam-1234	491	5	quotients	quotient	NOUN
ejpam-1234	491	6	.	.	PUNCT
ejpam-1234	492	1	duke	duke	PROPN
ejpam-1234	492	2	math	math	PROPN
ejpam-1234	492	3	.	.	PUNCT
ejpam-1234	493	1	j.	j.	PROPN
ejpam-1234	493	2	,	,	PUNCT
ejpam-1234	493	3	117(2):197–227	117(2):197–227	PROPN
ejpam-1234	493	4	,	,	PUNCT
ejpam-1234	493	5	2003	2003	NUM
ejpam-1234	493	6	.	.	PUNCT
ejpam-1234	494	1	[	[	X
ejpam-1234	494	2	8	8	X
ejpam-1234	494	3	]	]	PUNCT
ejpam-1234	494	4	j.	j.	PROPN
ejpam-1234	494	5	fogarty	fogarty	PROPN
ejpam-1234	494	6	.	.	PUNCT
ejpam-1234	495	1	algebraic	algebraic	ADJ
ejpam-1234	495	2	families	family	NOUN
ejpam-1234	495	3	on	on	ADP
ejpam-1234	495	4	an	an	DET
ejpam-1234	495	5	algebraic	algebraic	ADJ
ejpam-1234	495	6	surface	surface	NOUN
ejpam-1234	495	7	.	.	PUNCT
ejpam-1234	496	1	amer	amer	PROPN
ejpam-1234	496	2	.	.	PUNCT
ejpam-1234	497	1	j.	j.	PROPN
ejpam-1234	497	2	math	math	PROPN
ejpam-1234	497	3	,	,	PUNCT
ejpam-1234	497	4	90:511–521	90:511–521	NUM
ejpam-1234	497	5	,	,	PUNCT
ejpam-1234	497	6	1968	1968	NUM
ejpam-1234	497	7	.	.	PUNCT
ejpam-1234	498	1	[	[	X
ejpam-1234	498	2	9	9	NUM
ejpam-1234	498	3	]	]	X
ejpam-1234	498	4	r.	r.	PROPN
ejpam-1234	498	5	goldin	goldin	PROPN
ejpam-1234	498	6	,	,	PUNCT
ejpam-1234	498	7	t.	t.	PROPN
ejpam-1234	498	8	s.	s.	PROPN
ejpam-1234	498	9	holm	holm	PROPN
ejpam-1234	498	10	,	,	PUNCT
ejpam-1234	498	11	and	and	CCONJ
ejpam-1234	498	12	a.	a.	PROPN
ejpam-1234	498	13	knutson	knutson	PROPN
ejpam-1234	498	14	.	.	PUNCT
ejpam-1234	499	1	orbifold	orbifold	PROPN
ejpam-1234	499	2	cohomology	cohomology	NOUN
ejpam-1234	499	3	of	of	ADP
ejpam-1234	499	4	torus	torus	PROPN
ejpam-1234	499	5	quotients	quotient	VERB
ejpam-1234	499	6	.	.	PUNCT
ejpam-1234	500	1	duke	duke	PROPN
ejpam-1234	500	2	math	math	PROPN
ejpam-1234	500	3	.	.	PUNCT
ejpam-1234	501	1	j.	j.	PROPN
ejpam-1234	501	2	,	,	PUNCT
ejpam-1234	501	3	139(1):89–139	139(1):89–139	PROPN
ejpam-1234	501	4	,	,	PUNCT
ejpam-1234	501	5	2007	2007	NUM
ejpam-1234	501	6	.	.	PUNCT
ejpam-1234	502	1	[	[	X
ejpam-1234	502	2	10	10	NUM
ejpam-1234	502	3	]	]	PUNCT
ejpam-1234	502	4	t.	t.	PROPN
ejpam-1234	502	5	j.	j.	PROPN
ejpam-1234	502	6	jarvis	jarvis	PROPN
ejpam-1234	502	7	,	,	PUNCT
ejpam-1234	502	8	r.	r.	PROPN
ejpam-1234	502	9	kaufmann	kaufmann	PROPN
ejpam-1234	502	10	,	,	PUNCT
ejpam-1234	502	11	and	and	CCONJ
ejpam-1234	502	12	t.	t.	PROPN
ejpam-1234	502	13	kimura	kimura	PROPN
ejpam-1234	502	14	.	.	PUNCT
ejpam-1234	503	1	pointed	point	VERB
ejpam-1234	503	2	admissible	admissible	ADJ
ejpam-1234	503	3	g	g	NOUN
ejpam-1234	503	4	-	-	PUNCT
ejpam-1234	503	5	covers	cover	NOUN
ejpam-1234	503	6	and	and	CCONJ
ejpam-1234	503	7	g	g	NOUN
ejpam-1234	503	8	-	-	PUNCT
ejpam-1234	503	9	equivariant	equivariant	ADJ
ejpam-1234	503	10	cohomological	cohomological	ADJ
ejpam-1234	503	11	field	field	NOUN
ejpam-1234	503	12	theories	theory	NOUN
ejpam-1234	503	13	.	.	PUNCT
ejpam-1234	504	1	compos	compos	NOUN
ejpam-1234	504	2	.	.	PUNCT
ejpam-1234	505	1	math	math	NOUN
ejpam-1234	505	2	.	.	PUNCT
ejpam-1234	505	3	,	,	PUNCT
ejpam-1234	506	1	141(4):926–978	141(4):926–978	NUM
ejpam-1234	506	2	,	,	PUNCT
ejpam-1234	506	3	2005	2005	NUM
ejpam-1234	506	4	.	.	PUNCT
ejpam-1234	507	1	[	[	X
ejpam-1234	507	2	11	11	NUM
ejpam-1234	507	3	]	]	PUNCT
ejpam-1234	507	4	t.	t.	PROPN
ejpam-1234	507	5	j.	j.	PROPN
ejpam-1234	507	6	jarvis	jarvis	PROPN
ejpam-1234	507	7	,	,	PUNCT
ejpam-1234	507	8	r.	r.	PROPN
ejpam-1234	507	9	kaufmann	kaufmann	PROPN
ejpam-1234	507	10	,	,	PUNCT
ejpam-1234	507	11	and	and	CCONJ
ejpam-1234	507	12	t.	t.	PROPN
ejpam-1234	507	13	kimura	kimura	NOUN
ejpam-1234	507	14	.	.	PUNCT
ejpam-1234	508	1	stringy	stringy	ADJ
ejpam-1234	509	1	k	k	NOUN
ejpam-1234	509	2	-	-	NOUN
ejpam-1234	509	3	theory	theory	NOUN
ejpam-1234	509	4	and	and	CCONJ
ejpam-1234	509	5	the	the	DET
ejpam-1234	509	6	chern	chern	PROPN
ejpam-1234	509	7	character	character	NOUN
ejpam-1234	509	8	.	.	PUNCT
ejpam-1234	510	1	invent	invent	NOUN
ejpam-1234	510	2	.	.	PUNCT
ejpam-1234	511	1	math	math	NOUN
ejpam-1234	511	2	.	.	PUNCT
ejpam-1234	511	3	,	,	PUNCT
ejpam-1234	511	4	168(1):23–81	168(1):23–81	NUM
ejpam-1234	511	5	,	,	PUNCT
ejpam-1234	511	6	2007	2007	NUM
ejpam-1234	511	7	.	.	PUNCT
ejpam-1234	512	1	[	[	X
ejpam-1234	512	2	12	12	NUM
ejpam-1234	512	3	]	]	X
ejpam-1234	512	4	r.	r.	PROPN
ejpam-1234	512	5	m.	m.	PROPN
ejpam-1234	512	6	kaufmann	kaufmann	PROPN
ejpam-1234	512	7	.	.	PUNCT
ejpam-1234	513	1	orbifolding	orbifolde	VERB
ejpam-1234	513	2	frobenius	frobenius	PROPN
ejpam-1234	513	3	algebras	algebra	NOUN
ejpam-1234	513	4	.	.	PUNCT
ejpam-1234	514	1	internat	internat	PROPN
ejpam-1234	514	2	.	.	PUNCT
ejpam-1234	515	1	j.	j.	PROPN
ejpam-1234	515	2	math	math	PROPN
ejpam-1234	515	3	.	.	PUNCT
ejpam-1234	515	4	,	,	PUNCT
ejpam-1234	515	5	14(6):573–617	14(6):573–617	PROPN
ejpam-1234	515	6	,	,	PUNCT
ejpam-1234	515	7	2003	2003	NUM
ejpam-1234	515	8	.	.	PUNCT
ejpam-1234	516	1	references	reference	NOUN
ejpam-1234	516	2	508	508	NUM
ejpam-1234	516	3	[	[	SYM
ejpam-1234	516	4	13	13	NUM
ejpam-1234	516	5	]	]	PUNCT
ejpam-1234	516	6	r.	r.	PROPN
ejpam-1234	516	7	m.	m.	PROPN
ejpam-1234	516	8	kaufmann	kaufmann	PROPN
ejpam-1234	516	9	.	.	PUNCT
ejpam-1234	517	1	second	second	PROPN
ejpam-1234	517	2	quantized	quantize	VERB
ejpam-1234	517	3	frobenius	frobenius	NOUN
ejpam-1234	517	4	algebras	algebra	NOUN
ejpam-1234	517	5	.	.	PUNCT
ejpam-1234	518	1	comm	comm	NOUN
ejpam-1234	518	2	.	.	PUNCT
ejpam-1234	518	3	math	math	NOUN
ejpam-1234	518	4	.	.	PUNCT
ejpam-1234	519	1	phys	phy	NOUN
ejpam-1234	519	2	.	.	PUNCT
ejpam-1234	519	3	,	,	PUNCT
ejpam-1234	519	4	248(1):33	248(1):33	NOUN
ejpam-1234	519	5	–	–	PUNCT
ejpam-1234	519	6	83	83	NUM
ejpam-1234	519	7	,	,	PUNCT
ejpam-1234	519	8	2004	2004	NUM
ejpam-1234	519	9	.	.	PUNCT
ejpam-1234	520	1	[	[	X
ejpam-1234	520	2	14	14	NUM
ejpam-1234	520	3	]	]	PUNCT
ejpam-1234	520	4	m.	m.	NOUN
ejpam-1234	520	5	lehn	lehn	NOUN
ejpam-1234	520	6	and	and	CCONJ
ejpam-1234	520	7	c.	c.	PROPN
ejpam-1234	520	8	sorger	sorger	PROPN
ejpam-1234	520	9	.	.	PUNCT
ejpam-1234	521	1	the	the	DET
ejpam-1234	521	2	cup	cup	NOUN
ejpam-1234	521	3	product	product	NOUN
ejpam-1234	521	4	of	of	ADP
ejpam-1234	521	5	hilbert	hilbert	NOUN
ejpam-1234	521	6	schemes	scheme	NOUN
ejpam-1234	521	7	for	for	ADP
ejpam-1234	521	8	k3	k3	ADJ
ejpam-1234	521	9	surfaces	surface	NOUN
ejpam-1234	521	10	.	.	PUNCT
ejpam-1234	522	1	invent	invent	NOUN
ejpam-1234	522	2	.	.	PUNCT
ejpam-1234	523	1	math	math	NOUN
ejpam-1234	523	2	.	.	PUNCT
ejpam-1234	523	3	,	,	PUNCT
ejpam-1234	523	4	152(2):305–329	152(2):305–329	PROPN
ejpam-1234	523	5	,	,	PUNCT
ejpam-1234	523	6	2003	2003	NUM
ejpam-1234	523	7	.	.	PUNCT
ejpam-1234	524	1	[	[	X
ejpam-1234	524	2	15	15	NUM
ejpam-1234	524	3	]	]	X
ejpam-1234	524	4	e.	e.	PROPN
ejpam-1234	524	5	lerman	lerman	PROPN
ejpam-1234	524	6	and	and	CCONJ
ejpam-1234	524	7	a.	a.	NOUN
ejpam-1234	524	8	malkin	malkin	PROPN
ejpam-1234	524	9	.	.	PUNCT
ejpam-1234	525	1	hamiltonian	hamiltonian	ADJ
ejpam-1234	525	2	group	group	NOUN
ejpam-1234	525	3	actions	action	NOUN
ejpam-1234	525	4	on	on	ADP
ejpam-1234	525	5	symplectic	symplectic	ADJ
ejpam-1234	525	6	deligne	deligne	PROPN
ejpam-1234	525	7	-	-	PUNCT
ejpam-1234	525	8	mumford	mumford	NOUN
ejpam-1234	525	9	stacks	stack	NOUN
ejpam-1234	525	10	and	and	CCONJ
ejpam-1234	525	11	toric	toric	ADJ
ejpam-1234	525	12	orbifolds	orbifold	NOUN
ejpam-1234	525	13	.	.	PUNCT
ejpam-1234	526	1	adv	adv	PROPN
ejpam-1234	526	2	.	.	PUNCT
ejpam-1234	526	3	math	math	PROPN
ejpam-1234	526	4	.	.	PUNCT
ejpam-1234	526	5	,	,	PUNCT
ejpam-1234	527	1	229(2):984–1000	229(2):984–1000	NUM
ejpam-1234	527	2	,	,	PUNCT
ejpam-1234	527	3	2012	2012	NUM
ejpam-1234	527	4	.	.	PUNCT
ejpam-1234	528	1	[	[	X
ejpam-1234	528	2	16	16	NUM
ejpam-1234	528	3	]	]	X
ejpam-1234	528	4	w.	w.	PROPN
ejpam-1234	528	5	li	li	PROPN
ejpam-1234	528	6	,	,	PUNCT
ejpam-1234	528	7	z.	z.	PROPN
ejpam-1234	528	8	qin	qin	PROPN
ejpam-1234	528	9	,	,	PUNCT
ejpam-1234	528	10	and	and	CCONJ
ejpam-1234	528	11	w.	w.	PROPN
ejpam-1234	528	12	wang	wang	PROPN
ejpam-1234	528	13	.	.	PUNCT
ejpam-1234	529	1	ideals	ideal	NOUN
ejpam-1234	529	2	of	of	ADP
ejpam-1234	529	3	the	the	DET
ejpam-1234	529	4	cohomology	cohomology	NOUN
ejpam-1234	529	5	rings	ring	NOUN
ejpam-1234	529	6	of	of	ADP
ejpam-1234	529	7	hilbert	hilbert	NOUN
ejpam-1234	529	8	schemes	scheme	NOUN
ejpam-1234	529	9	and	and	CCONJ
ejpam-1234	529	10	their	their	PRON
ejpam-1234	529	11	applications	application	NOUN
ejpam-1234	529	12	.	.	PUNCT
ejpam-1234	530	1	trans	trans	PROPN
ejpam-1234	530	2	.	.	PUNCT
ejpam-1234	531	1	amer	amer	PROPN
ejpam-1234	531	2	.	.	PUNCT
ejpam-1234	531	3	math	math	PROPN
ejpam-1234	531	4	.	.	PUNCT
ejpam-1234	532	1	soc	soc	PROPN
ejpam-1234	532	2	.	.	PUNCT
ejpam-1234	532	3	,	,	PUNCT
ejpam-1234	532	4	356(1):245–265	356(1):245–265	NUM
ejpam-1234	532	5	(	(	PUNCT
ejpam-1234	532	6	electronic	electronic	ADJ
ejpam-1234	532	7	)	)	PUNCT
ejpam-1234	532	8	,	,	PUNCT
ejpam-1234	532	9	2004	2004	NUM
ejpam-1234	532	10	.	.	PUNCT
ejpam-1234	533	1	[	[	X
ejpam-1234	533	2	17	17	NUM
ejpam-1234	533	3	]	]	X
ejpam-1234	533	4	t.	t.	NOUN
ejpam-1234	533	5	matsumura	matsumura	PROPN
ejpam-1234	533	6	.	.	PUNCT
ejpam-1234	534	1	orbifold	orbifold	PROPN
ejpam-1234	534	2	cohomology	cohomology	NOUN
ejpam-1234	534	3	of	of	ADP
ejpam-1234	534	4	a	a	DET
ejpam-1234	534	5	wreath	wreath	NOUN
ejpam-1234	534	6	product	product	NOUN
ejpam-1234	534	7	orbifold	orbifold	NOUN
ejpam-1234	534	8	.	.	PUNCT
ejpam-1234	535	1	phd	phd	NOUN
ejpam-1234	535	2	dissertation	dissertation	NOUN
ejpam-1234	535	3	,	,	PUNCT
ejpam-1234	535	4	boston	boston	PROPN
ejpam-1234	535	5	university	university	PROPN
ejpam-1234	535	6	,	,	PUNCT
ejpam-1234	535	7	dept	dept	NOUN
ejpam-1234	535	8	.	.	PROPN
ejpam-1234	535	9	math	math	PROPN
ejpam-1234	535	10	.	.	PUNCT
ejpam-1234	535	11	,	,	PUNCT
ejpam-1234	535	12	august	august	PROPN
ejpam-1234	535	13	2007	2007	NUM
ejpam-1234	535	14	.	.	PUNCT
ejpam-1234	536	1	arxiv	arxiv	NOUN
ejpam-1234	536	2	:	:	PUNCT
ejpam-1234	536	3	math/0610269	math/0610269	NOUN
ejpam-1234	536	4	.	.	PUNCT
ejpam-1234	537	1	[	[	X
ejpam-1234	537	2	18	18	NUM
ejpam-1234	537	3	]	]	PUNCT
ejpam-1234	537	4	z.	z.	PROPN
ejpam-1234	537	5	qin	qin	PROPN
ejpam-1234	537	6	and	and	CCONJ
ejpam-1234	537	7	w.	w.	PROPN
ejpam-1234	537	8	wang	wang	PROPN
ejpam-1234	537	9	.	.	PUNCT
ejpam-1234	538	1	hilbert	hilbert	PROPN
ejpam-1234	538	2	schemes	scheme	NOUN
ejpam-1234	538	3	and	and	CCONJ
ejpam-1234	538	4	symmetric	symmetric	ADJ
ejpam-1234	538	5	products	product	NOUN
ejpam-1234	538	6	:	:	PUNCT
ejpam-1234	538	7	a	a	DET
ejpam-1234	538	8	dictionary	dictionary	NOUN
ejpam-1234	538	9	.	.	PUNCT
ejpam-1234	539	1	in	in	ADP
ejpam-1234	539	2	orbifolds	orbifold	NOUN
ejpam-1234	539	3	in	in	ADP
ejpam-1234	539	4	mathematics	mathematic	NOUN
ejpam-1234	539	5	and	and	CCONJ
ejpam-1234	539	6	physics	physics	PROPN
ejpam-1234	539	7	(	(	PUNCT
ejpam-1234	539	8	madison	madison	PROPN
ejpam-1234	539	9	,	,	PUNCT
ejpam-1234	539	10	wi	wi	PROPN
ejpam-1234	539	11	,	,	PUNCT
ejpam-1234	539	12	2001	2001	NUM
ejpam-1234	539	13	)	)	PUNCT
ejpam-1234	539	14	,	,	PUNCT
ejpam-1234	539	15	volume	volume	NOUN
ejpam-1234	539	16	310	310	NUM
ejpam-1234	539	17	of	of	ADP
ejpam-1234	539	18	contemp	contemp	NOUN
ejpam-1234	539	19	.	.	PUNCT
ejpam-1234	540	1	math	math	NOUN
ejpam-1234	540	2	.	.	PUNCT
ejpam-1234	541	1	,	,	PUNCT
ejpam-1234	541	2	pages	page	NOUN
ejpam-1234	541	3	233–257	233–257	NUM
ejpam-1234	541	4	.	.	PUNCT
ejpam-1234	542	1	amer	amer	PROPN
ejpam-1234	542	2	.	.	PUNCT
ejpam-1234	542	3	math	math	PROPN
ejpam-1234	542	4	.	.	PUNCT
ejpam-1234	543	1	soc	soc	PROPN
ejpam-1234	543	2	.	.	PUNCT
ejpam-1234	543	3	,	,	PUNCT
ejpam-1234	543	4	providence	providence	NOUN
ejpam-1234	543	5	,	,	PUNCT
ejpam-1234	543	6	ri	ri	NOUN
ejpam-1234	543	7	,	,	PUNCT
ejpam-1234	543	8	2002	2002	NUM
ejpam-1234	543	9	.	.	PUNCT
ejpam-1234	544	1	[	[	X
ejpam-1234	544	2	19	19	NUM
ejpam-1234	544	3	]	]	PUNCT
ejpam-1234	544	4	z.	z.	PROPN
ejpam-1234	544	5	qin	qin	PROPN
ejpam-1234	544	6	and	and	CCONJ
ejpam-1234	544	7	w.	w.	PROPN
ejpam-1234	544	8	wang	wang	PROPN
ejpam-1234	544	9	.	.	PUNCT
ejpam-1234	545	1	hilbert	hilbert	PROPN
ejpam-1234	545	2	schemes	scheme	NOUN
ejpam-1234	545	3	of	of	ADP
ejpam-1234	545	4	points	point	NOUN
ejpam-1234	545	5	on	on	ADP
ejpam-1234	545	6	the	the	DET
ejpam-1234	545	7	minimal	minimal	ADJ
ejpam-1234	545	8	resolution	resolution	NOUN
ejpam-1234	545	9	and	and	CCONJ
ejpam-1234	545	10	soliton	soliton	NOUN
ejpam-1234	545	11	equations	equation	NOUN
ejpam-1234	545	12	.	.	PUNCT
ejpam-1234	546	1	in	in	ADP
ejpam-1234	546	2	lie	lie	NOUN
ejpam-1234	546	3	algebras	algebra	NOUN
ejpam-1234	546	4	,	,	PUNCT
ejpam-1234	546	5	vertex	vertex	NOUN
ejpam-1234	546	6	operator	operator	NOUN
ejpam-1234	546	7	algebras	algebra	NOUN
ejpam-1234	546	8	and	and	CCONJ
ejpam-1234	546	9	their	their	PRON
ejpam-1234	546	10	applications	application	NOUN
ejpam-1234	546	11	,	,	PUNCT
ejpam-1234	546	12	volume	volume	NOUN
ejpam-1234	546	13	442	442	NUM
ejpam-1234	546	14	of	of	ADP
ejpam-1234	546	15	contemp	contemp	NOUN
ejpam-1234	546	16	.	.	PUNCT
ejpam-1234	547	1	math	math	NOUN
ejpam-1234	547	2	.	.	PUNCT
ejpam-1234	548	1	,	,	PUNCT
ejpam-1234	548	2	pages	page	NOUN
ejpam-1234	548	3	435–462	435–462	NUM
ejpam-1234	548	4	.	.	PUNCT
ejpam-1234	549	1	amer	amer	PROPN
ejpam-1234	549	2	.	.	PUNCT
ejpam-1234	549	3	math	math	PROPN
ejpam-1234	549	4	.	.	PUNCT
ejpam-1234	550	1	soc	soc	PROPN
ejpam-1234	550	2	.	.	PUNCT
ejpam-1234	550	3	,	,	PUNCT
ejpam-1234	550	4	providence	providence	NOUN
ejpam-1234	550	5	,	,	PUNCT
ejpam-1234	550	6	ri	ri	NOUN
ejpam-1234	550	7	,	,	PUNCT
ejpam-1234	550	8	2007	2007	NUM
ejpam-1234	550	9	.	.	PUNCT
ejpam-1234	551	1	[	[	X
ejpam-1234	551	2	20	20	NUM
ejpam-1234	551	3	]	]	PUNCT
ejpam-1234	551	4	m.	m.	NOUN
ejpam-1234	551	5	reid	reid	PROPN
ejpam-1234	551	6	.	.	PUNCT
ejpam-1234	552	1	canonical	canonical	ADJ
ejpam-1234	552	2	3	3	NUM
ejpam-1234	552	3	-	-	PUNCT
ejpam-1234	552	4	folds	fold	NOUN
ejpam-1234	552	5	.	.	PUNCT
ejpam-1234	553	1	in	in	ADP
ejpam-1234	553	2	journées	journées	PROPN
ejpam-1234	553	3	de	de	X
ejpam-1234	553	4	géometrie	géometrie	ADJ
ejpam-1234	553	5	algébrique	algébrique	ADJ
ejpam-1234	553	6	d’angers	d’anger	NOUN
ejpam-1234	553	7	,	,	PUNCT
ejpam-1234	553	8	juillet	juillet	PROPN
ejpam-1234	553	9	1979	1979	NUM
ejpam-1234	553	10	/	/	SYM
ejpam-1234	553	11	algebraic	algebraic	ADJ
ejpam-1234	553	12	geometry	geometry	NOUN
ejpam-1234	553	13	,	,	PUNCT
ejpam-1234	553	14	angers	anger	NOUN
ejpam-1234	553	15	,	,	PUNCT
ejpam-1234	553	16	1979	1979	NUM
ejpam-1234	553	17	,	,	PUNCT
ejpam-1234	553	18	pages	page	NOUN
ejpam-1234	553	19	273–310	273–310	NUM
ejpam-1234	553	20	.	.	PROPN
ejpam-1234	553	21	sijthoff	sijthoff	PROPN
ejpam-1234	553	22	&	&	CCONJ
ejpam-1234	553	23	noordhoff	noordhoff	PROPN
ejpam-1234	553	24	,	,	PUNCT
ejpam-1234	553	25	alphen	alphen	PROPN
ejpam-1234	553	26	aan	aan	PROPN
ejpam-1234	553	27	den	den	PROPN
ejpam-1234	553	28	rijn	rijn	PROPN
ejpam-1234	553	29	,	,	PUNCT
ejpam-1234	553	30	1980	1980	NUM
ejpam-1234	553	31	.	.	PUNCT
ejpam-1234	554	1	[	[	X
ejpam-1234	554	2	21	21	NUM
ejpam-1234	554	3	]	]	PUNCT
ejpam-1234	554	4	m.	m.	NOUN
ejpam-1234	554	5	romagny	romagny	PROPN
ejpam-1234	554	6	.	.	PUNCT
ejpam-1234	555	1	group	group	NOUN
ejpam-1234	555	2	actions	action	NOUN
ejpam-1234	555	3	on	on	ADP
ejpam-1234	555	4	stacks	stack	NOUN
ejpam-1234	555	5	and	and	CCONJ
ejpam-1234	555	6	applications	application	NOUN
ejpam-1234	555	7	.	.	PUNCT
ejpam-1234	556	1	michigan	michigan	PROPN
ejpam-1234	556	2	math	math	PROPN
ejpam-1234	556	3	.	.	PUNCT
ejpam-1234	557	1	j.	j.	PROPN
ejpam-1234	557	2	,	,	PUNCT
ejpam-1234	557	3	53(1):209	53(1):209	NUM
ejpam-1234	557	4	–	–	PUNCT
ejpam-1234	557	5	236	236	NUM
ejpam-1234	557	6	,	,	PUNCT
ejpam-1234	557	7	2005	2005	NUM
ejpam-1234	557	8	.	.	PUNCT
ejpam-1234	558	1	[	[	X
ejpam-1234	558	2	22	22	NUM
ejpam-1234	558	3	]	]	X
ejpam-1234	558	4	y.	y.	PROPN
ejpam-1234	558	5	ruan	ruan	PROPN
ejpam-1234	558	6	.	.	PUNCT
ejpam-1234	559	1	stringy	stringy	ADJ
ejpam-1234	559	2	orbifolds	orbifold	NOUN
ejpam-1234	559	3	.	.	PUNCT
ejpam-1234	560	1	in	in	ADP
ejpam-1234	560	2	orbifolds	orbifold	NOUN
ejpam-1234	560	3	in	in	ADP
ejpam-1234	560	4	mathematics	mathematic	NOUN
ejpam-1234	560	5	and	and	CCONJ
ejpam-1234	560	6	physics	physics	PROPN
ejpam-1234	560	7	(	(	PUNCT
ejpam-1234	560	8	madison	madison	PROPN
ejpam-1234	560	9	,	,	PUNCT
ejpam-1234	560	10	wi	wi	PROPN
ejpam-1234	560	11	,	,	PUNCT
ejpam-1234	560	12	2001	2001	NUM
ejpam-1234	560	13	)	)	PUNCT
ejpam-1234	560	14	,	,	PUNCT
ejpam-1234	560	15	volume	volume	NOUN
ejpam-1234	560	16	310	310	NUM
ejpam-1234	560	17	of	of	ADP
ejpam-1234	560	18	contemp	contemp	NOUN
ejpam-1234	560	19	.	.	PUNCT
ejpam-1234	561	1	math	math	NOUN
ejpam-1234	561	2	.	.	PUNCT
ejpam-1234	562	1	,	,	PUNCT
ejpam-1234	562	2	pages	page	NOUN
ejpam-1234	562	3	259–299	259–299	NUM
ejpam-1234	562	4	.	.	PUNCT
ejpam-1234	562	5	amer	amer	PROPN
ejpam-1234	562	6	.	.	PUNCT
ejpam-1234	562	7	math	math	PROPN
ejpam-1234	562	8	.	.	PUNCT
ejpam-1234	563	1	soc	soc	PROPN
ejpam-1234	563	2	.	.	PUNCT
ejpam-1234	563	3	,	,	PUNCT
ejpam-1234	563	4	providence	providence	NOUN
ejpam-1234	563	5	,	,	PUNCT
ejpam-1234	563	6	ri	ri	NOUN
ejpam-1234	563	7	,	,	PUNCT
ejpam-1234	563	8	2002	2002	NUM
ejpam-1234	563	9	.	.	PUNCT
ejpam-1234	564	1	[	[	X
ejpam-1234	564	2	23	23	NUM
ejpam-1234	564	3	]	]	X
ejpam-1234	564	4	v.	v.	PROPN
ejpam-1234	564	5	turaev	turaev	PROPN
ejpam-1234	564	6	.	.	PUNCT
ejpam-1234	565	1	homotopy	homotopy	PROPN
ejpam-1234	565	2	field	field	NOUN
ejpam-1234	565	3	theory	theory	NOUN
ejpam-1234	565	4	in	in	ADP
ejpam-1234	565	5	dimension	dimension	NOUN
ejpam-1234	565	6	2	2	NUM
ejpam-1234	565	7	and	and	CCONJ
ejpam-1234	565	8	group	group	NOUN
ejpam-1234	565	9	-	-	PUNCT
ejpam-1234	565	10	algebras	algebras	PROPN
ejpam-1234	565	11	.	.	PUNCT
ejpam-1234	566	1	arxiv	arxiv	PROPN
ejpam-1234	566	2	:	:	PUNCT
ejpam-1234	566	3	math/9910010	math/9910010	PROPN
ejpam-1234	566	4	,	,	PUNCT
ejpam-1234	566	5	october	october	PROPN
ejpam-1234	566	6	1999	1999	NUM
ejpam-1234	566	7	.	.	PUNCT
ejpam-1234	567	1	[	[	X
ejpam-1234	567	2	24	24	NUM
ejpam-1234	567	3	]	]	PUNCT
ejpam-1234	567	4	b.	b.	PROPN
ejpam-1234	567	5	uribe	uribe	PROPN
ejpam-1234	567	6	.	.	PROPN
ejpam-1234	568	1	orbifold	orbifold	PROPN
ejpam-1234	568	2	cohomology	cohomology	NOUN
ejpam-1234	568	3	of	of	ADP
ejpam-1234	568	4	the	the	DET
ejpam-1234	568	5	symmetric	symmetric	ADJ
ejpam-1234	568	6	product	product	NOUN
ejpam-1234	568	7	.	.	PUNCT
ejpam-1234	569	1	comm	comm	NOUN
ejpam-1234	569	2	.	.	PUNCT
ejpam-1234	570	1	anal	anal	PROPN
ejpam-1234	570	2	.	.	PUNCT
ejpam-1234	571	1	geom	geom	PROPN
ejpam-1234	571	2	.	.	PROPN
ejpam-1234	571	3	,	,	PUNCT
ejpam-1234	571	4	13(1):113–128	13(1):113–128	PROPN
ejpam-1234	571	5	,	,	PUNCT
ejpam-1234	571	6	2005	2005	NUM
ejpam-1234	571	7	.	.	PUNCT
ejpam-1234	572	1	[	[	X
ejpam-1234	572	2	25	25	NUM
ejpam-1234	572	3	]	]	X
ejpam-1234	572	4	w.	w.	PROPN
ejpam-1234	572	5	wang	wang	PROPN
ejpam-1234	572	6	.	.	PUNCT
ejpam-1234	573	1	equivariant	equivariant	PROPN
ejpam-1234	574	1	k	k	PROPN
ejpam-1234	574	2	-	-	PROPN
ejpam-1234	574	3	theory	theory	NOUN
ejpam-1234	574	4	,	,	PUNCT
ejpam-1234	574	5	wreath	wreath	NOUN
ejpam-1234	574	6	products	product	NOUN
ejpam-1234	574	7	,	,	PUNCT
ejpam-1234	574	8	and	and	CCONJ
ejpam-1234	574	9	heisenberg	heisenberg	PROPN
ejpam-1234	574	10	algebra	algebra	PROPN
ejpam-1234	574	11	.	.	PUNCT
ejpam-1234	575	1	duke	duke	PROPN
ejpam-1234	575	2	math	math	PROPN
ejpam-1234	575	3	.	.	PUNCT
ejpam-1234	576	1	j.	j.	PROPN
ejpam-1234	576	2	,	,	PUNCT
ejpam-1234	576	3	103(1):1–23	103(1):1–23	PROPN
ejpam-1234	576	4	,	,	PUNCT
ejpam-1234	576	5	2000	2000	NUM
ejpam-1234	576	6	.	.	PUNCT
ejpam-1234	577	1	[	[	X
ejpam-1234	577	2	26	26	NUM
ejpam-1234	577	3	]	]	X
ejpam-1234	577	4	w.	w.	PROPN
ejpam-1234	577	5	wang	wang	PROPN
ejpam-1234	577	6	and	and	CCONJ
ejpam-1234	577	7	j.	j.	PROPN
ejpam-1234	577	8	zhou	zhou	PROPN
ejpam-1234	577	9	.	.	PUNCT
ejpam-1234	578	1	orbifold	orbifold	PROPN
ejpam-1234	578	2	hodge	hodge	PROPN
ejpam-1234	578	3	numbers	number	NOUN
ejpam-1234	578	4	of	of	ADP
ejpam-1234	578	5	the	the	DET
ejpam-1234	578	6	wreath	wreath	NOUN
ejpam-1234	578	7	product	product	NOUN
ejpam-1234	578	8	orbifolds	orbifold	VERB
ejpam-1234	578	9	.	.	PUNCT
ejpam-1234	579	1	j.	j.	PROPN
ejpam-1234	579	2	geom	geom	PROPN
ejpam-1234	579	3	.	.	PUNCT
ejpam-1234	580	1	phys	phy	NOUN
ejpam-1234	580	2	.	.	PUNCT
ejpam-1234	580	3	,	,	PUNCT
ejpam-1234	580	4	38(2):152–169	38(2):152–169	NUM
ejpam-1234	580	5	,	,	PUNCT
ejpam-1234	580	6	2001	2001	NUM
ejpam-1234	580	7	.	.	PUNCT
ejpam-1234	581	1	references	reference	NOUN
ejpam-1234	581	2	509	509	NUM
ejpam-1234	581	3	appendix	appendix	ADJ
ejpam-1234	581	4	special	special	ADJ
ejpam-1234	581	5	σi	σi	PROPN
ejpam-1234	581	6	-frobenius	-frobenius	PROPN
ejpam-1234	581	7	algebras	algebra	NOUN
ejpam-1234	581	8	in	in	ADP
ejpam-1234	581	9	this	this	DET
ejpam-1234	581	10	section	section	NOUN
ejpam-1234	581	11	,	,	PUNCT
ejpam-1234	581	12	we	we	PRON
ejpam-1234	581	13	recall	recall	VERB
ejpam-1234	581	14	definitions	definition	NOUN
ejpam-1234	581	15	and	and	CCONJ
ejpam-1234	581	16	results	result	NOUN
ejpam-1234	581	17	about	about	ADP
ejpam-1234	581	18	special	special	ADJ
ejpam-1234	581	19	g	g	NOUN
ejpam-1234	581	20	-	-	PUNCT
ejpam-1234	581	21	frobenius	frobenius	NOUN
ejpam-1234	581	22	algebras	algebra	NOUN
ejpam-1234	581	23	from	from	ADP
ejpam-1234	581	24	[	[	X
ejpam-1234	581	25	12	12	NUM
ejpam-1234	581	26	,	,	PUNCT
ejpam-1234	581	27	13	13	NUM
ejpam-1234	581	28	]	]	PUNCT
ejpam-1234	581	29	and	and	CCONJ
ejpam-1234	581	30	the	the	DET
ejpam-1234	581	31	construction	construction	NOUN
ejpam-1234	581	32	of	of	ADP
ejpam-1234	581	33	lehn	lehn	NOUN
ejpam-1234	581	34	-	-	PUNCT
ejpam-1234	581	35	sorger	sorger	NOUN
ejpam-1234	581	36	’s	’s	PART
ejpam-1234	581	37	algebras	algebra	NOUN
ejpam-1234	582	1	[	[	X
ejpam-1234	582	2	14	14	NUM
ejpam-1234	582	3	]	]	PUNCT
ejpam-1234	582	4	.	.	PUNCT
ejpam-1234	583	1	definition	definition	NOUN
ejpam-1234	583	2	8	8	NUM
ejpam-1234	583	3	(	(	PUNCT
ejpam-1234	583	4	[	[	X
ejpam-1234	583	5	definition	definition	NOUN
ejpam-1234	583	6	4.1	4.1	NUM
ejpam-1234	583	7	and	and	CCONJ
ejpam-1234	583	8	4.2	4.2	NUM
ejpam-1234	583	9	,	,	PUNCT
ejpam-1234	583	10	12	12	NUM
ejpam-1234	583	11	]	]	PUNCT
ejpam-1234	583	12	)	)	PUNCT
ejpam-1234	583	13	.	.	PUNCT
ejpam-1234	584	1	a	a	DET
ejpam-1234	584	2	special	special	ADJ
ejpam-1234	584	3	g	g	NOUN
ejpam-1234	584	4	-	-	PUNCT
ejpam-1234	584	5	frobenius	frobenius	NOUN
ejpam-1234	584	6	algebra	algebra	NOUN
ejpam-1234	584	7	(	(	PUNCT
ejpam-1234	584	8	h	h	NOUN
ejpam-1234	584	9	,	,	PUNCT
ejpam-1234	584	10	ρ	ρ	PROPN
ejpam-1234	584	11	,	,	PUNCT
ejpam-1234	584	12	·	·	PUNCT
ejpam-1234	584	13	,	,	PUNCT
ejpam-1234	584	14	{	{	PUNCT
ejpam-1234	584	15	1g},η	1g},η	PROPN
ejpam-1234	584	16	)	)	PUNCT
ejpam-1234	584	17	is	be	AUX
ejpam-1234	584	18	a	a	DET
ejpam-1234	584	19	g	g	NOUN
ejpam-1234	584	20	-	-	PUNCT
ejpam-1234	584	21	frobenius	frobenius	NOUN
ejpam-1234	584	22	algebra	algebra	NOUN
ejpam-1234	584	23	(	(	PUNCT
ejpam-1234	584	24	h	h	NOUN
ejpam-1234	584	25	,	,	PUNCT
ejpam-1234	584	26	ρ	ρ	PROPN
ejpam-1234	584	27	,	,	PUNCT
ejpam-1234	584	28	·	·	PUNCT
ejpam-1234	584	29	,	,	PUNCT
ejpam-1234	584	30	1e	1e	NUM
ejpam-1234	584	31	,	,	PUNCT
ejpam-1234	584	32	η	η	PROPN
ejpam-1234	584	33	)	)	PUNCT
ejpam-1234	584	34	with	with	ADP
ejpam-1234	584	35	the	the	DET
ejpam-1234	584	36	choice	choice	NOUN
ejpam-1234	584	37	of	of	ADP
ejpam-1234	584	38	1	1	NUM
ejpam-1234	584	39	g	g	NOUN
ejpam-1234	584	40	∈	∈	PROPN
ejpam-1234	584	41	hg	hg	NOUN
ejpam-1234	584	42	such	such	ADJ
ejpam-1234	584	43	that	that	DET
ejpam-1234	584	44	hg	hg	NOUN
ejpam-1234	584	45	=	=	NOUN
ejpam-1234	584	46	he	he	PRON
ejpam-1234	584	47	·	·	PUNCT
ejpam-1234	584	48	1	1	NUM
ejpam-1234	584	49	g	g	NOUN
ejpam-1234	584	50	and	and	CCONJ
ejpam-1234	584	51	ϕg(1h	ϕg(1h	NUM
ejpam-1234	584	52	)	)	PUNCT
ejpam-1234	585	1	=	=	SYM
ejpam-1234	585	2	ϕg	ϕg	PROPN
ejpam-1234	585	3	,	,	PUNCT
ejpam-1234	585	4	h1ghg−1	h1ghg−1	PROPN
ejpam-1234	585	5	for	for	ADP
ejpam-1234	585	6	some	some	PRON
ejpam-1234	585	7	ϕg	ϕg	NOUN
ejpam-1234	585	8	,	,	PUNCT
ejpam-1234	585	9	h	h	PROPN
ejpam-1234	585	10	∈	∈	PROPN
ejpam-1234	586	1	k×.	k×.	PROPN
ejpam-1234	586	2	let	let	VERB
ejpam-1234	586	3	rg	rg	X
ejpam-1234	586	4	:	:	PUNCT
ejpam-1234	586	5	he	he	PRON
ejpam-1234	586	6	−→hg	−→hg	NOUN
ejpam-1234	586	7	be	be	AUX
ejpam-1234	586	8	given	give	VERB
ejpam-1234	586	9	by	by	ADP
ejpam-1234	586	10	a	a	DET
ejpam-1234	586	11	7→	7→	NUM
ejpam-1234	586	12	a	a	DET
ejpam-1234	586	13	·	·	SYM
ejpam-1234	586	14	1	1	NUM
ejpam-1234	586	15	g	g	NOUN
ejpam-1234	586	16	and	and	CCONJ
ejpam-1234	586	17	let	let	VERB
ejpam-1234	586	18	ig	ig	PRON
ejpam-1234	586	19	:	:	PUNCT
ejpam-1234	586	20	=	=	SYM
ejpam-1234	586	21	ker	ker	PROPN
ejpam-1234	586	22	g.	g.	PROPN
ejpam-1234	586	23	let	let	VERB
ejpam-1234	586	24	ig	ig	PRON
ejpam-1234	586	25	be	be	AUX
ejpam-1234	586	26	a	a	DET
ejpam-1234	586	27	section	section	NOUN
ejpam-1234	586	28	of	of	ADP
ejpam-1234	586	29	rg	rg	PROPN
ejpam-1234	586	30	.	.	PUNCT
ejpam-1234	587	1	a	a	DET
ejpam-1234	587	2	special	special	ADJ
ejpam-1234	587	3	g	g	NOUN
ejpam-1234	587	4	-	-	PUNCT
ejpam-1234	587	5	reconstruction	reconstruction	NOUN
ejpam-1234	587	6	datum	datum	NOUN
ejpam-1234	587	7	is	be	AUX
ejpam-1234	587	8	a	a	DET
ejpam-1234	587	9	collection	collection	NOUN
ejpam-1234	587	10	of	of	ADP
ejpam-1234	587	11	frobenius	frobenius	ADJ
ejpam-1234	587	12	algebras	algebra	NOUN
ejpam-1234	587	13	(	(	PUNCT
ejpam-1234	587	14	hg	hg	NOUN
ejpam-1234	587	15	,	,	PUNCT
ejpam-1234	587	16	·	·	PUNCT
ejpam-1234	587	17	,	,	PUNCT
ejpam-1234	587	18	ηg	ηg	PRON
ejpam-1234	587	19	,	,	PUNCT
ejpam-1234	587	20	1	1	NUM
ejpam-1234	587	21	g	g	NOUN
ejpam-1234	587	22	)	)	PUNCT
ejpam-1234	587	23	,	,	PUNCT
ejpam-1234	587	24	g	g	PROPN
ejpam-1234	587	25	∈	∈	PROPN
ejpam-1234	587	26	g	g	NOUN
ejpam-1234	587	27	with	with	ADP
ejpam-1234	587	28	an	an	DET
ejpam-1234	587	29	action	action	NOUN
ejpam-1234	587	30	ρ	ρ	NOUN
ejpam-1234	587	31	of	of	ADP
ejpam-1234	587	32	g	g	PROPN
ejpam-1234	587	33	on	on	ADP
ejpam-1234	587	34	he	he	PRON
ejpam-1234	587	35	and	and	CCONJ
ejpam-1234	587	36	cyclic	cyclic	ADJ
ejpam-1234	587	37	he	he	PRON
ejpam-1234	587	38	-	-	PUNCT
ejpam-1234	587	39	algebra	algebra	NOUN
ejpam-1234	587	40	structures	structure	NOUN
ejpam-1234	587	41	on	on	ADP
ejpam-1234	587	42	(	(	PUNCT
ejpam-1234	587	43	hg	hg	NOUN
ejpam-1234	587	44	,	,	PUNCT
ejpam-1234	587	45	·	·	PUNCT
ejpam-1234	587	46	,	,	PUNCT
ejpam-1234	587	47	1	1	NUM
ejpam-1234	587	48	g	g	NOUN
ejpam-1234	587	49	)	)	PUNCT
ejpam-1234	587	50	such	such	ADJ
ejpam-1234	587	51	that	that	SCONJ
ejpam-1234	587	52	hg	hg	NOUN
ejpam-1234	587	53	and	and	CCONJ
ejpam-1234	587	54	hg−1	hg−1	NOUN
ejpam-1234	587	55	are	be	AUX
ejpam-1234	587	56	isomorphic	isomorphic	ADJ
ejpam-1234	587	57	as	as	SCONJ
ejpam-1234	587	58	he	he	PRON
ejpam-1234	587	59	-	-	PUNCT
ejpam-1234	587	60	algebras	algebra	NOUN
ejpam-1234	587	61	and	and	CCONJ
ejpam-1234	587	62	η(ρg(a),ρg(b	η(ρg(a),ρg(b	NOUN
ejpam-1234	587	63	)	)	PUNCT
ejpam-1234	587	64	)	)	PUNCT
ejpam-1234	588	1	=	=	SYM
ejpam-1234	588	2	η(a	η(a	PROPN
ejpam-1234	588	3	,	,	PUNCT
ejpam-1234	588	4	b	b	NOUN
ejpam-1234	588	5	)	)	PUNCT
ejpam-1234	588	6	.	.	PUNCT
ejpam-1234	589	1	lemma	lemma	PROPN
ejpam-1234	589	2	6	6	NUM
ejpam-1234	589	3	(	(	PUNCT
ejpam-1234	589	4	[	[	X
ejpam-1234	589	5	proposition	proposition	NOUN
ejpam-1234	589	6	4.1	4.1	NUM
ejpam-1234	589	7	,	,	PUNCT
ejpam-1234	589	8	12	12	NUM
ejpam-1234	589	9	]	]	PUNCT
ejpam-1234	589	10	)	)	PUNCT
ejpam-1234	589	11	.	.	PUNCT
ejpam-1234	590	1	a	a	DET
ejpam-1234	590	2	special	special	ADJ
ejpam-1234	590	3	g	g	NOUN
ejpam-1234	590	4	-	-	PUNCT
ejpam-1234	590	5	frobenius	frobenius	NOUN
ejpam-1234	590	6	algebra	algebra	NOUN
ejpam-1234	590	7	(	(	PUNCT
ejpam-1234	590	8	h	h	NOUN
ejpam-1234	590	9	,	,	PUNCT
ejpam-1234	590	10	ρ	ρ	PROPN
ejpam-1234	590	11	,	,	PUNCT
ejpam-1234	590	12	·	·	PUNCT
ejpam-1234	590	13	,	,	PUNCT
ejpam-1234	590	14	{	{	PUNCT
ejpam-1234	590	15	1g},η	1g},η	PROPN
ejpam-1234	590	16	)	)	PUNCT
ejpam-1234	590	17	defines	define	VERB
ejpam-1234	590	18	a	a	DET
ejpam-1234	590	19	special	special	ADJ
ejpam-1234	590	20	g	g	NOUN
ejpam-1234	590	21	-	-	PUNCT
ejpam-1234	590	22	reconstruction	reconstruction	NOUN
ejpam-1234	590	23	datum	datum	NOUN
ejpam-1234	590	24	{	{	PUNCT
ejpam-1234	590	25	(	(	PUNCT
ejpam-1234	590	26	hg	hg	X
ejpam-1234	590	27	,	,	PUNCT
ejpam-1234	590	28	·	·	PUNCT
ejpam-1234	590	29	,	,	PUNCT
ejpam-1234	590	30	ηg	ηg	PRON
ejpam-1234	590	31	,	,	PUNCT
ejpam-1234	590	32	1	1	NUM
ejpam-1234	590	33	g	g	NOUN
ejpam-1234	590	34	)	)	PUNCT
ejpam-1234	590	35	,	,	PUNCT
ejpam-1234	590	36	g	g	PROPN
ejpam-1234	590	37	∈	∈	PROPN
ejpam-1234	590	38	g	g	PROPN
ejpam-1234	590	39	,	,	PUNCT
ejpam-1234	590	40	ρ	ρ	NOUN
ejpam-1234	590	41	}	}	PUNCT
ejpam-1234	590	42	.	.	PUNCT
ejpam-1234	591	1	the	the	DET
ejpam-1234	591	2	structure	structure	NOUN
ejpam-1234	591	3	of	of	ADP
ejpam-1234	591	4	a	a	DET
ejpam-1234	591	5	frobenius	frobenius	ADJ
ejpam-1234	591	6	algebra	algebra	NOUN
ejpam-1234	591	7	in	in	ADP
ejpam-1234	591	8	hg	hg	PROPN
ejpam-1234	591	9	is	be	AUX
ejpam-1234	591	10	given	give	VERB
ejpam-1234	591	11	by	by	ADP
ejpam-1234	591	12	ag	ag	PROPN
ejpam-1234	591	13	·	·	PUNCT
ejpam-1234	591	14	bg	bg	PROPN
ejpam-1234	591	15	:	:	PUNCT
ejpam-1234	591	16	=	=	SYM
ejpam-1234	591	17	ig(ag	ig(ag	X
ejpam-1234	591	18	)	)	PUNCT
ejpam-1234	591	19	·	·	PUNCT
ejpam-1234	591	20	ig(bg	ig(bg	PROPN
ejpam-1234	591	21	)	)	PUNCT
ejpam-1234	591	22	·	·	PUNCT
ejpam-1234	591	23	1	1	NUM
ejpam-1234	591	24	g	g	NOUN
ejpam-1234	591	25	and	and	CCONJ
ejpam-1234	591	26	ηg(ag	ηg(ag	ADJ
ejpam-1234	591	27	,	,	PUNCT
ejpam-1234	591	28	bg	bg	PROPN
ejpam-1234	591	29	)	)	PUNCT
ejpam-1234	591	30	:	:	PUNCT
ejpam-1234	592	1	=	=	PUNCT
ejpam-1234	592	2	η(ig(ag)1	η(ig(ag)1	PRON
ejpam-1234	592	3	g	g	NOUN
ejpam-1234	592	4	,	,	PUNCT
ejpam-1234	592	5	ig(bg)1g−1	ig(bg)1g−1	PROPN
ejpam-1234	592	6	)	)	PUNCT
ejpam-1234	592	7	.	.	PUNCT
ejpam-1234	593	1	definition	definition	NOUN
ejpam-1234	593	2	9	9	NUM
ejpam-1234	593	3	(	(	PUNCT
ejpam-1234	593	4	[	[	PUNCT
ejpam-1234	593	5	definition	definition	NOUN
ejpam-1234	593	6	4.3	4.3	NUM
ejpam-1234	593	7	and	and	CCONJ
ejpam-1234	593	8	4.4	4.4	NUM
ejpam-1234	593	9	,	,	PUNCT
ejpam-1234	593	10	12	12	NUM
ejpam-1234	593	11	]	]	PUNCT
ejpam-1234	593	12	)	)	PUNCT
ejpam-1234	593	13	.	.	PUNCT
ejpam-1234	594	1	let	let	VERB
ejpam-1234	594	2	{	{	PUNCT
ejpam-1234	594	3	(	(	PUNCT
ejpam-1234	594	4	hg	hg	X
ejpam-1234	594	5	,	,	PUNCT
ejpam-1234	594	6	·	·	PUNCT
ejpam-1234	594	7	g	g	NOUN
ejpam-1234	594	8	,	,	PUNCT
ejpam-1234	594	9	ηg	ηg	PRON
ejpam-1234	594	10	,	,	PUNCT
ejpam-1234	594	11	1	1	NUM
ejpam-1234	594	12	g	g	NOUN
ejpam-1234	594	13	)	)	PUNCT
ejpam-1234	594	14	,	,	PUNCT
ejpam-1234	594	15	g	g	PROPN
ejpam-1234	594	16	∈	∈	PROPN
ejpam-1234	594	17	g	g	PROPN
ejpam-1234	594	18	,	,	PUNCT
ejpam-1234	594	19	ρ	ρ	PROPN
ejpam-1234	594	20	}	}	PUNCT
ejpam-1234	594	21	be	be	AUX
ejpam-1234	594	22	a	a	DET
ejpam-1234	594	23	special	special	ADJ
ejpam-1234	594	24	greconstruction	greconstruction	NOUN
ejpam-1234	594	25	datum	datum	NOUN
ejpam-1234	594	26	.	.	PUNCT
ejpam-1234	595	1	a	a	DET
ejpam-1234	595	2	graded	grade	VERB
ejpam-1234	595	3	cocycle	cocycle	NOUN
ejpam-1234	595	4	is	be	AUX
ejpam-1234	595	5	a	a	DET
ejpam-1234	595	6	map	map	NOUN
ejpam-1234	595	7	γ	γ	X
ejpam-1234	595	8	:	:	PUNCT
ejpam-1234	595	9	g	g	PROPN
ejpam-1234	595	10	×	×	NOUN
ejpam-1234	595	11	g	g	NOUN
ejpam-1234	595	12	−→	−→	NOUN
ejpam-1234	595	13	he	he	PRON
ejpam-1234	595	14	,	,	PUNCT
ejpam-1234	595	15	(	(	PUNCT
ejpam-1234	595	16	g	g	NOUN
ejpam-1234	595	17	,	,	PUNCT
ejpam-1234	595	18	h	h	NOUN
ejpam-1234	595	19	)	)	PUNCT
ejpam-1234	595	20	7→	7→	NOUN
ejpam-1234	596	1	γg	γg	ADV
ejpam-1234	596	2	,	,	PUNCT
ejpam-1234	596	3	h	h	NOUN
ejpam-1234	596	4	such	such	ADJ
ejpam-1234	596	5	that	that	SCONJ
ejpam-1234	596	6	γg	γg	ADV
ejpam-1234	596	7	,	,	PUNCT
ejpam-1234	596	8	hγgh	hγgh	NOUN
ejpam-1234	596	9	,	,	PUNCT
ejpam-1234	596	10	k	k	PROPN
ejpam-1234	596	11	≡	≡	PROPN
ejpam-1234	596	12	γg	γg	ADV
ejpam-1234	596	13	,	,	PUNCT
ejpam-1234	596	14	hkγh	hkγh	PROPN
ejpam-1234	596	15	,	,	PUNCT
ejpam-1234	596	16	k	k	PROPN
ejpam-1234	596	17	mod	mod	PROPN
ejpam-1234	596	18	ighk	ighk	PROPN
ejpam-1234	596	19	.	.	PUNCT
ejpam-1234	597	1	a	a	DET
ejpam-1234	597	2	graded	grade	VERB
ejpam-1234	597	3	cocycle	cocycle	NOUN
ejpam-1234	597	4	γ	γ	X
ejpam-1234	597	5	is	be	AUX
ejpam-1234	597	6	compatible	compatible	ADJ
ejpam-1234	597	7	with	with	ADP
ejpam-1234	597	8	the	the	DET
ejpam-1234	597	9	special	special	ADJ
ejpam-1234	597	10	greconstruction	greconstruction	NOUN
ejpam-1234	597	11	datum	datum	NOUN
ejpam-1234	597	12	if	if	SCONJ
ejpam-1234	597	13	(	(	PUNCT
ejpam-1234	597	14	ig	ig	PROPN
ejpam-1234	597	15	+	+	NOUN
ejpam-1234	597	16	ih)γg	ih)γg	PUNCT
ejpam-1234	597	17	,	,	PUNCT
ejpam-1234	597	18	h	h	PROPN
ejpam-1234	597	19	⊂	⊂	PROPN
ejpam-1234	597	20	igh	igh	PROPN
ejpam-1234	597	21	(	(	PUNCT
ejpam-1234	597	22	section	section	NOUN
ejpam-1234	597	23	independence	independence	NOUN
ejpam-1234	597	24	)	)	PUNCT
ejpam-1234	597	25	,	,	PUNCT
ejpam-1234	597	26	γg	γg	ADV
ejpam-1234	597	27	,	,	PUNCT
ejpam-1234	597	28	g−1	g−1	PROPN
ejpam-1234	597	29	=	=	PUNCT
ejpam-1234	597	30	řg(1	řg(1	NOUN
ejpam-1234	597	31	g	g	NOUN
ejpam-1234	597	32	)	)	PUNCT
ejpam-1234	597	33	(	(	PUNCT
ejpam-1234	597	34	metric	metric	ADJ
ejpam-1234	597	35	compatibility	compatibility	NOUN
ejpam-1234	597	36	)	)	PUNCT
ejpam-1234	597	37	and	and	CCONJ
ejpam-1234	597	38	γe	γe	NOUN
ejpam-1234	597	39	,	,	PUNCT
ejpam-1234	597	40	h	h	NOUN
ejpam-1234	598	1	=	=	SYM
ejpam-1234	598	2	1e	1e	NUM
ejpam-1234	598	3	mod	mod	PROPN
ejpam-1234	598	4	ih	ih	PROPN
ejpam-1234	598	5	where	where	SCONJ
ejpam-1234	598	6	η	η	PROPN
ejpam-1234	598	7	♯	♯	PROPN
ejpam-1234	598	8	g	g	PROPN
ejpam-1234	598	9	:	:	PUNCT
ejpam-1234	598	10	ag	ag	PROPN
ejpam-1234	598	11	7→	7→	PROPN
ejpam-1234	598	12	ηg(ag	ηg(ag	PRON
ejpam-1234	598	13	,	,	PUNCT
ejpam-1234	598	14	)	)	PUNCT
ejpam-1234	598	15	and	and	CCONJ
ejpam-1234	598	16	řg	řg	PROPN
ejpam-1234	598	17	:	:	PUNCT
ejpam-1234	598	18	=	=	SYM
ejpam-1234	598	19	(	(	PUNCT
ejpam-1234	598	20	η	η	PROPN
ejpam-1234	598	21	♯	♯	PROPN
ejpam-1234	598	22	e	e	PROPN
ejpam-1234	598	23	)	)	PUNCT
ejpam-1234	598	24	−1	−1	NOUN
ejpam-1234	598	25	◦	◦	NOUN
ejpam-1234	598	26	r∗g	r∗g	NUM
ejpam-1234	598	27	◦	◦	VERB
ejpam-1234	598	28	η	η	PROPN
ejpam-1234	598	29	♯	♯	PROPN
ejpam-1234	598	30	g	g	PROPN
ejpam-1234	598	31	.	.	PUNCT
ejpam-1234	599	1	we	we	PRON
ejpam-1234	599	2	identify	identify	VERB
ejpam-1234	599	3	two	two	NUM
ejpam-1234	599	4	cocycle	cocycle	NOUN
ejpam-1234	599	5	γ	γ	NOUN
ejpam-1234	599	6	and	and	CCONJ
ejpam-1234	599	7	γ′	γ′	PROPN
ejpam-1234	599	8	if	if	SCONJ
ejpam-1234	599	9	γg	γg	ADV
ejpam-1234	599	10	,	,	PUNCT
ejpam-1234	599	11	h	h	PROPN
ejpam-1234	599	12	≡	≡	PROPN
ejpam-1234	599	13	γ	γ	VERB
ejpam-1234	599	14	′	′	NUM
ejpam-1234	599	15	g	g	PROPN
ejpam-1234	599	16	,	,	PUNCT
ejpam-1234	599	17	h	h	PROPN
ejpam-1234	599	18	mod	mod	PROPN
ejpam-1234	599	19	igh	igh	PROPN
ejpam-1234	599	20	.	.	PUNCT
ejpam-1234	600	1	a	a	DET
ejpam-1234	600	2	non	non	ADJ
ejpam-1234	600	3	-	-	ADJ
ejpam-1234	600	4	abelian	abelian	ADJ
ejpam-1234	600	5	cocycle	cocycle	NOUN
ejpam-1234	600	6	is	be	AUX
ejpam-1234	600	7	a	a	DET
ejpam-1234	600	8	map	map	NOUN
ejpam-1234	600	9	ϕ	ϕ	NOUN
ejpam-1234	600	10	:	:	PUNCT
ejpam-1234	600	11	g	g	PROPN
ejpam-1234	600	12	×	×	NOUN
ejpam-1234	600	13	g	g	NOUN
ejpam-1234	600	14	−→	−→	NOUN
ejpam-1234	601	1	k×	k×	AUX
ejpam-1234	601	2	satisfying	satisfy	VERB
ejpam-1234	601	3	ϕgh	ϕgh	ADV
ejpam-1234	601	4	,	,	PUNCT
ejpam-1234	601	5	k	k	PROPN
ejpam-1234	601	6	=	=	PUNCT
ejpam-1234	601	7	ϕg	ϕg	PROPN
ejpam-1234	601	8	,	,	PUNCT
ejpam-1234	601	9	hkh−1ϕh	hkh−1ϕh	PROPN
ejpam-1234	601	10	,	,	PUNCT
ejpam-1234	601	11	k	k	PROPN
ejpam-1234	601	12	and	and	CCONJ
ejpam-1234	601	13	ϕe	ϕe	INTJ
ejpam-1234	601	14	,	,	PUNCT
ejpam-1234	601	15	g	g	PROPN
ejpam-1234	601	16	=	=	SYM
ejpam-1234	601	17	ϕg	ϕg	PROPN
ejpam-1234	601	18	,	,	PUNCT
ejpam-1234	601	19	e	e	X
ejpam-1234	601	20	=	=	NOUN
ejpam-1234	601	21	1	1	X
ejpam-1234	601	22	.	.	PUNCT
ejpam-1234	601	23	a	a	DET
ejpam-1234	601	24	graded	grade	VERB
ejpam-1234	601	25	cocycle	cocycle	NOUN
ejpam-1234	601	26	γ	γ	NOUN
ejpam-1234	601	27	and	and	CCONJ
ejpam-1234	601	28	a	a	DET
ejpam-1234	601	29	non	non	ADJ
ejpam-1234	601	30	-	-	ADJ
ejpam-1234	601	31	abelian	abelian	ADJ
ejpam-1234	601	32	cocycle	cocycle	PROPN
ejpam-1234	601	33	ϕ	ϕ	PROPN
ejpam-1234	601	34	form	form	NOUN
ejpam-1234	601	35	a	a	DET
ejpam-1234	601	36	compatible	compatible	ADJ
ejpam-1234	601	37	pair	pair	NOUN
ejpam-1234	601	38	if	if	SCONJ
ejpam-1234	601	39	ϕg	ϕg	X
ejpam-1234	601	40	,	,	PUNCT
ejpam-1234	601	41	hγghg−1,g	hγghg−1,g	NOUN
ejpam-1234	602	1	=	=	SYM
ejpam-1234	602	2	γg	γg	ADV
ejpam-1234	602	3	,	,	PUNCT
ejpam-1234	602	4	h	h	NOUN
ejpam-1234	602	5	and	and	CCONJ
ejpam-1234	602	6	ϕk	ϕk	PROPN
ejpam-1234	602	7	,	,	PUNCT
ejpam-1234	602	8	gϕk	gϕk	NOUN
ejpam-1234	602	9	,	,	PUNCT
ejpam-1234	602	10	hγkgk−1,khk−1	hγkgk−1,khk−1	VERB
ejpam-1234	602	11	=	=	SYM
ejpam-1234	602	12	ϕk(γg	ϕk(γg	NOUN
ejpam-1234	602	13	,	,	PUNCT
ejpam-1234	602	14	h)ϕk	h)ϕk	PROPN
ejpam-1234	602	15	,	,	PUNCT
ejpam-1234	602	16	gh	gh	PROPN
ejpam-1234	602	17	.	.	PROPN
ejpam-1234	602	18	theorem	theorem	VERB
ejpam-1234	602	19	7	7	NUM
ejpam-1234	602	20	(	(	PUNCT
ejpam-1234	602	21	reconstruction	reconstruction	NOUN
ejpam-1234	602	22	theorem	theorem	NOUN
ejpam-1234	602	23	[	[	PUNCT
ejpam-1234	602	24	theorem	theorem	ADJ
ejpam-1234	602	25	4.1	4.1	NUM
ejpam-1234	602	26	,	,	PUNCT
ejpam-1234	602	27	12	12	NUM
ejpam-1234	602	28	]	]	PUNCT
ejpam-1234	602	29	)	)	PUNCT
ejpam-1234	602	30	.	.	PUNCT
ejpam-1234	603	1	let	let	VERB
ejpam-1234	603	2	{	{	PUNCT
ejpam-1234	603	3	(	(	PUNCT
ejpam-1234	603	4	hg	hg	X
ejpam-1234	603	5	,	,	PUNCT
ejpam-1234	603	6	·	·	PUNCT
ejpam-1234	603	7	g	g	NOUN
ejpam-1234	603	8	,	,	PUNCT
ejpam-1234	603	9	ηg	ηg	PRON
ejpam-1234	603	10	,	,	PUNCT
ejpam-1234	603	11	1	1	NUM
ejpam-1234	603	12	g	g	NOUN
ejpam-1234	603	13	)	)	PUNCT
ejpam-1234	603	14	,	,	PUNCT
ejpam-1234	603	15	g	g	PROPN
ejpam-1234	603	16	∈	∈	PROPN
ejpam-1234	603	17	g	g	PROPN
ejpam-1234	603	18	,	,	PUNCT
ejpam-1234	603	19	ρ	ρ	PROPN
ejpam-1234	603	20	}	}	PUNCT
ejpam-1234	603	21	be	be	AUX
ejpam-1234	603	22	a	a	DET
ejpam-1234	603	23	special	special	ADJ
ejpam-1234	603	24	g	g	NOUN
ejpam-1234	603	25	-	-	PUNCT
ejpam-1234	603	26	reconstruction	reconstruction	NOUN
ejpam-1234	603	27	datum	datum	NOUN
ejpam-1234	603	28	.	.	PUNCT
ejpam-1234	604	1	then	then	ADV
ejpam-1234	604	2	the	the	DET
ejpam-1234	604	3	structures	structure	NOUN
ejpam-1234	604	4	of	of	ADP
ejpam-1234	604	5	special	special	ADJ
ejpam-1234	604	6	g	g	NOUN
ejpam-1234	604	7	-	-	PUNCT
ejpam-1234	604	8	frobenius	frobenius	NOUN
ejpam-1234	604	9	algebras	algebra	NOUN
ejpam-1234	604	10	inducing	induce	VERB
ejpam-1234	604	11	the	the	DET
ejpam-1234	604	12	given	give	VERB
ejpam-1234	604	13	reconstruction	reconstruction	NOUN
ejpam-1234	604	14	datum	datum	NOUN
ejpam-1234	604	15	correspond	correspond	VERB
ejpam-1234	604	16	bijectively	bijectively	ADV
ejpam-1234	604	17	to	to	AUX
ejpam-1234	604	18	compatible	compatible	ADJ
ejpam-1234	604	19	pairs	pair	NOUN
ejpam-1234	604	20	of	of	ADP
ejpam-1234	604	21	a	a	DET
ejpam-1234	604	22	non	non	ADJ
ejpam-1234	604	23	-	-	ADJ
ejpam-1234	604	24	abelian	abelian	ADJ
ejpam-1234	604	25	cocycle	cocycle	PROPN
ejpam-1234	604	26	ϕ	ϕ	PROPN
ejpam-1234	604	27	and	and	CCONJ
ejpam-1234	604	28	a	a	DET
ejpam-1234	604	29	section	section	NOUN
ejpam-1234	604	30	independent	independent	ADJ
ejpam-1234	604	31	cocycle	cocycle	NOUN
ejpam-1234	604	32	γ	γ	PROPN
ejpam-1234	604	33	compatible	compatible	ADJ
ejpam-1234	604	34	with	with	ADP
ejpam-1234	604	35	the	the	DET
ejpam-1234	604	36	given	give	VERB
ejpam-1234	604	37	special	special	ADJ
ejpam-1234	604	38	g	g	NOUN
ejpam-1234	604	39	-	-	PUNCT
ejpam-1234	604	40	reconstruction	reconstruction	NOUN
ejpam-1234	604	41	datum	datum	NOUN
ejpam-1234	604	42	,	,	PUNCT
ejpam-1234	604	43	such	such	ADJ
ejpam-1234	604	44	that	that	SCONJ
ejpam-1234	604	45	ϕg	ϕg	NOUN
ejpam-1234	604	46	,	,	PUNCT
ejpam-1234	604	47	g	g	NOUN
ejpam-1234	604	48	=	=	SYM
ejpam-1234	604	49	1	1	NUM
ejpam-1234	604	50	and	and	CCONJ
ejpam-1234	604	51	trhg	trhg	NOUN
ejpam-1234	604	52	(	(	PUNCT
ejpam-1234	604	53	lc	lc	PROPN
ejpam-1234	604	54	◦	◦	NOUN
ejpam-1234	604	55	ρh	ρh	NOUN
ejpam-1234	604	56	)	)	PUNCT
ejpam-1234	604	57	=	=	SYM
ejpam-1234	604	58	trhh	trhh	PROPN
ejpam-1234	604	59	(	(	PUNCT
ejpam-1234	604	60	ρg−1	ρg−1	PROPN
ejpam-1234	604	61	◦	◦	PROPN
ejpam-1234	604	62	lc	lc	PROPN
ejpam-1234	604	63	)	)	PUNCT
ejpam-1234	604	64	for	for	ADP
ejpam-1234	604	65	any	any	DET
ejpam-1234	604	66	c	c	PROPN
ejpam-1234	604	67	∈h[g	∈h[g	PROPN
ejpam-1234	604	68	,	,	PUNCT
ejpam-1234	604	69	h	h	NOUN
ejpam-1234	604	70	]	]	PUNCT
ejpam-1234	604	71	.	.	PUNCT
ejpam-1234	605	1	remark	remark	PROPN
ejpam-1234	605	2	10	10	NUM
ejpam-1234	605	3	.	.	PUNCT
ejpam-1234	606	1	given	give	VERB
ejpam-1234	606	2	ϕg	ϕg	PROPN
ejpam-1234	606	3	,	,	PUNCT
ejpam-1234	606	4	h	h	NOUN
ejpam-1234	606	5	and	and	CCONJ
ejpam-1234	606	6	γg	γg	ADV
ejpam-1234	606	7	,	,	PUNCT
ejpam-1234	606	8	h	h	NOUN
ejpam-1234	606	9	,	,	PUNCT
ejpam-1234	606	10	the	the	DET
ejpam-1234	606	11	multiplication	multiplication	NOUN
ejpam-1234	606	12	on	on	ADP
ejpam-1234	606	13	h	h	NOUN
ejpam-1234	606	14	=	=	SYM
ejpam-1234	606	15	⊕ghg	⊕ghg	NOUN
ejpam-1234	606	16	is	be	AUX
ejpam-1234	606	17	given	give	VERB
ejpam-1234	606	18	by	by	ADP
ejpam-1234	606	19	ag	ag	PROPN
ejpam-1234	606	20	·	·	PUNCT
ejpam-1234	606	21	bh	bh	NOUN
ejpam-1234	606	22	:	:	PUNCT
ejpam-1234	606	23	=	=	SYM
ejpam-1234	606	24	rgh(ig(ag	rgh(ig(ag	NOUN
ejpam-1234	606	25	)	)	PUNCT
ejpam-1234	606	26	·	·	PUNCT
ejpam-1234	606	27	e	e	X
ejpam-1234	606	28	ih(bh	ih(bh	PROPN
ejpam-1234	606	29	)	)	PUNCT
ejpam-1234	606	30	·	·	PUNCT
ejpam-1234	607	1	e	e	X
ejpam-1234	607	2	γg	γg	ADV
ejpam-1234	607	3	,	,	PUNCT
ejpam-1234	607	4	h	h	NOUN
ejpam-1234	607	5	)	)	PUNCT
ejpam-1234	607	6	,	,	PUNCT
ejpam-1234	607	7	the	the	DET
ejpam-1234	607	8	action	action	NOUN
ejpam-1234	607	9	ρg	ρg	NOUN
ejpam-1234	607	10	on	on	ADP
ejpam-1234	607	11	hh	hh	PROPN
ejpam-1234	607	12	is	be	AUX
ejpam-1234	607	13	defined	define	VERB
ejpam-1234	607	14	by	by	ADP
ejpam-1234	607	15	ϕg(bh	ϕg(bh	PROPN
ejpam-1234	607	16	)	)	PUNCT
ejpam-1234	607	17	:	:	PUNCT
ejpam-1234	608	1	=	=	SYM
ejpam-1234	608	2	rghg−1(ϕg	rghg−1(ϕg	NOUN
ejpam-1234	608	3	,	,	PUNCT
ejpam-1234	608	4	hρg(ih(bh	hρg(ih(bh	PROPN
ejpam-1234	608	5	)	)	PUNCT
ejpam-1234	608	6	)	)	PUNCT
ejpam-1234	608	7	)	)	PUNCT
ejpam-1234	608	8	,	,	PUNCT
ejpam-1234	608	9	and	and	CCONJ
ejpam-1234	608	10	the	the	DET
ejpam-1234	608	11	metric	metric	NOUN
ejpam-1234	608	12	is	be	AUX
ejpam-1234	608	13	defined	define	VERB
ejpam-1234	608	14	by	by	ADP
ejpam-1234	608	15	η(ag	η(ag	PROPN
ejpam-1234	608	16	,	,	PUNCT
ejpam-1234	608	17	bg−1	bg−1	PROPN
ejpam-1234	608	18	)	)	PUNCT
ejpam-1234	608	19	:	:	PUNCT
ejpam-1234	608	20	=	=	SYM
ejpam-1234	608	21	ηe(ig(ag	ηe(ig(ag	X
ejpam-1234	608	22	)	)	PUNCT
ejpam-1234	608	23	·	·	PUNCT
ejpam-1234	608	24	e	e	NOUN
ejpam-1234	608	25	ig−1(bg−1	ig−1(bg−1	PROPN
ejpam-1234	608	26	)	)	PUNCT
ejpam-1234	608	27	·	·	PUNCT
ejpam-1234	608	28	e	e	X
ejpam-1234	608	29	γg	γg	ADV
ejpam-1234	608	30	,	,	PUNCT
ejpam-1234	608	31	g−1,1e	g−1,1e	NOUN
ejpam-1234	608	32	)	)	PUNCT
ejpam-1234	608	33	and	and	CCONJ
ejpam-1234	608	34	ηe(ag	ηe(ag	PROPN
ejpam-1234	608	35	,	,	PUNCT
ejpam-1234	608	36	bh	bh	NOUN
ejpam-1234	608	37	)	)	PUNCT
ejpam-1234	608	38	=	=	SYM
ejpam-1234	608	39	0	0	PUNCT
ejpam-1234	609	1	if	if	SCONJ
ejpam-1234	609	2	gh	gh	PROPN
ejpam-1234	609	3	6=	6=	PROPN
ejpam-1234	609	4	e.	e.	PROPN
ejpam-1234	609	5	those	those	DET
ejpam-1234	609	6	definition	definition	NOUN
ejpam-1234	609	7	is	be	AUX
ejpam-1234	609	8	independent	independent	ADJ
ejpam-1234	609	9	from	from	ADP
ejpam-1234	609	10	the	the	DET
ejpam-1234	609	11	choice	choice	NOUN
ejpam-1234	609	12	of	of	ADP
ejpam-1234	609	13	sections	section	NOUN
ejpam-1234	609	14	ig	ig	PROPN
ejpam-1234	609	15	because	because	SCONJ
ejpam-1234	609	16	of	of	ADP
ejpam-1234	609	17	the	the	DET
ejpam-1234	609	18	section	section	NOUN
ejpam-1234	609	19	independence	independence	NOUN
ejpam-1234	609	20	of	of	ADP
ejpam-1234	609	21	γ	γ	PROPN
ejpam-1234	609	22	.	.	PROPN
ejpam-1234	609	23	on	on	ADP
ejpam-1234	609	24	the	the	DET
ejpam-1234	609	25	other	other	ADJ
ejpam-1234	609	26	hand	hand	NOUN
ejpam-1234	609	27	,	,	PUNCT
ejpam-1234	609	28	given	give	VERB
ejpam-1234	609	29	a	a	DET
ejpam-1234	609	30	g	g	NOUN
ejpam-1234	609	31	-	-	PUNCT
ejpam-1234	609	32	frobenius	frobenius	NOUN
ejpam-1234	609	33	algebra	algebra	NOUN
ejpam-1234	609	34	,	,	PUNCT
ejpam-1234	609	35	γ	γ	PROPN
ejpam-1234	609	36	and	and	CCONJ
ejpam-1234	609	37	ϕ	ϕ	PROPN
ejpam-1234	609	38	are	be	AUX
ejpam-1234	609	39	defined	define	VERB
ejpam-1234	609	40	by	by	ADP
ejpam-1234	609	41	1g1h	1g1h	NOUN
ejpam-1234	609	42	=	=	NOUN
ejpam-1234	609	43	γg	γg	ADV
ejpam-1234	609	44	,	,	PUNCT
ejpam-1234	609	45	h	h	PROPN
ejpam-1234	609	46	·	·	PUNCT
ejpam-1234	609	47	1gh	1gh	NOUN
ejpam-1234	609	48	(	(	PUNCT
ejpam-1234	609	49	γg	γg	ADV
ejpam-1234	609	50	,	,	PUNCT
ejpam-1234	609	51	h	h	NOUN
ejpam-1234	609	52	∈he	∈he	NOUN
ejpam-1234	609	53	)	)	PUNCT
ejpam-1234	609	54	and	and	CCONJ
ejpam-1234	609	55	ϕg(1h	ϕg(1h	NUM
ejpam-1234	609	56	)	)	PUNCT
ejpam-1234	610	1	=	=	SYM
ejpam-1234	610	2	ϕg	ϕg	PROPN
ejpam-1234	610	3	,	,	PUNCT
ejpam-1234	610	4	h1ghg−1	h1ghg−1	PROPN
ejpam-1234	610	5	(	(	PUNCT
ejpam-1234	610	6	ϕg	ϕg	INTJ
ejpam-1234	610	7	,	,	PUNCT
ejpam-1234	610	8	h	h	NOUN
ejpam-1234	610	9	∈	∈	PROPN
ejpam-1234	610	10	k×	k×	PROPN
ejpam-1234	610	11	)	)	PUNCT
ejpam-1234	610	12	.	.	PUNCT
ejpam-1234	611	1	definition	definition	NOUN
ejpam-1234	611	2	10	10	NUM
ejpam-1234	611	3	(	(	PUNCT
ejpam-1234	611	4	normality	normality	NOUN
ejpam-1234	611	5	)	)	PUNCT
ejpam-1234	611	6	.	.	PUNCT
ejpam-1234	612	1	let	let	VERB
ejpam-1234	612	2	i	i	PRON
ejpam-1234	612	3	be	be	AUX
ejpam-1234	612	4	a	a	DET
ejpam-1234	612	5	finite	finite	ADJ
ejpam-1234	612	6	set	set	NOUN
ejpam-1234	612	7	of	of	ADP
ejpam-1234	612	8	cardinality	cardinality	NOUN
ejpam-1234	612	9	|i	|i	VERB
ejpam-1234	612	10	|	|	ADV
ejpam-1234	612	11	=	=	SYM
ejpam-1234	612	12	n.	n.	NOUN
ejpam-1234	612	13	consider	consider	VERB
ejpam-1234	612	14	a	a	DET
ejpam-1234	612	15	special	special	ADJ
ejpam-1234	612	16	σi	σi	X
ejpam-1234	612	17	frobenius	frobenius	NOUN
ejpam-1234	612	18	algebra	algebra	NOUN
ejpam-1234	612	19	(	(	PUNCT
ejpam-1234	612	20	h	h	NOUN
ejpam-1234	612	21	,	,	PUNCT
ejpam-1234	612	22	ρ	ρ	PROPN
ejpam-1234	612	23	,	,	PUNCT
ejpam-1234	612	24	·	·	PUNCT
ejpam-1234	612	25	,	,	PUNCT
ejpam-1234	612	26	{	{	PUNCT
ejpam-1234	612	27	1σ},η	1σ},η	NUM
ejpam-1234	612	28	)	)	PUNCT
ejpam-1234	612	29	.	.	PUNCT
ejpam-1234	613	1	two	two	NUM
ejpam-1234	613	2	permutations	permutation	NOUN
ejpam-1234	613	3	σ	σ	NOUN
ejpam-1234	613	4	,	,	PUNCT
ejpam-1234	613	5	τ	τ	PROPN
ejpam-1234	613	6	∈	∈	PROPN
ejpam-1234	613	7	σ	σ	NOUN
ejpam-1234	613	8	are	be	AUX
ejpam-1234	613	9	transversal	transversal	ADJ
ejpam-1234	613	10	if	if	SCONJ
ejpam-1234	613	11	|σ|+	|σ|+	PROPN
ejpam-1234	613	12	|τ|	|τ|	ADP
ejpam-1234	613	13	=	=	PUNCT
ejpam-1234	613	14	|στ|	|στ|	PROPN
ejpam-1234	613	15	.	.	PUNCT
ejpam-1234	614	1	the	the	DET
ejpam-1234	614	2	graded	grade	VERB
ejpam-1234	614	3	cocycle	cocycle	NOUN
ejpam-1234	614	4	γ	γ	PROPN
ejpam-1234	614	5	induced	induce	VERB
ejpam-1234	614	6	by	by	ADP
ejpam-1234	614	7	a	a	DET
ejpam-1234	614	8	special	special	ADJ
ejpam-1234	614	9	σi	σi	NOUN
ejpam-1234	614	10	-frobenius	-frobenius	PROPN
ejpam-1234	614	11	algebra	algebra	NOUN
ejpam-1234	614	12	is	be	AUX
ejpam-1234	614	13	normalized	normalize	VERB
ejpam-1234	614	14	if	if	SCONJ
ejpam-1234	614	15	γσ	γσ	INTJ
ejpam-1234	614	16	,	,	PUNCT
ejpam-1234	614	17	τ	τ	PROPN
ejpam-1234	614	18	=	=	PUNCT
ejpam-1234	614	19	1e	1e	PROPN
ejpam-1234	614	20	for	for	ADP
ejpam-1234	614	21	all	all	DET
ejpam-1234	614	22	transversal	transversal	ADJ
ejpam-1234	614	23	pair	pair	NOUN
ejpam-1234	614	24	σ	σ	PROPN
ejpam-1234	614	25	,	,	PUNCT
ejpam-1234	614	26	τ	τ	PROPN
ejpam-1234	614	27	with	with	ADP
ejpam-1234	614	28	|τ|=	|τ|=	PROPN
ejpam-1234	614	29	1	1	NUM
ejpam-1234	614	30	[	[	X
ejpam-1234	614	31	definition	definition	NOUN
ejpam-1234	614	32	6.4	6.4	NUM
ejpam-1234	614	33	,	,	PUNCT
ejpam-1234	614	34	13	13	NUM
ejpam-1234	614	35	]	]	PUNCT
ejpam-1234	614	36	.	.	PUNCT
ejpam-1234	615	1	references	reference	NOUN
ejpam-1234	615	2	510	510	NUM
ejpam-1234	615	3	theorem	theorem	NOUN
ejpam-1234	615	4	8	8	NUM
ejpam-1234	615	5	(	(	PUNCT
ejpam-1234	615	6	[	[	X
ejpam-1234	615	7	theorem	theorem	ADJ
ejpam-1234	615	8	6.5	6.5	NUM
ejpam-1234	615	9	,	,	PUNCT
ejpam-1234	615	10	13	13	NUM
ejpam-1234	615	11	]	]	PUNCT
ejpam-1234	615	12	)	)	PUNCT
ejpam-1234	615	13	.	.	PUNCT
ejpam-1234	616	1	if	if	SCONJ
ejpam-1234	616	2	γ	γ	PROPN
ejpam-1234	616	3	is	be	AUX
ejpam-1234	616	4	normalized	normalize	VERB
ejpam-1234	616	5	,	,	PUNCT
ejpam-1234	616	6	then	then	ADV
ejpam-1234	616	7	γ	γ	PROPN
ejpam-1234	616	8	is	be	AUX
ejpam-1234	616	9	completely	completely	ADV
ejpam-1234	616	10	determined	determine	VERB
ejpam-1234	616	11	by	by	ADP
ejpam-1234	616	12	γτ	γτ	PROPN
ejpam-1234	616	13	,	,	PUNCT
ejpam-1234	616	14	τ	τ	PROPN
ejpam-1234	616	15	=	=	SYM
ejpam-1234	616	16	řτ(1τ	řτ(1τ	PROPN
ejpam-1234	616	17	)	)	PUNCT
ejpam-1234	616	18	with	with	ADP
ejpam-1234	616	19	|τ|=	|τ|=	PROPN
ejpam-1234	616	20	1	1	NUM
ejpam-1234	616	21	.	.	PUNCT
ejpam-1234	616	22	lehn	lehn	NOUN
ejpam-1234	616	23	-	-	PUNCT
ejpam-1234	616	24	sorger	sorger	NOUN
ejpam-1234	616	25	’s	’s	PART
ejpam-1234	616	26	algebras	algebra	NOUN
ejpam-1234	616	27	let	let	VERB
ejpam-1234	616	28	(	(	PUNCT
ejpam-1234	616	29	a	a	DET
ejpam-1234	616	30	,	,	PUNCT
ejpam-1234	616	31	·	·	PUNCT
ejpam-1234	616	32	,	,	PUNCT
ejpam-1234	616	33	1,η	1,η	NUM
ejpam-1234	616	34	)	)	PUNCT
ejpam-1234	616	35	be	be	VERB
ejpam-1234	616	36	a	a	DET
ejpam-1234	616	37	commutative	commutative	ADJ
ejpam-1234	616	38	graded	grade	VERB
ejpam-1234	616	39	frobenius	frobenius	ADJ
ejpam-1234	616	40	algebra	algebra	NOUN
ejpam-1234	616	41	of	of	ADP
ejpam-1234	616	42	degree	degree	NOUN
ejpam-1234	616	43	2d	2d	NOUN
ejpam-1234	616	44	.	.	PUNCT
ejpam-1234	617	1	if	if	SCONJ
ejpam-1234	617	2	j	j	PROPN
ejpam-1234	617	3	is	be	AUX
ejpam-1234	617	4	a	a	DET
ejpam-1234	617	5	finite	finite	ADJ
ejpam-1234	617	6	set	set	NOUN
ejpam-1234	617	7	,	,	PUNCT
ejpam-1234	617	8	then	then	ADV
ejpam-1234	617	9	the	the	DET
ejpam-1234	617	10	tensor	tensor	NOUN
ejpam-1234	617	11	product	product	NOUN
ejpam-1234	617	12	a⊗j	a⊗j	NOUN
ejpam-1234	617	13	over	over	ADP
ejpam-1234	617	14	j	j	PROPN
ejpam-1234	617	15	is	be	AUX
ejpam-1234	617	16	naturally	naturally	ADV
ejpam-1234	617	17	a	a	DET
ejpam-1234	617	18	commutative	commutative	ADJ
ejpam-1234	617	19	graded	grade	VERB
ejpam-1234	617	20	frobenius	frobenius	NOUN
ejpam-1234	617	21	algebra	algebra	NOUN
ejpam-1234	617	22	.	.	PUNCT
ejpam-1234	618	1	if	if	SCONJ
ejpam-1234	618	2	φ	φ	PROPN
ejpam-1234	618	3	:	:	PUNCT
ejpam-1234	618	4	j1	j1	PROPN
ejpam-1234	618	5	։	։	PROPN
ejpam-1234	618	6	j2	j2	PROPN
ejpam-1234	618	7	is	be	AUX
ejpam-1234	618	8	a	a	DET
ejpam-1234	618	9	surjective	surjective	ADJ
ejpam-1234	618	10	map	map	NOUN
ejpam-1234	618	11	between	between	ADP
ejpam-1234	618	12	finite	finite	ADJ
ejpam-1234	618	13	sets	set	NOUN
ejpam-1234	618	14	,	,	PUNCT
ejpam-1234	618	15	then	then	ADV
ejpam-1234	618	16	there	there	PRON
ejpam-1234	618	17	is	be	VERB
ejpam-1234	618	18	an	an	DET
ejpam-1234	618	19	induced	induced	ADJ
ejpam-1234	618	20	homomorphism	homomorphism	NOUN
ejpam-1234	618	21	φ∗	φ∗	NOUN
ejpam-1234	618	22	:	:	PUNCT
ejpam-1234	619	1	a⊗j1	a⊗j1	INTJ
ejpam-1234	619	2	։	։	VERB
ejpam-1234	619	3	a⊗j2	a⊗j2	PROPN
ejpam-1234	619	4	defined	define	VERB
ejpam-1234	619	5	by	by	ADP
ejpam-1234	619	6	⊗	⊗	PROPN
ejpam-1234	619	7	i∈j1	i∈j1	PROPN
ejpam-1234	619	8	ai	ai	VERB
ejpam-1234	619	9	7→	7→	PROPN
ejpam-1234	619	10	⊗	⊗	PROPN
ejpam-1234	619	11	j∈j2	j∈j2	PROPN
ejpam-1234	619	12	�	�	PROPN
ejpam-1234	619	13	∏	∏	PROPN
ejpam-1234	620	1	φ(i)=	φ(i)=	PROPN
ejpam-1234	620	2	j	j	PROPN
ejpam-1234	620	3	ai	ai	VERB
ejpam-1234	620	4	�	�	PROPN
ejpam-1234	620	5	.	.	PUNCT
ejpam-1234	621	1	by	by	ADP
ejpam-1234	621	2	using	use	VERB
ejpam-1234	621	3	the	the	DET
ejpam-1234	621	4	metric	metric	NOUN
ejpam-1234	621	5	,	,	PUNCT
ejpam-1234	621	6	we	we	PRON
ejpam-1234	621	7	can	can	AUX
ejpam-1234	621	8	identify	identify	VERB
ejpam-1234	621	9	a	a	DET
ejpam-1234	621	10	frobenius	frobenius	ADJ
ejpam-1234	621	11	algebra	algebra	NOUN
ejpam-1234	621	12	with	with	ADP
ejpam-1234	621	13	its	its	PRON
ejpam-1234	621	14	vector	vector	NOUN
ejpam-1234	621	15	space	space	NOUN
ejpam-1234	621	16	dual	dual	ADJ
ejpam-1234	621	17	,	,	PUNCT
ejpam-1234	621	18	and	and	CCONJ
ejpam-1234	621	19	thus	thus	ADV
ejpam-1234	621	20	we	we	PRON
ejpam-1234	621	21	also	also	ADV
ejpam-1234	621	22	have	have	VERB
ejpam-1234	621	23	an	an	DET
ejpam-1234	621	24	induced	induced	ADJ
ejpam-1234	621	25	map	map	NOUN
ejpam-1234	621	26	φ∗	φ∗	NOUN
ejpam-1234	621	27	:	:	PUNCT
ejpam-1234	622	1	a⊗j2	a⊗j2	VERB
ejpam-1234	622	2	−→	−→	NOUN
ejpam-1234	622	3	a⊗j1	a⊗j1	PROPN
ejpam-1234	622	4	.	.	PUNCT
ejpam-1234	623	1	let	let	VERB
ejpam-1234	623	2	i	i	PRON
ejpam-1234	623	3	be	be	AUX
ejpam-1234	623	4	a	a	DET
ejpam-1234	623	5	finite	finite	ADJ
ejpam-1234	623	6	set	set	NOUN
ejpam-1234	623	7	of	of	ADP
ejpam-1234	623	8	cardinality	cardinality	NOUN
ejpam-1234	623	9	|i	|i	VERB
ejpam-1234	623	10	|	|	ADV
ejpam-1234	623	11	=	=	PUNCT
ejpam-1234	623	12	n.	n.	NOUN
ejpam-1234	623	13	the	the	DET
ejpam-1234	623	14	underlying	underlie	VERB
ejpam-1234	623	15	vector	vector	NOUN
ejpam-1234	623	16	space	space	NOUN
ejpam-1234	623	17	for	for	ADP
ejpam-1234	623	18	the	the	DET
ejpam-1234	623	19	lehn	lehn	NOUN
ejpam-1234	623	20	-	-	PUNCT
ejpam-1234	623	21	sorger	sorger	NOUN
ejpam-1234	623	22	’s	’s	PART
ejpam-1234	623	23	algebra	algebra	NOUN
ejpam-1234	623	24	associated	associate	VERB
ejpam-1234	623	25	to	to	ADP
ejpam-1234	623	26	a	a	PRON
ejpam-1234	623	27	is	be	AUX
ejpam-1234	623	28	a{σ	a{σ	NOUN
ejpam-1234	623	29	}	}	PUNCT
ejpam-1234	623	30	:	:	PUNCT
ejpam-1234	623	31	=	=	PUNCT
ejpam-1234	623	32	⊕	⊕	PROPN
ejpam-1234	623	33	σ∈σi	σ∈σi	NOUN
ejpam-1234	623	34	a⊗iσ	a⊗iσ	NOUN
ejpam-1234	623	35	where	where	SCONJ
ejpam-1234	623	36	iσ	iσ	ADV
ejpam-1234	623	37	is	be	AUX
ejpam-1234	623	38	the	the	DET
ejpam-1234	623	39	set	set	NOUN
ejpam-1234	623	40	of	of	ADP
ejpam-1234	623	41	orbits	orbit	NOUN
ejpam-1234	623	42	in	in	ADP
ejpam-1234	623	43	i	i	PRON
ejpam-1234	623	44	by	by	ADP
ejpam-1234	623	45	the	the	DET
ejpam-1234	623	46	action	action	NOUN
ejpam-1234	623	47	of	of	ADP
ejpam-1234	623	48	the	the	DET
ejpam-1234	623	49	subgroup	subgroup	PROPN
ejpam-1234	623	50	〈	〈	PROPN
ejpam-1234	623	51	σ	σ	PROPN
ejpam-1234	623	52	〉	〉	NOUN
ejpam-1234	623	53	generated	generate	VERB
ejpam-1234	623	54	by	by	ADP
ejpam-1234	623	55	σ	σ	PROPN
ejpam-1234	623	56	.	.	PUNCT
ejpam-1234	624	1	there	there	PRON
ejpam-1234	624	2	is	be	VERB
ejpam-1234	624	3	an	an	DET
ejpam-1234	624	4	obvious	obvious	ADJ
ejpam-1234	624	5	σi	σi	NOUN
ejpam-1234	624	6	-graded	-graded	ADJ
ejpam-1234	624	7	σi	σi	NOUN
ejpam-1234	624	8	-module	-module	NOUN
ejpam-1234	624	9	structure	structure	NOUN
ejpam-1234	624	10	.	.	PUNCT
ejpam-1234	625	1	the	the	DET
ejpam-1234	625	2	q	q	NOUN
ejpam-1234	625	3	-	-	PUNCT
ejpam-1234	625	4	grading	grading	NOUN
ejpam-1234	625	5	is	be	AUX
ejpam-1234	625	6	given	give	VERB
ejpam-1234	625	7	by	by	ADP
ejpam-1234	625	8	degq	degq	NOUN
ejpam-1234	625	9	aσ	aσ	NOUN
ejpam-1234	625	10	:	:	PUNCT
ejpam-1234	625	11	=	=	SYM
ejpam-1234	625	12	|aσ|+	|aσ|+	PROPN
ejpam-1234	625	13	d	d	X
ejpam-1234	625	14	·	·	PUNCT
ejpam-1234	625	15	|σ|	|σ|	ADV
ejpam-1234	625	16	,	,	PUNCT
ejpam-1234	625	17	aσ	aσ	PRON
ejpam-1234	625	18	∈	∈	VERB
ejpam-1234	625	19	a	a	DET
ejpam-1234	625	20	⊗iσ	⊗iσ	NOUN
ejpam-1234	625	21	(	(	PUNCT
ejpam-1234	625	22	13	13	NUM
ejpam-1234	625	23	)	)	PUNCT
ejpam-1234	625	24	where	where	SCONJ
ejpam-1234	625	25	|aσ|	|aσ|	PROPN
ejpam-1234	625	26	is	be	AUX
ejpam-1234	625	27	the	the	DET
ejpam-1234	625	28	degree	degree	NOUN
ejpam-1234	625	29	in	in	ADP
ejpam-1234	625	30	a⊗iσ	a⊗iσ	NOUN
ejpam-1234	625	31	and	and	CCONJ
ejpam-1234	625	32	|σ|	|σ|	PROPN
ejpam-1234	625	33	is	be	AUX
ejpam-1234	625	34	the	the	DET
ejpam-1234	625	35	minimum	minimum	ADJ
ejpam-1234	625	36	transpositions	transposition	NOUN
ejpam-1234	625	37	to	to	PART
ejpam-1234	625	38	express	express	VERB
ejpam-1234	625	39	σ	σ	PROPN
ejpam-1234	625	40	.	.	PUNCT
ejpam-1234	626	1	the	the	DET
ejpam-1234	626	2	euler	euler	NOUN
ejpam-1234	626	3	class	class	PROPN
ejpam-1234	626	4	e	e	PROPN
ejpam-1234	626	5	of	of	ADP
ejpam-1234	626	6	a	a	DET
ejpam-1234	626	7	frobenius	frobenius	NOUN
ejpam-1234	626	8	algebra	algebra	NOUN
ejpam-1234	626	9	a	a	PRON
ejpam-1234	626	10	is	be	AUX
ejpam-1234	626	11	defined	define	VERB
ejpam-1234	626	12	as	as	ADP
ejpam-1234	626	13	the	the	DET
ejpam-1234	626	14	image	image	NOUN
ejpam-1234	626	15	of	of	ADP
ejpam-1234	626	16	1	1	NUM
ejpam-1234	626	17	under	under	ADP
ejpam-1234	626	18	the	the	DET
ejpam-1234	626	19	map	map	NOUN
ejpam-1234	626	20	a	a	DET
ejpam-1234	626	21	−→	−→	NOUN
ejpam-1234	626	22	a	a	DET
ejpam-1234	626	23	⊗	⊗	NOUN
ejpam-1234	626	24	a	a	DET
ejpam-1234	626	25	−→	−→	NOUN
ejpam-1234	626	26	a	a	PRON
ejpam-1234	626	27	where	where	SCONJ
ejpam-1234	626	28	the	the	DET
ejpam-1234	626	29	first	first	ADJ
ejpam-1234	626	30	map	map	NOUN
ejpam-1234	626	31	is	be	AUX
ejpam-1234	626	32	the	the	DET
ejpam-1234	626	33	comultiplication	comultiplication	NOUN
ejpam-1234	626	34	and	and	CCONJ
ejpam-1234	626	35	the	the	DET
ejpam-1234	626	36	second	second	ADJ
ejpam-1234	626	37	map	map	NOUN
ejpam-1234	626	38	is	be	AUX
ejpam-1234	626	39	the	the	DET
ejpam-1234	626	40	multiplication	multiplication	NOUN
ejpam-1234	626	41	.	.	PUNCT
ejpam-1234	627	1	the	the	DET
ejpam-1234	627	2	graph	graph	NOUN
ejpam-1234	627	3	defect	defect	NOUN
ejpam-1234	627	4	gd(σ	gd(σ	NOUN
ejpam-1234	627	5	,	,	PUNCT
ejpam-1234	627	6	τ	τ	X
ejpam-1234	627	7	)	)	PUNCT
ejpam-1234	627	8	:	:	PUNCT
ejpam-1234	628	1	iσ	iσ	VERB
ejpam-1234	628	2	,	,	PUNCT
ejpam-1234	628	3	τ	τ	PROPN
ejpam-1234	628	4	−→	−→	NOUN
ejpam-1234	628	5	z≥0	z≥0	PROPN
ejpam-1234	628	6	is	be	AUX
ejpam-1234	628	7	defined	define	VERB
ejpam-1234	628	8	by	by	ADP
ejpam-1234	628	9	gd(σ	gd(σ	NOUN
ejpam-1234	628	10	,	,	PUNCT
ejpam-1234	628	11	τ)c	τ)c	NOUN
ejpam-1234	628	12	=	=	SYM
ejpam-1234	628	13	1	1	NUM
ejpam-1234	628	14	2	2	NUM
ejpam-1234	628	15	(	(	PUNCT
ejpam-1234	628	16	|c|+	|c|+	NOUN
ejpam-1234	628	17	2−	2−	NUM
ejpam-1234	628	18	|c/〈σ〉|	|c/〈σ〉|	PROPN
ejpam-1234	628	19	−	−	PROPN
ejpam-1234	628	20	|c/〈τ〉|	|c/〈τ〉|	PROPN
ejpam-1234	628	21	−	−	PROPN
ejpam-1234	628	22	|c	|c	NOUN
ejpam-1234	628	23	/	/	SYM
ejpam-1234	628	24	στ|	στ|	NOUN
ejpam-1234	628	25	)	)	PUNCT
ejpam-1234	628	26	.	.	PUNCT
ejpam-1234	629	1	using	use	VERB
ejpam-1234	629	2	these	these	PRON
ejpam-1234	629	3	,	,	PUNCT
ejpam-1234	629	4	the	the	DET
ejpam-1234	629	5	lehn	lehn	NOUN
ejpam-1234	629	6	-	-	PUNCT
ejpam-1234	629	7	sorger	sorger	NOUN
ejpam-1234	629	8	’s	’s	PART
ejpam-1234	629	9	product	product	NOUN
ejpam-1234	629	10	is	be	AUX
ejpam-1234	629	11	defined	define	VERB
ejpam-1234	629	12	by	by	ADP
ejpam-1234	629	13	aσ	aσ	PRON
ejpam-1234	629	14	·	·	PUNCT
ejpam-1234	629	15	bτ	bτ	PROPN
ejpam-1234	630	1	=	=	SYM
ejpam-1234	630	2	f	f	PROPN
ejpam-1234	630	3	∗	∗	NOUN
ejpam-1234	630	4			PROPN
ejpam-1234	630	5			NOUN
ejpam-1234	630	6			PROPN
ejpam-1234	630	7	fσ∗aσ	fσ∗aσ	NOUN
ejpam-1234	630	8	·	·	PUNCT
ejpam-1234	631	1	fτ∗bτ	fτ∗bτ	PUNCT
ejpam-1234	631	2	·	·	PUNCT
ejpam-1234	631	3			PROPN
ejpam-1234	631	4			NOUN
ejpam-1234	631	5			PROPN
ejpam-1234	631	6	⊗	⊗	PROPN
ejpam-1234	631	7	c∈iσ	c∈iσ	NOUN
ejpam-1234	631	8	,	,	PUNCT
ejpam-1234	631	9	τ	τ	PROPN
ejpam-1234	631	10	egd(σ	egd(σ	PROPN
ejpam-1234	631	11	,	,	PUNCT
ejpam-1234	631	12	τ)c	τ)c	NOUN
ejpam-1234	631	13			NOUN
ejpam-1234	631	14			NOUN
ejpam-1234	631	15			PUNCT
ejpam-1234	632	1			PROPN
ejpam-1234	632	2			VERB
ejpam-1234	632	3			PUNCT
ejpam-1234	633	1	where	where	SCONJ
ejpam-1234	633	2	fσ	fσ	X
ejpam-1234	633	3	:	:	PUNCT
ejpam-1234	633	4	iσ	iσ	AUX
ejpam-1234	633	5	։	։	PROPN
ejpam-1234	633	6	iσ	iσ	PROPN
ejpam-1234	633	7	,	,	PUNCT
ejpam-1234	633	8	τ	τ	PROPN
ejpam-1234	633	9	,	,	PUNCT
ejpam-1234	633	10	fτ	fτ	X
ejpam-1234	633	11	:	:	PUNCT
ejpam-1234	633	12	iτ։	iτ։	NOUN
ejpam-1234	633	13	iσ	iσ	ADP
ejpam-1234	633	14	,	,	PUNCT
ejpam-1234	633	15	τ	τ	PROPN
ejpam-1234	633	16	and	and	CCONJ
ejpam-1234	633	17	f	f	PROPN
ejpam-1234	633	18	:	:	PUNCT
ejpam-1234	633	19	iστ։	iστ։	NOUN
ejpam-1234	633	20	iσ	iσ	PROPN
ejpam-1234	633	21	,	,	PUNCT
ejpam-1234	633	22	τ	τ	PROPN
ejpam-1234	633	23	.	.	PUNCT
ejpam-1234	633	24	note	note	VERB
ejpam-1234	633	25	that	that	SCONJ
ejpam-1234	633	26	,	,	PUNCT
ejpam-1234	633	27	if	if	SCONJ
ejpam-1234	633	28	σ	σ	PROPN
ejpam-1234	633	29	,	,	PUNCT
ejpam-1234	633	30	τ	τ	PROPN
ejpam-1234	633	31	are	be	AUX
ejpam-1234	633	32	transversal	transversal	ADJ
ejpam-1234	633	33	,	,	PUNCT
ejpam-1234	633	34	then	then	ADV
ejpam-1234	633	35	it	it	PRON
ejpam-1234	633	36	is	be	AUX
ejpam-1234	633	37	straightforward	straightforward	ADJ
ejpam-1234	633	38	computation	computation	NOUN
ejpam-1234	633	39	to	to	PART
ejpam-1234	633	40	see	see	VERB
ejpam-1234	633	41	that	that	SCONJ
ejpam-1234	633	42	gd(σ	gd(σ	NOUN
ejpam-1234	633	43	,	,	PUNCT
ejpam-1234	633	44	τ	τ	X
ejpam-1234	633	45	)	)	PUNCT
ejpam-1234	634	1	=	=	SYM
ejpam-1234	634	2	0	0	X
ejpam-1234	634	3	.	.	PUNCT
ejpam-1234	635	1	thus	thus	ADV
ejpam-1234	635	2	it	it	PRON
ejpam-1234	635	3	is	be	AUX
ejpam-1234	635	4	also	also	ADV
ejpam-1234	635	5	easy	easy	ADJ
ejpam-1234	635	6	to	to	PART
ejpam-1234	635	7	see	see	VERB
ejpam-1234	635	8	that	that	SCONJ
ejpam-1234	635	9	the	the	DET
ejpam-1234	635	10	induced	induce	VERB
ejpam-1234	635	11	graded	grade	VERB
ejpam-1234	635	12	cocycle	cocycle	NOUN
ejpam-1234	635	13	γ	γ	X
ejpam-1234	635	14	is	be	AUX
ejpam-1234	635	15	normalized	normalize	VERB
ejpam-1234	635	16	.	.	PUNCT
ejpam-1234	636	1	theorem	theorem	ADJ
ejpam-1234	636	2	9	9	NUM
ejpam-1234	636	3	(	(	PUNCT
ejpam-1234	636	4	[	[	X
ejpam-1234	636	5	14	14	NUM
ejpam-1234	636	6	,	,	PUNCT
ejpam-1234	636	7	13	13	NUM
ejpam-1234	636	8	]	]	NUM
ejpam-1234	636	9	)	)	PUNCT
ejpam-1234	636	10	.	.	PUNCT
ejpam-1234	637	1	a{σi	a{σi	PROPN
ejpam-1234	637	2	}	}	PUNCT
ejpam-1234	637	3	is	be	AUX
ejpam-1234	637	4	a	a	DET
ejpam-1234	637	5	graded	grade	VERB
ejpam-1234	637	6	special	special	ADJ
ejpam-1234	637	7	σi	σi	NOUN
ejpam-1234	637	8	-frobenius	-frobenius	PROPN
ejpam-1234	637	9	algebra	algebra	NOUN
ejpam-1234	637	10	and	and	CCONJ
ejpam-1234	637	11	its	its	PRON
ejpam-1234	637	12	graded	grade	VERB
ejpam-1234	637	13	cocycle	cocycle	NOUN
ejpam-1234	637	14	γ	γ	X
ejpam-1234	637	15	is	be	AUX
ejpam-1234	637	16	normalized	normalize	VERB
ejpam-1234	637	17	.	.	PUNCT