id	sid	tid	token	lemma	pos
ejpam-1949	1	1	european	european	PROPN
ejpam-1949	1	2	journal	journal	PROPN
ejpam-1949	1	3	of	of	ADP
ejpam-1949	1	4	pure	pure	ADJ
ejpam-1949	1	5	and	and	CCONJ
ejpam-1949	1	6	applied	apply	VERB
ejpam-1949	1	7	mathematics	mathematic	NOUN
ejpam-1949	1	8	vol	vol	NOUN
ejpam-1949	1	9	.	.	PUNCT
ejpam-1949	2	1	7	7	NUM
ejpam-1949	2	2	,	,	PUNCT
ejpam-1949	2	3	no	no	INTJ
ejpam-1949	2	4	.	.	NOUN
ejpam-1949	2	5	1	1	NUM
ejpam-1949	2	6	,	,	PUNCT
ejpam-1949	2	7	2014	2014	NUM
ejpam-1949	2	8	,	,	PUNCT
ejpam-1949	2	9	65	65	NUM
ejpam-1949	2	10	-	-	SYM
ejpam-1949	2	11	76	76	NUM
ejpam-1949	2	12	issn	issn	PROPN
ejpam-1949	2	13	1307	1307	NUM
ejpam-1949	2	14	-	-	SYM
ejpam-1949	2	15	5543	5543	NUM
ejpam-1949	2	16	–	–	PUNCT
ejpam-1949	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1949	2	18	relative	relative	ADJ
ejpam-1949	2	19	differential	differential	PROPN
ejpam-1949	2	20	k	k	NOUN
ejpam-1949	2	21	-	-	NOUN
ejpam-1949	2	22	theory	theory	NOUN
ejpam-1949	2	23	adnane	adnane	NOUN
ejpam-1949	2	24	elmrabty∗	elmrabty∗	PROPN
ejpam-1949	2	25	,	,	PUNCT
ejpam-1949	2	26	mohamed	mohamed	PROPN
ejpam-1949	2	27	maghfoul	maghfoul	PROPN
ejpam-1949	2	28	department	department	PROPN
ejpam-1949	2	29	of	of	ADP
ejpam-1949	2	30	mathematics	mathematic	NOUN
ejpam-1949	2	31	,	,	PUNCT
ejpam-1949	2	32	faculty	faculty	NOUN
ejpam-1949	2	33	of	of	ADP
ejpam-1949	2	34	sciences	science	NOUN
ejpam-1949	2	35	,	,	PUNCT
ejpam-1949	2	36	ibn	ibn	PROPN
ejpam-1949	2	37	tofail	tofail	NOUN
ejpam-1949	2	38	university	university	PROPN
ejpam-1949	2	39	,	,	PUNCT
ejpam-1949	2	40	kenitra	kenitra	PROPN
ejpam-1949	2	41	,	,	PUNCT
ejpam-1949	2	42	morocco	morocco	PROPN
ejpam-1949	2	43	abstract	abstract	NOUN
ejpam-1949	2	44	.	.	PUNCT
ejpam-1949	3	1	let	let	VERB
ejpam-1949	3	2	ρ	ρ	NOUN
ejpam-1949	3	3	:	:	PUNCT
ejpam-1949	3	4	y	y	PROPN
ejpam-1949	3	5	→	→	PUNCT
ejpam-1949	3	6	x	x	PUNCT
ejpam-1949	3	7	be	be	AUX
ejpam-1949	3	8	a	a	DET
ejpam-1949	3	9	smooth	smooth	ADJ
ejpam-1949	3	10	map	map	NOUN
ejpam-1949	3	11	between	between	ADP
ejpam-1949	3	12	two	two	NUM
ejpam-1949	3	13	smooth	smooth	ADJ
ejpam-1949	3	14	compact	compact	ADJ
ejpam-1949	3	15	manifolds	manifold	NOUN
ejpam-1949	3	16	.	.	PUNCT
ejpam-1949	4	1	we	we	PRON
ejpam-1949	4	2	define	define	VERB
ejpam-1949	4	3	the	the	DET
ejpam-1949	4	4	relative	relative	ADJ
ejpam-1949	4	5	differential	differential	NOUN
ejpam-1949	4	6	k	k	PROPN
ejpam-1949	4	7	-	-	ADJ
ejpam-1949	4	8	theory	theory	NOUN
ejpam-1949	4	9	group	group	NOUN
ejpam-1949	4	10	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	4	11	)	)	PUNCT
ejpam-1949	4	12	and	and	CCONJ
ejpam-1949	4	13	show	show	VERB
ejpam-1949	4	14	that	that	SCONJ
ejpam-1949	4	15	it	it	PRON
ejpam-1949	4	16	fits	fit	VERB
ejpam-1949	4	17	into	into	ADP
ejpam-1949	4	18	a	a	DET
ejpam-1949	4	19	six	six	NUM
ejpam-1949	4	20	-	-	PUNCT
ejpam-1949	4	21	term	term	NOUN
ejpam-1949	4	22	exact	exact	ADJ
ejpam-1949	4	23	sequence	sequence	NOUN
ejpam-1949	4	24	.	.	PUNCT
ejpam-1949	5	1	we	we	PRON
ejpam-1949	5	2	define	define	VERB
ejpam-1949	5	3	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	5	4	,	,	PUNCT
ejpam-1949	5	5	r	r	NOUN
ejpam-1949	5	6	/	/	SYM
ejpam-1949	5	7	z	z	NOUN
ejpam-1949	5	8	)	)	PUNCT
ejpam-1949	5	9	,	,	PUNCT
ejpam-1949	5	10	the	the	DET
ejpam-1949	5	11	k	k	NOUN
ejpam-1949	5	12	-	-	NOUN
ejpam-1949	5	13	theory	theory	NOUN
ejpam-1949	5	14	of	of	ADP
ejpam-1949	5	15	ρ	ρ	PROPN
ejpam-1949	5	16	with	with	ADP
ejpam-1949	5	17	r	r	NOUN
ejpam-1949	5	18	/	/	SYM
ejpam-1949	5	19	z	z	NOUN
ejpam-1949	5	20	coefficients	coefficient	NOUN
ejpam-1949	5	21	.	.	PUNCT
ejpam-1949	6	1	it	it	PRON
ejpam-1949	6	2	turns	turn	VERB
ejpam-1949	6	3	out	out	ADP
ejpam-1949	6	4	that	that	DET
ejpam-1949	6	5	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	6	6	,	,	PUNCT
ejpam-1949	6	7	r	r	NOUN
ejpam-1949	6	8	/	/	SYM
ejpam-1949	6	9	z	z	NOUN
ejpam-1949	6	10	)	)	PUNCT
ejpam-1949	6	11	is	be	AUX
ejpam-1949	6	12	isomorphic	isomorphic	ADJ
ejpam-1949	6	13	to	to	ADP
ejpam-1949	6	14	the	the	DET
ejpam-1949	6	15	group	group	NOUN
ejpam-1949	6	16	of	of	ADP
ejpam-1949	6	17	homomorphisms	homomorphism	NOUN
ejpam-1949	6	18	from	from	ADP
ejpam-1949	6	19	the	the	DET
ejpam-1949	6	20	relative	relative	ADJ
ejpam-1949	6	21	k	k	NOUN
ejpam-1949	6	22	-	-	NOUN
ejpam-1949	6	23	homology	homology	NOUN
ejpam-1949	6	24	of	of	ADP
ejpam-1949	6	25	ρ	ρ	PROPN
ejpam-1949	7	1	[	[	X
ejpam-1949	7	2	8	8	NUM
ejpam-1949	7	3	]	]	PUNCT
ejpam-1949	7	4	to	to	ADP
ejpam-1949	7	5	r	r	NOUN
ejpam-1949	7	6	/	/	SYM
ejpam-1949	7	7	z	z	NOUN
ejpam-1949	7	8	up	up	ADP
ejpam-1949	7	9	to	to	ADP
ejpam-1949	7	10	a	a	DET
ejpam-1949	7	11	degree	degree	NOUN
ejpam-1949	7	12	-	-	PUNCT
ejpam-1949	7	13	shift	shift	NOUN
ejpam-1949	7	14	by	by	ADP
ejpam-1949	7	15	one	one	NUM
ejpam-1949	7	16	.	.	PUNCT
ejpam-1949	8	1	2010	2010	NUM
ejpam-1949	8	2	mathematics	mathematic	NOUN
ejpam-1949	8	3	subject	subject	NOUN
ejpam-1949	8	4	classifications	classification	NOUN
ejpam-1949	8	5	:	:	PUNCT
ejpam-1949	8	6	19k33	19k33	NUM
ejpam-1949	8	7	,	,	PUNCT
ejpam-1949	8	8	51h25	51h25	NUM
ejpam-1949	8	9	key	key	ADJ
ejpam-1949	8	10	words	word	NOUN
ejpam-1949	8	11	and	and	CCONJ
ejpam-1949	8	12	phrases	phrase	NOUN
ejpam-1949	8	13	:	:	PUNCT
ejpam-1949	8	14	differential	differential	ADJ
ejpam-1949	8	15	k	k	NOUN
ejpam-1949	8	16	-	-	NOUN
ejpam-1949	8	17	characters	character	NOUN
ejpam-1949	8	18	,	,	PUNCT
ejpam-1949	8	19	geometric	geometric	ADJ
ejpam-1949	8	20	k	k	NOUN
ejpam-1949	8	21	-	-	NOUN
ejpam-1949	8	22	homology	homology	NOUN
ejpam-1949	8	23	,	,	PUNCT
ejpam-1949	8	24	r	r	NOUN
ejpam-1949	8	25	/	/	SYM
ejpam-1949	8	26	z	z	NOUN
ejpam-1949	8	27	k	k	NOUN
ejpam-1949	8	28	-	-	NOUN
ejpam-1949	8	29	theory	theory	NOUN
ejpam-1949	8	30	1	1	NUM
ejpam-1949	8	31	.	.	PUNCT
ejpam-1949	9	1	introduction	introduction	NOUN
ejpam-1949	9	2	differential	differential	NOUN
ejpam-1949	9	3	k	k	NOUN
ejpam-1949	9	4	-	-	NOUN
ejpam-1949	9	5	theory	theory	NOUN
ejpam-1949	9	6	is	be	AUX
ejpam-1949	9	7	a	a	DET
ejpam-1949	9	8	generalized	generalized	ADJ
ejpam-1949	9	9	differential	differential	ADJ
ejpam-1949	9	10	cohomology	cohomology	NOUN
ejpam-1949	9	11	theory	theory	NOUN
ejpam-1949	9	12	introduced	introduce	VERB
ejpam-1949	9	13	by	by	ADP
ejpam-1949	9	14	freed	freed	NOUN
ejpam-1949	9	15	and	and	CCONJ
ejpam-1949	9	16	hopkins	hopkin	NOUN
ejpam-1949	9	17	[	[	X
ejpam-1949	9	18	5	5	NUM
ejpam-1949	9	19	]	]	PUNCT
ejpam-1949	9	20	as	as	ADP
ejpam-1949	9	21	a	a	DET
ejpam-1949	9	22	refinement	refinement	NOUN
ejpam-1949	9	23	of	of	ADP
ejpam-1949	9	24	topological	topological	ADJ
ejpam-1949	9	25	k	k	PROPN
ejpam-1949	9	26	-	-	NOUN
ejpam-1949	9	27	theory	theory	NOUN
ejpam-1949	9	28	for	for	ADP
ejpam-1949	9	29	a	a	DET
ejpam-1949	9	30	concrete	concrete	ADJ
ejpam-1949	9	31	description	description	NOUN
ejpam-1949	9	32	of	of	ADP
ejpam-1949	9	33	rr	rr	NOUN
ejpam-1949	9	34	-	-	PUNCT
ejpam-1949	9	35	fields	field	NOUN
ejpam-1949	9	36	in	in	ADP
ejpam-1949	9	37	string	string	NOUN
ejpam-1949	9	38	theory	theory	NOUN
ejpam-1949	9	39	.	.	PUNCT
ejpam-1949	10	1	this	this	DET
ejpam-1949	10	2	theory	theory	NOUN
ejpam-1949	10	3	encode	encode	VERB
ejpam-1949	10	4	geometric	geometric	ADJ
ejpam-1949	10	5	as	as	ADV
ejpam-1949	10	6	well	well	ADV
ejpam-1949	10	7	as	as	ADP
ejpam-1949	10	8	topological	topological	ADJ
ejpam-1949	10	9	information	information	NOUN
ejpam-1949	10	10	.	.	PUNCT
ejpam-1949	11	1	roughly	roughly	ADV
ejpam-1949	11	2	speaking	speak	VERB
ejpam-1949	11	3	,	,	PUNCT
ejpam-1949	11	4	differential	differential	ADJ
ejpam-1949	11	5	k	k	NOUN
ejpam-1949	11	6	-	-	NOUN
ejpam-1949	11	7	theory	theory	NOUN
ejpam-1949	11	8	combines	combine	VERB
ejpam-1949	11	9	topological	topological	ADJ
ejpam-1949	11	10	k	k	NOUN
ejpam-1949	11	11	-	-	NOUN
ejpam-1949	11	12	theory	theory	NOUN
ejpam-1949	11	13	with	with	ADP
ejpam-1949	11	14	differential	differential	ADJ
ejpam-1949	11	15	forms	form	NOUN
ejpam-1949	11	16	[	[	X
ejpam-1949	11	17	3–7	3–7	NOUN
ejpam-1949	11	18	,	,	PUNCT
ejpam-1949	11	19	9	9	NUM
ejpam-1949	11	20	]	]	PUNCT
ejpam-1949	11	21	.	.	PUNCT
ejpam-1949	12	1	benameur	benameur	NOUN
ejpam-1949	12	2	and	and	CCONJ
ejpam-1949	12	3	maghfoul	maghfoul	ADJ
ejpam-1949	12	4	[	[	X
ejpam-1949	12	5	2	2	NUM
ejpam-1949	12	6	]	]	PUNCT
ejpam-1949	12	7	pointed	point	VERB
ejpam-1949	12	8	out	out	ADP
ejpam-1949	12	9	the	the	DET
ejpam-1949	12	10	relevance	relevance	NOUN
ejpam-1949	12	11	to	to	PART
ejpam-1949	12	12	differential	differential	VERB
ejpam-1949	12	13	k	k	NOUN
ejpam-1949	12	14	-	-	NOUN
ejpam-1949	12	15	characters	character	NOUN
ejpam-1949	12	16	of	of	ADP
ejpam-1949	12	17	a	a	DET
ejpam-1949	12	18	description	description	NOUN
ejpam-1949	12	19	of	of	ADP
ejpam-1949	12	20	differential	differential	ADJ
ejpam-1949	12	21	flat	flat	ADJ
ejpam-1949	12	22	k	k	NOUN
ejpam-1949	12	23	-	-	NOUN
ejpam-1949	12	24	theory	theory	NOUN
ejpam-1949	12	25	.	.	PUNCT
ejpam-1949	13	1	the	the	DET
ejpam-1949	13	2	group	group	NOUN
ejpam-1949	13	3	of	of	ADP
ejpam-1949	13	4	differential	differential	ADJ
ejpam-1949	13	5	k	k	NOUN
ejpam-1949	13	6	-	-	NOUN
ejpam-1949	13	7	characters	character	NOUN
ejpam-1949	13	8	on	on	ADP
ejpam-1949	13	9	a	a	DET
ejpam-1949	13	10	smooth	smooth	ADJ
ejpam-1949	13	11	compact	compact	ADJ
ejpam-1949	13	12	manifold	manifold	NOUN
ejpam-1949	13	13	x	x	AUX
ejpam-1949	13	14	is	be	AUX
ejpam-1949	13	15	defined	define	VERB
ejpam-1949	13	16	as	as	ADP
ejpam-1949	13	17	the	the	DET
ejpam-1949	13	18	k	k	ADJ
ejpam-1949	13	19	-	-	ADJ
ejpam-1949	13	20	theoretic	theoretic	ADJ
ejpam-1949	13	21	version	version	NOUN
ejpam-1949	13	22	of	of	ADP
ejpam-1949	13	23	the	the	DET
ejpam-1949	13	24	group	group	NOUN
ejpam-1949	13	25	of	of	ADP
ejpam-1949	13	26	cheeger	cheeger	ADJ
ejpam-1949	13	27	-	-	PUNCT
ejpam-1949	13	28	simons	simon	NOUN
ejpam-1949	13	29	differential	differential	ADJ
ejpam-1949	13	30	characters	character	NOUN
ejpam-1949	13	31	on	on	ADP
ejpam-1949	13	32	x	x	PUNCT
ejpam-1949	13	33	using	use	VERB
ejpam-1949	13	34	the	the	DET
ejpam-1949	13	35	(	(	PUNCT
ejpam-1949	13	36	m	m	PROPN
ejpam-1949	13	37	,	,	PUNCT
ejpam-1949	13	38	e	e	NOUN
ejpam-1949	13	39	,	,	PUNCT
ejpam-1949	13	40	f	f	NOUN
ejpam-1949	13	41	)	)	PUNCT
ejpam-1949	13	42	-picture	-picture	NOUN
ejpam-1949	13	43	of	of	ADP
ejpam-1949	13	44	baum	baum	NOUN
ejpam-1949	13	45	-	-	PUNCT
ejpam-1949	13	46	douglas	douglas	PROPN
ejpam-1949	13	47	for	for	ADP
ejpam-1949	13	48	k	k	PROPN
ejpam-1949	13	49	-	-	NOUN
ejpam-1949	13	50	homology	homology	NOUN
ejpam-1949	13	51	.	.	PUNCT
ejpam-1949	14	1	recall	recall	VERB
ejpam-1949	14	2	that	that	SCONJ
ejpam-1949	14	3	a	a	DET
ejpam-1949	14	4	geometric	geometric	ADJ
ejpam-1949	14	5	k	k	NOUN
ejpam-1949	14	6	-	-	NOUN
ejpam-1949	14	7	cycle	cycle	NOUN
ejpam-1949	14	8	of	of	ADP
ejpam-1949	14	9	baum	baum	PROPN
ejpam-1949	14	10	-	-	PUNCT
ejpam-1949	14	11	douglas	douglas	PROPN
ejpam-1949	14	12	over	over	ADP
ejpam-1949	14	13	x	x	PROPN
ejpam-1949	14	14	is	be	AUX
ejpam-1949	14	15	a	a	DET
ejpam-1949	14	16	triple	triple	ADJ
ejpam-1949	14	17	(	(	PUNCT
ejpam-1949	14	18	m	m	PROPN
ejpam-1949	14	19	,	,	PUNCT
ejpam-1949	14	20	e	e	NOUN
ejpam-1949	14	21	,	,	PUNCT
ejpam-1949	14	22	f	f	PROPN
ejpam-1949	14	23	)	)	PUNCT
ejpam-1949	14	24	such	such	ADJ
ejpam-1949	14	25	that	that	PRON
ejpam-1949	14	26	:	:	PUNCT
ejpam-1949	14	27	m	m	NOUN
ejpam-1949	14	28	is	be	AUX
ejpam-1949	14	29	a	a	DET
ejpam-1949	14	30	smooth	smooth	ADJ
ejpam-1949	14	31	compact	compact	ADJ
ejpam-1949	14	32	spinc	spinc	NOUN
ejpam-1949	14	33	manifold	manifold	ADJ
ejpam-1949	14	34	without	without	ADP
ejpam-1949	14	35	boundary	boundary	NOUN
ejpam-1949	14	36	,	,	PUNCT
ejpam-1949	14	37	e	e	X
ejpam-1949	14	38	is	be	AUX
ejpam-1949	14	39	a	a	DET
ejpam-1949	14	40	hermitian	hermitian	ADJ
ejpam-1949	14	41	vector	vector	NOUN
ejpam-1949	14	42	bundle	bundle	NOUN
ejpam-1949	14	43	over	over	ADP
ejpam-1949	14	44	m	m	PROPN
ejpam-1949	14	45	with	with	ADP
ejpam-1949	14	46	a	a	DET
ejpam-1949	14	47	fixed	fix	VERB
ejpam-1949	14	48	hermitian	hermitian	ADJ
ejpam-1949	14	49	connection	connection	NOUN
ejpam-1949	14	50	∇e	∇e	NOUN
ejpam-1949	14	51	,	,	PUNCT
ejpam-1949	14	52	and	and	CCONJ
ejpam-1949	14	53	f	f	X
ejpam-1949	14	54	:	:	PUNCT
ejpam-1949	14	55	m	m	VERB
ejpam-1949	14	56	→	→	NOUN
ejpam-1949	14	57	x	x	X
ejpam-1949	14	58	is	be	AUX
ejpam-1949	14	59	a	a	DET
ejpam-1949	14	60	smooth	smooth	ADJ
ejpam-1949	14	61	map	map	NOUN
ejpam-1949	14	62	.	.	PUNCT
ejpam-1949	15	1	let	let	VERB
ejpam-1949	15	2	c∗(x	c∗(x	NOUN
ejpam-1949	15	3	)	)	PUNCT
ejpam-1949	15	4	be	be	AUX
ejpam-1949	15	5	the	the	DET
ejpam-1949	15	6	semigroup	semigroup	NOUN
ejpam-1949	15	7	for	for	ADP
ejpam-1949	15	8	the	the	DET
ejpam-1949	15	9	disjoint	disjoint	PROPN
ejpam-1949	15	10	union	union	NOUN
ejpam-1949	15	11	of	of	ADP
ejpam-1949	15	12	equivalence	equivalence	NOUN
ejpam-1949	15	13	classes	class	NOUN
ejpam-1949	15	14	of	of	ADP
ejpam-1949	15	15	k	k	NOUN
ejpam-1949	15	16	-	-	NOUN
ejpam-1949	15	17	cycles	cycle	NOUN
ejpam-1949	15	18	over	over	ADP
ejpam-1949	15	19	x	x	PUNCT
ejpam-1949	15	20	generated	generate	VERB
ejpam-1949	15	21	by	by	ADP
ejpam-1949	15	22	direct	direct	ADJ
ejpam-1949	15	23	sum	sum	NOUN
ejpam-1949	15	24	and	and	CCONJ
ejpam-1949	15	25	vector	vector	NOUN
ejpam-1949	15	26	bundle	bundle	NOUN
ejpam-1949	15	27	modification	modification	NOUN
ejpam-1949	16	1	[	[	X
ejpam-1949	16	2	1	1	NUM
ejpam-1949	16	3	]	]	PUNCT
ejpam-1949	16	4	.	.	PUNCT
ejpam-1949	17	1	a	a	DET
ejpam-1949	17	2	differential	differential	ADJ
ejpam-1949	17	3	k	k	NOUN
ejpam-1949	17	4	-	-	NOUN
ejpam-1949	17	5	character	character	NOUN
ejpam-1949	17	6	on	on	ADP
ejpam-1949	17	7	x	x	SYM
ejpam-1949	17	8	is	be	AUX
ejpam-1949	17	9	a	a	DET
ejpam-1949	17	10	semigroup	semigroup	ADJ
ejpam-1949	17	11	homomorphism	homomorphism	NOUN
ejpam-1949	17	12	h	h	NOUN
ejpam-1949	17	13	:	:	PUNCT
ejpam-1949	17	14	c∗(x	c∗(x	NOUN
ejpam-1949	17	15	)	)	PUNCT
ejpam-1949	18	1	→	→	PUNCT
ejpam-1949	18	2	r	r	X
ejpam-1949	18	3	/	/	SYM
ejpam-1949	18	4	z	z	NOUN
ejpam-1949	18	5	such	such	ADJ
ejpam-1949	18	6	that	that	SCONJ
ejpam-1949	18	7	its	its	PRON
ejpam-1949	18	8	restriction	restriction	NOUN
ejpam-1949	18	9	to	to	ADP
ejpam-1949	18	10	the	the	DET
ejpam-1949	18	11	boundaries	boundary	NOUN
ejpam-1949	18	12	is	be	AUX
ejpam-1949	18	13	given	give	VERB
ejpam-1949	18	14	by	by	ADP
ejpam-1949	18	15	the	the	DET
ejpam-1949	18	16	following	follow	VERB
ejpam-1949	18	17	formula	formula	NOUN
ejpam-1949	18	18	:	:	PUNCT
ejpam-1949	18	19	h(∂w	h(∂w	PROPN
ejpam-1949	18	20	,	,	PUNCT
ejpam-1949	18	21	ε|∂w	ε|∂w	NOUN
ejpam-1949	18	22	,	,	PUNCT
ejpam-1949	18	23	g|∂w	g|∂w	PROPN
ejpam-1949	18	24	)	)	PUNCT
ejpam-1949	18	25	:	:	PUNCT
ejpam-1949	18	26	=	=	PUNCT
ejpam-1949	18	27	∫	∫	PROPN
ejpam-1949	18	28	w	w	PROPN
ejpam-1949	18	29	g∗(w)ch(ε)t	g∗(w)ch(ε)t	PROPN
ejpam-1949	18	30	d(w	d(w	PROPN
ejpam-1949	18	31	)	)	PUNCT
ejpam-1949	18	32	mod	mod	PROPN
ejpam-1949	19	1	z	z	X
ejpam-1949	19	2	,	,	PUNCT
ejpam-1949	19	3	∗corresponding	∗corresponde	VERB
ejpam-1949	19	4	author	author	NOUN
ejpam-1949	19	5	.	.	PUNCT
ejpam-1949	20	1	email	email	NOUN
ejpam-1949	20	2	addresses	address	NOUN
ejpam-1949	20	3	:	:	PUNCT
ejpam-1949	20	4	elmrabty_adnane@yahoo.fr	elmrabty_adnane@yahoo.fr	X
ejpam-1949	20	5	(	(	PUNCT
ejpam-1949	20	6	a.	a.	NOUN
ejpam-1949	20	7	elmrabty	elmrabty	NOUN
ejpam-1949	20	8	)	)	PUNCT
ejpam-1949	20	9	,	,	PUNCT
ejpam-1949	20	10	mmaghfoul@lycos.com	mmaghfoul@lycos.com	X
ejpam-1949	20	11	(	(	PUNCT
ejpam-1949	20	12	m.	m.	NOUN
ejpam-1949	20	13	maghfoul	maghfoul	PROPN
ejpam-1949	20	14	)	)	PUNCT
ejpam-1949	20	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1949	21	1	65	65	NUM
ejpam-1949	22	1	c	c	X
ejpam-1949	22	2	©	©	NOUN
ejpam-1949	22	3	2014	2014	NUM
ejpam-1949	22	4	ejpam	ejpam	NOUN
ejpam-1949	22	5	all	all	DET
ejpam-1949	22	6	rights	right	NOUN
ejpam-1949	22	7	reserved	reserve	VERB
ejpam-1949	22	8	.	.	PUNCT
ejpam-1949	23	1	a.	a.	NOUN
ejpam-1949	23	2	elmrabty	elmrabty	NOUN
ejpam-1949	23	3	,	,	PUNCT
ejpam-1949	23	4	m.	m.	NOUN
ejpam-1949	23	5	maghfoul	maghfoul	PROPN
ejpam-1949	23	6	/	/	SYM
ejpam-1949	23	7	eur	eur	PROPN
ejpam-1949	23	8	.	.	PUNCT
ejpam-1949	24	1	j.	j.	PROPN
ejpam-1949	24	2	pure	pure	PROPN
ejpam-1949	24	3	appl	appl	PROPN
ejpam-1949	24	4	.	.	PROPN
ejpam-1949	24	5	math	math	PROPN
ejpam-1949	24	6	,	,	PUNCT
ejpam-1949	24	7	7	7	NUM
ejpam-1949	24	8	(	(	PUNCT
ejpam-1949	24	9	2014	2014	NUM
ejpam-1949	24	10	)	)	PUNCT
ejpam-1949	24	11	,	,	PUNCT
ejpam-1949	24	12	65	65	NUM
ejpam-1949	24	13	-	-	SYM
ejpam-1949	24	14	76	76	NUM
ejpam-1949	24	15	66	66	NUM
ejpam-1949	24	16	where	where	SCONJ
ejpam-1949	24	17	w	w	NOUN
ejpam-1949	24	18	is	be	AUX
ejpam-1949	24	19	a	a	DET
ejpam-1949	24	20	closed	closed	ADJ
ejpam-1949	24	21	differential	differential	ADJ
ejpam-1949	24	22	form	form	NOUN
ejpam-1949	24	23	on	on	ADP
ejpam-1949	24	24	x	x	PUNCT
ejpam-1949	24	25	with	with	ADP
ejpam-1949	24	26	integer	integer	PROPN
ejpam-1949	24	27	k	k	NOUN
ejpam-1949	24	28	-	-	PUNCT
ejpam-1949	24	29	periods	periods	ADJ
ejpam-1949	24	30	[	[	X
ejpam-1949	24	31	2	2	NUM
ejpam-1949	24	32	]	]	PUNCT
ejpam-1949	24	33	,	,	PUNCT
ejpam-1949	24	34	ch(ε	ch(ε	X
ejpam-1949	24	35	)	)	PUNCT
ejpam-1949	24	36	is	be	AUX
ejpam-1949	24	37	the	the	DET
ejpam-1949	24	38	chern	chern	ADJ
ejpam-1949	24	39	form	form	NOUN
ejpam-1949	24	40	of	of	ADP
ejpam-1949	24	41	the	the	DET
ejpam-1949	24	42	connection	connection	NOUN
ejpam-1949	24	43	∇ε	∇ε	VERB
ejpam-1949	24	44	on	on	ADP
ejpam-1949	24	45	ε	ε	PROPN
ejpam-1949	24	46	,	,	PUNCT
ejpam-1949	24	47	and	and	CCONJ
ejpam-1949	24	48	t	t	PROPN
ejpam-1949	24	49	d(w	d(w	PROPN
ejpam-1949	24	50	)	)	PUNCT
ejpam-1949	24	51	is	be	AUX
ejpam-1949	24	52	the	the	DET
ejpam-1949	24	53	todd	todd	ADJ
ejpam-1949	24	54	form	form	NOUN
ejpam-1949	24	55	of	of	ADP
ejpam-1949	24	56	the	the	DET
ejpam-1949	24	57	tangent	tangent	ADJ
ejpam-1949	24	58	bundle	bundle	NOUN
ejpam-1949	24	59	of	of	ADP
ejpam-1949	24	60	w	w	PROPN
ejpam-1949	24	61	.	.	PUNCT
ejpam-1949	25	1	the	the	DET
ejpam-1949	25	2	purpose	purpose	NOUN
ejpam-1949	25	3	of	of	ADP
ejpam-1949	25	4	this	this	DET
ejpam-1949	25	5	paper	paper	NOUN
ejpam-1949	25	6	is	be	AUX
ejpam-1949	25	7	to	to	PART
ejpam-1949	25	8	construct	construct	VERB
ejpam-1949	25	9	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	25	10	)	)	PUNCT
ejpam-1949	25	11	,	,	PUNCT
ejpam-1949	25	12	the	the	DET
ejpam-1949	25	13	relative	relative	ADJ
ejpam-1949	25	14	differential	differential	NOUN
ejpam-1949	25	15	k	k	NOUN
ejpam-1949	25	16	-	-	NOUN
ejpam-1949	25	17	theory	theory	NOUN
ejpam-1949	25	18	of	of	ADP
ejpam-1949	25	19	a	a	DET
ejpam-1949	25	20	smooth	smooth	ADJ
ejpam-1949	25	21	map	map	NOUN
ejpam-1949	25	22	ρ	ρ	NOUN
ejpam-1949	25	23	:	:	PUNCT
ejpam-1949	26	1	y	y	PROPN
ejpam-1949	26	2	→	→	SYM
ejpam-1949	26	3	x	x	X
ejpam-1949	26	4	between	between	ADP
ejpam-1949	26	5	two	two	NUM
ejpam-1949	26	6	smooth	smooth	ADJ
ejpam-1949	26	7	compact	compact	ADJ
ejpam-1949	26	8	manifolds	manifold	NOUN
ejpam-1949	26	9	.	.	PUNCT
ejpam-1949	27	1	to	to	PART
ejpam-1949	27	2	motivate	motivate	VERB
ejpam-1949	27	3	our	our	PRON
ejpam-1949	27	4	construction	construction	NOUN
ejpam-1949	27	5	,	,	PUNCT
ejpam-1949	27	6	the	the	DET
ejpam-1949	27	7	group	group	NOUN
ejpam-1949	27	8	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	27	9	)	)	PUNCT
ejpam-1949	27	10	must	must	AUX
ejpam-1949	27	11	recovers	recover	VERB
ejpam-1949	27	12	the	the	DET
ejpam-1949	27	13	usual	usual	ADJ
ejpam-1949	27	14	non	non	ADJ
ejpam-1949	27	15	-	-	ADJ
ejpam-1949	27	16	relative	relative	ADJ
ejpam-1949	27	17	group	group	NOUN
ejpam-1949	27	18	of	of	ADP
ejpam-1949	27	19	differential	differential	ADJ
ejpam-1949	27	20	k	k	NOUN
ejpam-1949	27	21	-	-	NOUN
ejpam-1949	27	22	characters	character	NOUN
ejpam-1949	27	23	on	on	ADP
ejpam-1949	27	24	x	x	X
ejpam-1949	27	25	.	.	PUNCT
ejpam-1949	28	1	we	we	PRON
ejpam-1949	28	2	define	define	VERB
ejpam-1949	28	3	the	the	DET
ejpam-1949	28	4	k	k	NOUN
ejpam-1949	28	5	-	-	NOUN
ejpam-1949	28	6	theory	theory	NOUN
ejpam-1949	28	7	of	of	ADP
ejpam-1949	28	8	ρ	ρ	PROPN
ejpam-1949	28	9	:	:	PUNCT
ejpam-1949	28	10	y	y	PROPN
ejpam-1949	28	11	→	→	PUNCT
ejpam-1949	28	12	x	x	X
ejpam-1949	28	13	with	with	ADP
ejpam-1949	28	14	r	r	NOUN
ejpam-1949	28	15	/	/	SYM
ejpam-1949	28	16	z	z	NOUN
ejpam-1949	28	17	coefficients	coefficient	NOUN
ejpam-1949	28	18	and	and	CCONJ
ejpam-1949	28	19	show	show	VERB
ejpam-1949	28	20	that	that	SCONJ
ejpam-1949	28	21	it	it	PRON
ejpam-1949	28	22	is	be	AUX
ejpam-1949	28	23	isomorphic	isomorphic	ADJ
ejpam-1949	28	24	to	to	ADP
ejpam-1949	28	25	the	the	DET
ejpam-1949	28	26	group	group	NOUN
ejpam-1949	28	27	of	of	ADP
ejpam-1949	28	28	homomorphisms	homomorphism	NOUN
ejpam-1949	28	29	from	from	ADP
ejpam-1949	28	30	the	the	DET
ejpam-1949	28	31	relative	relative	ADJ
ejpam-1949	28	32	k	k	NOUN
ejpam-1949	28	33	-	-	NOUN
ejpam-1949	28	34	homology	homology	NOUN
ejpam-1949	28	35	of	of	ADP
ejpam-1949	28	36	ρ	ρ	PROPN
ejpam-1949	28	37	[	[	X
ejpam-1949	28	38	8	8	NUM
ejpam-1949	28	39	]	]	PUNCT
ejpam-1949	28	40	to	to	ADP
ejpam-1949	28	41	r	r	NOUN
ejpam-1949	28	42	/	/	SYM
ejpam-1949	28	43	z	z	NOUN
ejpam-1949	28	44	up	up	ADP
ejpam-1949	28	45	to	to	ADP
ejpam-1949	28	46	a	a	DET
ejpam-1949	28	47	degree	degree	NOUN
ejpam-1949	28	48	-	-	PUNCT
ejpam-1949	28	49	shift	shift	NOUN
ejpam-1949	28	50	by	by	ADP
ejpam-1949	28	51	one	one	NUM
ejpam-1949	28	52	.	.	PUNCT
ejpam-1949	29	1	the	the	DET
ejpam-1949	29	2	paper	paper	NOUN
ejpam-1949	29	3	is	be	AUX
ejpam-1949	29	4	organized	organize	VERB
ejpam-1949	29	5	as	as	SCONJ
ejpam-1949	29	6	follows	follow	VERB
ejpam-1949	29	7	:	:	PUNCT
ejpam-1949	29	8	in	in	ADP
ejpam-1949	29	9	section	section	NOUN
ejpam-1949	29	10	2	2	NUM
ejpam-1949	29	11	,	,	PUNCT
ejpam-1949	29	12	we	we	PRON
ejpam-1949	29	13	recall	recall	VERB
ejpam-1949	29	14	the	the	DET
ejpam-1949	29	15	definition	definition	NOUN
ejpam-1949	29	16	of	of	ADP
ejpam-1949	29	17	the	the	DET
ejpam-1949	29	18	group	group	NOUN
ejpam-1949	29	19	of	of	ADP
ejpam-1949	29	20	differential	differential	ADJ
ejpam-1949	29	21	k	k	NOUN
ejpam-1949	29	22	-	-	NOUN
ejpam-1949	29	23	characters	character	NOUN
ejpam-1949	29	24	and	and	CCONJ
ejpam-1949	29	25	study	study	VERB
ejpam-1949	29	26	some	some	PRON
ejpam-1949	29	27	of	of	ADP
ejpam-1949	29	28	its	its	PRON
ejpam-1949	29	29	properties	property	NOUN
ejpam-1949	29	30	.	.	PUNCT
ejpam-1949	30	1	in	in	ADP
ejpam-1949	30	2	section	section	NOUN
ejpam-1949	30	3	3	3	NUM
ejpam-1949	30	4	,	,	PUNCT
ejpam-1949	30	5	we	we	PRON
ejpam-1949	30	6	define	define	VERB
ejpam-1949	30	7	the	the	DET
ejpam-1949	30	8	relative	relative	ADJ
ejpam-1949	30	9	differential	differential	NOUN
ejpam-1949	30	10	k	k	NOUN
ejpam-1949	30	11	-	-	NOUN
ejpam-1949	30	12	theory	theory	NOUN
ejpam-1949	30	13	of	of	ADP
ejpam-1949	30	14	a	a	DET
ejpam-1949	30	15	smooth	smooth	ADJ
ejpam-1949	30	16	map	map	NOUN
ejpam-1949	31	1	ρ	ρ	NOUN
ejpam-1949	31	2	:	:	PUNCT
ejpam-1949	31	3	y	y	PROPN
ejpam-1949	31	4	→	→	SYM
ejpam-1949	31	5	x	x	X
ejpam-1949	31	6	between	between	ADP
ejpam-1949	31	7	two	two	NUM
ejpam-1949	31	8	smooth	smooth	ADJ
ejpam-1949	31	9	compact	compact	ADJ
ejpam-1949	31	10	manifolds	manifold	NOUN
ejpam-1949	31	11	and	and	CCONJ
ejpam-1949	31	12	show	show	VERB
ejpam-1949	31	13	that	that	SCONJ
ejpam-1949	31	14	it	it	PRON
ejpam-1949	31	15	fits	fit	VERB
ejpam-1949	31	16	into	into	ADP
ejpam-1949	31	17	a	a	DET
ejpam-1949	31	18	six	six	NUM
ejpam-1949	31	19	-	-	PUNCT
ejpam-1949	31	20	term	term	NOUN
ejpam-1949	31	21	exact	exact	ADJ
ejpam-1949	31	22	sequence	sequence	NOUN
ejpam-1949	31	23	.	.	PUNCT
ejpam-1949	32	1	finally	finally	ADV
ejpam-1949	32	2	,	,	PUNCT
ejpam-1949	32	3	section	section	NOUN
ejpam-1949	32	4	4	4	NUM
ejpam-1949	32	5	is	be	AUX
ejpam-1949	32	6	concerned	concern	VERB
ejpam-1949	32	7	with	with	ADP
ejpam-1949	32	8	the	the	DET
ejpam-1949	32	9	definition	definition	NOUN
ejpam-1949	32	10	of	of	ADP
ejpam-1949	32	11	the	the	DET
ejpam-1949	32	12	k	k	NOUN
ejpam-1949	32	13	-	-	NOUN
ejpam-1949	32	14	theory	theory	NOUN
ejpam-1949	32	15	of	of	ADP
ejpam-1949	32	16	a	a	DET
ejpam-1949	32	17	smooth	smooth	ADJ
ejpam-1949	32	18	map	map	NOUN
ejpam-1949	32	19	ρ	ρ	NOUN
ejpam-1949	32	20	:	:	PUNCT
ejpam-1949	32	21	y	y	PROPN
ejpam-1949	32	22	→	→	PUNCT
ejpam-1949	32	23	x	x	X
ejpam-1949	32	24	with	with	ADP
ejpam-1949	32	25	r	r	NOUN
ejpam-1949	32	26	/	/	SYM
ejpam-1949	32	27	z	z	NOUN
ejpam-1949	32	28	coefficients	coefficient	NOUN
ejpam-1949	32	29	and	and	CCONJ
ejpam-1949	32	30	the	the	DET
ejpam-1949	32	31	construction	construction	NOUN
ejpam-1949	32	32	of	of	ADP
ejpam-1949	32	33	an	an	DET
ejpam-1949	32	34	isomorphism	isomorphism	NOUN
ejpam-1949	32	35	between	between	ADP
ejpam-1949	32	36	this	this	DET
ejpam-1949	32	37	group	group	NOUN
ejpam-1949	32	38	and	and	CCONJ
ejpam-1949	32	39	the	the	DET
ejpam-1949	32	40	group	group	NOUN
ejpam-1949	32	41	of	of	ADP
ejpam-1949	32	42	homomorphisms	homomorphism	NOUN
ejpam-1949	32	43	from	from	ADP
ejpam-1949	32	44	the	the	DET
ejpam-1949	32	45	relative	relative	ADJ
ejpam-1949	32	46	k	k	NOUN
ejpam-1949	32	47	-	-	NOUN
ejpam-1949	32	48	homology	homology	NOUN
ejpam-1949	32	49	of	of	ADP
ejpam-1949	32	50	ρ	ρ	PROPN
ejpam-1949	33	1	[	[	X
ejpam-1949	33	2	8	8	NUM
ejpam-1949	33	3	]	]	PUNCT
ejpam-1949	33	4	to	to	ADP
ejpam-1949	33	5	r	r	PROPN
ejpam-1949	33	6	/	/	SYM
ejpam-1949	33	7	z.	z.	PROPN
ejpam-1949	33	8	2	2	NUM
ejpam-1949	33	9	.	.	X
ejpam-1949	33	10	differential	differential	ADJ
ejpam-1949	33	11	k	k	NOUN
ejpam-1949	33	12	-	-	NOUN
ejpam-1949	33	13	characters	character	NOUN
ejpam-1949	33	14	in	in	ADP
ejpam-1949	33	15	this	this	DET
ejpam-1949	33	16	section	section	NOUN
ejpam-1949	33	17	,	,	PUNCT
ejpam-1949	33	18	we	we	PRON
ejpam-1949	33	19	give	give	VERB
ejpam-1949	33	20	the	the	DET
ejpam-1949	33	21	construction	construction	NOUN
ejpam-1949	33	22	of	of	ADP
ejpam-1949	33	23	the	the	DET
ejpam-1949	33	24	group	group	NOUN
ejpam-1949	33	25	of	of	ADP
ejpam-1949	33	26	differential	differential	ADJ
ejpam-1949	33	27	k	k	NOUN
ejpam-1949	33	28	-	-	NOUN
ejpam-1949	33	29	characters	character	NOUN
ejpam-1949	33	30	following	follow	VERB
ejpam-1949	33	31	[	[	X
ejpam-1949	33	32	2	2	NUM
ejpam-1949	33	33	]	]	PUNCT
ejpam-1949	33	34	.	.	PUNCT
ejpam-1949	34	1	as	as	SCONJ
ejpam-1949	34	2	mentioned	mention	VERB
ejpam-1949	34	3	in	in	ADP
ejpam-1949	34	4	the	the	DET
ejpam-1949	34	5	introduction	introduction	NOUN
ejpam-1949	34	6	,	,	PUNCT
ejpam-1949	34	7	in	in	ADP
ejpam-1949	34	8	this	this	DET
ejpam-1949	34	9	construction	construction	NOUN
ejpam-1949	34	10	we	we	PRON
ejpam-1949	34	11	use	use	VERB
ejpam-1949	34	12	the	the	DET
ejpam-1949	34	13	(	(	PUNCT
ejpam-1949	34	14	m	m	PROPN
ejpam-1949	34	15	,	,	PUNCT
ejpam-1949	34	16	e	e	NOUN
ejpam-1949	34	17	,	,	PUNCT
ejpam-1949	34	18	f	f	NOUN
ejpam-1949	34	19	)	)	PUNCT
ejpam-1949	34	20	-picture	-picture	NOUN
ejpam-1949	34	21	of	of	ADP
ejpam-1949	34	22	baum	baum	NOUN
ejpam-1949	34	23	-	-	PUNCT
ejpam-1949	34	24	douglas	douglas	PROPN
ejpam-1949	34	25	for	for	ADP
ejpam-1949	34	26	k	k	PROPN
ejpam-1949	34	27	-	-	NOUN
ejpam-1949	34	28	homology	homology	NOUN
ejpam-1949	35	1	[	[	X
ejpam-1949	35	2	1	1	NUM
ejpam-1949	35	3	]	]	PUNCT
ejpam-1949	35	4	.	.	PUNCT
ejpam-1949	36	1	definition	definition	NOUN
ejpam-1949	36	2	1	1	NUM
ejpam-1949	36	3	.	.	PUNCT
ejpam-1949	37	1	let	let	VERB
ejpam-1949	37	2	x	x	PRON
ejpam-1949	37	3	be	be	AUX
ejpam-1949	37	4	a	a	DET
ejpam-1949	37	5	smooth	smooth	ADJ
ejpam-1949	37	6	compact	compact	ADJ
ejpam-1949	37	7	manifold	manifold	NOUN
ejpam-1949	37	8	.	.	PUNCT
ejpam-1949	38	1	a	a	DET
ejpam-1949	38	2	k	k	NOUN
ejpam-1949	38	3	-	-	NOUN
ejpam-1949	38	4	chain	chain	NOUN
ejpam-1949	38	5	over	over	ADP
ejpam-1949	38	6	x	x	PRON
ejpam-1949	38	7	is	be	AUX
ejpam-1949	38	8	a	a	DET
ejpam-1949	38	9	triple	triple	ADJ
ejpam-1949	38	10	(	(	PUNCT
ejpam-1949	38	11	w	w	PROPN
ejpam-1949	38	12	,	,	PUNCT
ejpam-1949	38	13	ε	ε	PROPN
ejpam-1949	38	14	,	,	PUNCT
ejpam-1949	38	15	g	g	NOUN
ejpam-1949	38	16	)	)	PUNCT
ejpam-1949	38	17	such	such	ADJ
ejpam-1949	38	18	that	that	PRON
ejpam-1949	39	1	•	•	NUM
ejpam-1949	39	2	w	w	NOUN
ejpam-1949	39	3	is	be	AUX
ejpam-1949	39	4	a	a	DET
ejpam-1949	39	5	smooth	smooth	ADJ
ejpam-1949	39	6	compact	compact	ADJ
ejpam-1949	39	7	spinc	spinc	NOUN
ejpam-1949	39	8	manifold	manifold	NOUN
ejpam-1949	39	9	;	;	PUNCT
ejpam-1949	39	10	•	•	NUM
ejpam-1949	39	11	ε	ε	PROPN
ejpam-1949	39	12	is	be	AUX
ejpam-1949	39	13	a	a	DET
ejpam-1949	39	14	hermitian	hermitian	ADJ
ejpam-1949	39	15	vector	vector	NOUN
ejpam-1949	39	16	bundle	bundle	NOUN
ejpam-1949	39	17	over	over	ADP
ejpam-1949	39	18	w	w	NOUN
ejpam-1949	39	19	with	with	ADP
ejpam-1949	39	20	a	a	DET
ejpam-1949	39	21	fixed	fix	VERB
ejpam-1949	39	22	hermitian	hermitian	ADJ
ejpam-1949	39	23	connection	connection	NOUN
ejpam-1949	39	24	∇ε	∇ε	PROPN
ejpam-1949	39	25	;	;	PUNCT
ejpam-1949	39	26	and	and	CCONJ
ejpam-1949	39	27	•	•	ADV
ejpam-1949	39	28	g	g	NOUN
ejpam-1949	39	29	:	:	PUNCT
ejpam-1949	39	30	w	w	X
ejpam-1949	39	31	→	→	PUNCT
ejpam-1949	39	32	x	x	X
ejpam-1949	39	33	is	be	AUX
ejpam-1949	39	34	a	a	DET
ejpam-1949	39	35	smooth	smooth	ADJ
ejpam-1949	39	36	map	map	NOUN
ejpam-1949	39	37	.	.	PUNCT
ejpam-1949	40	1	there	there	PRON
ejpam-1949	40	2	are	be	VERB
ejpam-1949	40	3	no	no	DET
ejpam-1949	40	4	connectedness	connectedness	NOUN
ejpam-1949	40	5	requirements	requirement	NOUN
ejpam-1949	40	6	made	make	VERB
ejpam-1949	40	7	upon	upon	SCONJ
ejpam-1949	40	8	w	w	NOUN
ejpam-1949	40	9	,	,	PUNCT
ejpam-1949	40	10	and	and	CCONJ
ejpam-1949	40	11	hence	hence	ADV
ejpam-1949	40	12	the	the	DET
ejpam-1949	40	13	bundle	bundle	NOUN
ejpam-1949	40	14	ε	ε	PROPN
ejpam-1949	40	15	can	can	AUX
ejpam-1949	40	16	have	have	VERB
ejpam-1949	40	17	different	different	ADJ
ejpam-1949	40	18	fibre	fibre	NOUN
ejpam-1949	40	19	dimensions	dimension	NOUN
ejpam-1949	40	20	on	on	ADP
ejpam-1949	40	21	the	the	DET
ejpam-1949	40	22	different	different	ADJ
ejpam-1949	40	23	connected	connected	ADJ
ejpam-1949	40	24	components	component	NOUN
ejpam-1949	40	25	of	of	ADP
ejpam-1949	40	26	w.	w.	PROPN
ejpam-1949	40	27	it	it	PRON
ejpam-1949	40	28	follows	follow	VERB
ejpam-1949	40	29	that	that	SCONJ
ejpam-1949	40	30	disjoint	disjoint	PROPN
ejpam-1949	40	31	union	union	PROPN
ejpam-1949	40	32	(	(	PUNCT
ejpam-1949	40	33	w	w	PROPN
ejpam-1949	40	34	,	,	PUNCT
ejpam-1949	40	35	ε	ε	PROPN
ejpam-1949	40	36	,	,	PUNCT
ejpam-1949	40	37	g)t	g)t	X
ejpam-1949	40	38	(	(	PUNCT
ejpam-1949	40	39	w	w	PROPN
ejpam-1949	40	40	′,ε′	′,ε′	PROPN
ejpam-1949	40	41	,	,	PUNCT
ejpam-1949	40	42	g	g	NOUN
ejpam-1949	40	43	′	′	NUM
ejpam-1949	40	44	)	)	PUNCT
ejpam-1949	41	1	:	:	PUNCT
ejpam-1949	41	2	=	=	SYM
ejpam-1949	41	3	(	(	PUNCT
ejpam-1949	41	4	w	w	NOUN
ejpam-1949	41	5	tw	tw	PROPN
ejpam-1949	41	6	′,ε	′,ε	PROPN
ejpam-1949	41	7	t	t	PROPN
ejpam-1949	41	8	ε′	ε′	PROPN
ejpam-1949	41	9	,	,	PUNCT
ejpam-1949	41	10	g	g	PROPN
ejpam-1949	41	11	t	t	PROPN
ejpam-1949	41	12	g	g	PROPN
ejpam-1949	41	13	′	′	NUM
ejpam-1949	41	14	)	)	PUNCT
ejpam-1949	41	15	is	be	AUX
ejpam-1949	41	16	a	a	DET
ejpam-1949	41	17	well	well	ADV
ejpam-1949	41	18	-	-	PUNCT
ejpam-1949	41	19	defined	define	VERB
ejpam-1949	41	20	operation	operation	NOUN
ejpam-1949	41	21	on	on	ADP
ejpam-1949	41	22	the	the	DET
ejpam-1949	41	23	set	set	NOUN
ejpam-1949	41	24	of	of	ADP
ejpam-1949	41	25	k	k	NOUN
ejpam-1949	41	26	-	-	PUNCT
ejpam-1949	41	27	chains	chain	NOUN
ejpam-1949	41	28	over	over	ADP
ejpam-1949	41	29	x	x	X
ejpam-1949	41	30	.	.	PUNCT
ejpam-1949	42	1	isomorphism	isomorphism	NOUN
ejpam-1949	42	2	.	.	PUNCT
ejpam-1949	43	1	two	two	NUM
ejpam-1949	43	2	k	k	NOUN
ejpam-1949	43	3	-	-	PUNCT
ejpam-1949	43	4	chains	chain	NOUN
ejpam-1949	43	5	(	(	PUNCT
ejpam-1949	43	6	w	w	PROPN
ejpam-1949	43	7	,	,	PUNCT
ejpam-1949	43	8	ε	ε	PROPN
ejpam-1949	43	9	,	,	PUNCT
ejpam-1949	43	10	g	g	NOUN
ejpam-1949	43	11	)	)	PUNCT
ejpam-1949	43	12	and	and	CCONJ
ejpam-1949	43	13	(	(	PUNCT
ejpam-1949	43	14	w	w	PROPN
ejpam-1949	43	15	′,ε′	′,ε′	PROPN
ejpam-1949	43	16	,	,	PUNCT
ejpam-1949	43	17	g	g	NOUN
ejpam-1949	43	18	′	′	NOUN
ejpam-1949	43	19	)	)	PUNCT
ejpam-1949	43	20	over	over	ADV
ejpam-1949	43	21	x	x	PUNCT
ejpam-1949	43	22	are	be	AUX
ejpam-1949	43	23	isomorphic	isomorphic	ADJ
ejpam-1949	43	24	if	if	SCONJ
ejpam-1949	43	25	there	there	PRON
ejpam-1949	43	26	exists	exist	VERB
ejpam-1949	43	27	a	a	DET
ejpam-1949	43	28	diffeomorphism	diffeomorphism	NOUN
ejpam-1949	43	29	h	h	NOUN
ejpam-1949	43	30	:	:	PUNCT
ejpam-1949	43	31	w	w	ADP
ejpam-1949	43	32	→w	→w	PUNCT
ejpam-1949	43	33	′	′	NUM
ejpam-1949	43	34	such	such	ADJ
ejpam-1949	43	35	that	that	DET
ejpam-1949	43	36	•	•	NOUN
ejpam-1949	43	37	h	h	NOUN
ejpam-1949	43	38	preserves	preserve	VERB
ejpam-1949	43	39	the	the	DET
ejpam-1949	43	40	spinc	spinc	PROPN
ejpam-1949	43	41	structures	structure	NOUN
ejpam-1949	43	42	;	;	PUNCT
ejpam-1949	43	43	•	•	NUM
ejpam-1949	43	44	h∗ε′	h∗ε′	PUNCT
ejpam-1949	43	45	∼=	∼=	PROPN
ejpam-1949	43	46	ε	ε	PROPN
ejpam-1949	43	47	;	;	PUNCT
ejpam-1949	43	48	and	and	CCONJ
ejpam-1949	43	49	a.	a.	NOUN
ejpam-1949	43	50	elmrabty	elmrabty	NOUN
ejpam-1949	43	51	,	,	PUNCT
ejpam-1949	43	52	m.	m.	NOUN
ejpam-1949	43	53	maghfoul	maghfoul	PROPN
ejpam-1949	43	54	/	/	SYM
ejpam-1949	43	55	eur	eur	PROPN
ejpam-1949	43	56	.	.	PUNCT
ejpam-1949	44	1	j.	j.	PROPN
ejpam-1949	44	2	pure	pure	PROPN
ejpam-1949	44	3	appl	appl	PROPN
ejpam-1949	44	4	.	.	PROPN
ejpam-1949	44	5	math	math	PROPN
ejpam-1949	44	6	,	,	PUNCT
ejpam-1949	44	7	7	7	NUM
ejpam-1949	44	8	(	(	PUNCT
ejpam-1949	44	9	2014	2014	NUM
ejpam-1949	44	10	)	)	PUNCT
ejpam-1949	44	11	,	,	PUNCT
ejpam-1949	44	12	65	65	NUM
ejpam-1949	44	13	-	-	SYM
ejpam-1949	44	14	76	76	NUM
ejpam-1949	44	15	67	67	NUM
ejpam-1949	44	16	•	•	NOUN
ejpam-1949	44	17	the	the	DET
ejpam-1949	44	18	diagram	diagram	NOUN
ejpam-1949	44	19	w	w	PROPN
ejpam-1949	44	20	g	g	PROPN
ejpam-1949	44	21	�	�	PROPN
ejpam-1949	44	22	�	�	PROPN
ejpam-1949	44	23	h	h	PROPN
ejpam-1949	44	24	//	//	PROPN
ejpam-1949	45	1	w	w	NOUN
ejpam-1949	45	2	′	′	NUM
ejpam-1949	45	3	g	g	PROPN
ejpam-1949	45	4	′	′	NUM
ejpam-1949	45	5	}	}	PUNCT
ejpam-1949	45	6	}	}	PUNCT
ejpam-1949	45	7	x	x	SYM
ejpam-1949	45	8	commutes	commute	NOUN
ejpam-1949	45	9	.	.	PUNCT
ejpam-1949	46	1	a	a	DET
ejpam-1949	46	2	k	k	NOUN
ejpam-1949	46	3	-	-	NOUN
ejpam-1949	46	4	cycle	cycle	NOUN
ejpam-1949	46	5	is	be	AUX
ejpam-1949	46	6	a	a	DET
ejpam-1949	46	7	k	k	NOUN
ejpam-1949	46	8	-	-	NOUN
ejpam-1949	46	9	chain	chain	NOUN
ejpam-1949	46	10	(	(	PUNCT
ejpam-1949	46	11	m	m	PROPN
ejpam-1949	46	12	,	,	PUNCT
ejpam-1949	46	13	e	e	PROPN
ejpam-1949	46	14	,	,	PUNCT
ejpam-1949	46	15	f	f	PROPN
ejpam-1949	46	16	)	)	PUNCT
ejpam-1949	46	17	without	without	ADP
ejpam-1949	46	18	boundary	boundary	NOUN
ejpam-1949	46	19	;	;	PUNCT
ejpam-1949	46	20	that	that	PRON
ejpam-1949	46	21	is	be	AUX
ejpam-1949	46	22	∂m	∂m	PROPN
ejpam-1949	46	23	=	=	PUNCT
ejpam-1949	46	24	;	;	PUNCT
ejpam-1949	46	25	.	.	PUNCT
ejpam-1949	47	1	the	the	DET
ejpam-1949	47	2	boundary	boundary	ADJ
ejpam-1949	47	3	∂	∂	NOUN
ejpam-1949	47	4	(	(	PUNCT
ejpam-1949	47	5	w	w	PROPN
ejpam-1949	47	6	,	,	PUNCT
ejpam-1949	47	7	ε	ε	PROPN
ejpam-1949	47	8	,	,	PUNCT
ejpam-1949	47	9	g	g	NOUN
ejpam-1949	47	10	)	)	PUNCT
ejpam-1949	47	11	of	of	ADP
ejpam-1949	47	12	a	a	DET
ejpam-1949	47	13	k	k	NOUN
ejpam-1949	47	14	-	-	NOUN
ejpam-1949	47	15	chain	chain	NOUN
ejpam-1949	47	16	(	(	PUNCT
ejpam-1949	47	17	w	w	PROPN
ejpam-1949	47	18	,	,	PUNCT
ejpam-1949	47	19	ε	ε	PROPN
ejpam-1949	47	20	,	,	PUNCT
ejpam-1949	47	21	g	g	NOUN
ejpam-1949	47	22	)	)	PUNCT
ejpam-1949	47	23	is	be	AUX
ejpam-1949	47	24	the	the	DET
ejpam-1949	47	25	k	k	NOUN
ejpam-1949	47	26	-	-	NOUN
ejpam-1949	47	27	cycle	cycle	NOUN
ejpam-1949	47	28	(	(	PUNCT
ejpam-1949	47	29	∂w	∂w	PROPN
ejpam-1949	47	30	,	,	PUNCT
ejpam-1949	47	31	ε|∂w	ε|∂w	NOUN
ejpam-1949	47	32	,	,	PUNCT
ejpam-1949	47	33	g|∂w	g|∂w	PROPN
ejpam-1949	47	34	)	)	PUNCT
ejpam-1949	47	35	.	.	PUNCT
ejpam-1949	48	1	we	we	PRON
ejpam-1949	48	2	are	be	AUX
ejpam-1949	48	3	going	go	VERB
ejpam-1949	48	4	to	to	PART
ejpam-1949	48	5	construct	construct	VERB
ejpam-1949	48	6	an	an	DET
ejpam-1949	48	7	abelian	abelian	ADJ
ejpam-1949	48	8	group	group	NOUN
ejpam-1949	48	9	from	from	ADP
ejpam-1949	48	10	the	the	DET
ejpam-1949	48	11	set	set	NOUN
ejpam-1949	48	12	of	of	ADP
ejpam-1949	48	13	isomorphism	isomorphism	NOUN
ejpam-1949	48	14	classes	class	NOUN
ejpam-1949	48	15	of	of	ADP
ejpam-1949	48	16	k	k	NOUN
ejpam-1949	48	17	-	-	NOUN
ejpam-1949	48	18	cycles	cycle	NOUN
ejpam-1949	48	19	over	over	ADP
ejpam-1949	48	20	x	x	NOUN
ejpam-1949	48	21	so	so	SCONJ
ejpam-1949	48	22	as	as	SCONJ
ejpam-1949	48	23	to	to	PART
ejpam-1949	48	24	obtain	obtain	VERB
ejpam-1949	48	25	the	the	DET
ejpam-1949	48	26	geometric	geometric	ADJ
ejpam-1949	48	27	k	k	ADJ
ejpam-1949	48	28	-	-	PUNCT
ejpam-1949	48	29	homology	homology	NOUN
ejpam-1949	48	30	group	group	NOUN
ejpam-1949	48	31	of	of	ADP
ejpam-1949	48	32	x	x	X
ejpam-1949	48	33	.	.	PUNCT
ejpam-1949	49	1	in	in	ADP
ejpam-1949	49	2	order	order	NOUN
ejpam-1949	49	3	to	to	PART
ejpam-1949	49	4	define	define	VERB
ejpam-1949	49	5	the	the	DET
ejpam-1949	49	6	relation	relation	NOUN
ejpam-1949	49	7	in	in	ADP
ejpam-1949	49	8	this	this	DET
ejpam-1949	49	9	group	group	NOUN
ejpam-1949	49	10	we	we	PRON
ejpam-1949	49	11	need	need	VERB
ejpam-1949	49	12	to	to	PART
ejpam-1949	49	13	introduce	introduce	VERB
ejpam-1949	49	14	several	several	ADJ
ejpam-1949	49	15	kinds	kind	NOUN
ejpam-1949	49	16	of	of	ADP
ejpam-1949	49	17	relations	relation	NOUN
ejpam-1949	49	18	involving	involve	VERB
ejpam-1949	49	19	k	k	NOUN
ejpam-1949	49	20	-	-	NOUN
ejpam-1949	49	21	cycles	cycle	NOUN
ejpam-1949	49	22	.	.	PUNCT
ejpam-1949	50	1	vector	vector	NOUN
ejpam-1949	50	2	bundle	bundle	NOUN
ejpam-1949	50	3	modification	modification	NOUN
ejpam-1949	50	4	.	.	PUNCT
ejpam-1949	51	1	let	let	AUX
ejpam-1949	51	2	(	(	PUNCT
ejpam-1949	51	3	w	w	PROPN
ejpam-1949	51	4	,	,	PUNCT
ejpam-1949	51	5	ε	ε	PROPN
ejpam-1949	51	6	,	,	PUNCT
ejpam-1949	51	7	g	g	NOUN
ejpam-1949	51	8	)	)	PUNCT
ejpam-1949	51	9	be	be	AUX
ejpam-1949	51	10	a	a	DET
ejpam-1949	51	11	k	k	NOUN
ejpam-1949	51	12	-	-	NOUN
ejpam-1949	51	13	chain	chain	NOUN
ejpam-1949	51	14	over	over	ADP
ejpam-1949	51	15	x	x	PUNCT
ejpam-1949	51	16	and	and	CCONJ
ejpam-1949	51	17	let	let	VERB
ejpam-1949	51	18	h	h	PRON
ejpam-1949	51	19	be	be	AUX
ejpam-1949	51	20	a	a	DET
ejpam-1949	51	21	spinc	spinc	NOUN
ejpam-1949	51	22	euclidean	euclidean	ADJ
ejpam-1949	51	23	vector	vector	NOUN
ejpam-1949	51	24	bundle	bundle	NOUN
ejpam-1949	51	25	over	over	ADP
ejpam-1949	51	26	w	w	NOUN
ejpam-1949	51	27	with	with	ADP
ejpam-1949	51	28	even	even	ADV
ejpam-1949	51	29	-	-	PUNCT
ejpam-1949	51	30	dimensional	dimensional	ADJ
ejpam-1949	51	31	fibers	fiber	NOUN
ejpam-1949	51	32	.	.	PUNCT
ejpam-1949	52	1	let	let	VERB
ejpam-1949	52	2	1w	1w	NUM
ejpam-1949	52	3	denote	denote	VERB
ejpam-1949	52	4	the	the	DET
ejpam-1949	52	5	trivial	trivial	ADJ
ejpam-1949	52	6	real	real	ADJ
ejpam-1949	52	7	line	line	NOUN
ejpam-1949	52	8	bundle	bundle	NOUN
ejpam-1949	52	9	over	over	ADP
ejpam-1949	52	10	w.	w.	PROPN
ejpam-1949	52	11	we	we	PRON
ejpam-1949	52	12	denote	denote	VERB
ejpam-1949	52	13	by	by	ADP
ejpam-1949	52	14	cw	cw	NOUN
ejpam-1949	52	15	:	:	PUNCT
ejpam-1949	52	16	=	=	SYM
ejpam-1949	52	17	s(h	s(h	PROPN
ejpam-1949	52	18	⊕	⊕	PROPN
ejpam-1949	52	19	1w	1w	NUM
ejpam-1949	52	20	)	)	PUNCT
ejpam-1949	52	21	,	,	PUNCT
ejpam-1949	52	22	the	the	DET
ejpam-1949	52	23	unit	unit	NOUN
ejpam-1949	52	24	sphere	sphere	NOUN
ejpam-1949	52	25	bundle	bundle	PROPN
ejpam-1949	52	26	of	of	ADP
ejpam-1949	52	27	h	h	PROPN
ejpam-1949	52	28	⊕	⊕	PROPN
ejpam-1949	52	29	1w	1w	NUM
ejpam-1949	52	30	.	.	PUNCT
ejpam-1949	53	1	let	let	VERB
ejpam-1949	53	2	π	π	NOUN
ejpam-1949	53	3	:	:	PUNCT
ejpam-1949	53	4	cw	cw	NOUN
ejpam-1949	53	5	→	→	PUNCT
ejpam-1949	53	6	w	w	AUX
ejpam-1949	53	7	be	be	AUX
ejpam-1949	53	8	the	the	DET
ejpam-1949	53	9	bundle	bundle	NOUN
ejpam-1949	53	10	projection	projection	NOUN
ejpam-1949	53	11	.	.	PUNCT
ejpam-1949	54	1	the	the	DET
ejpam-1949	54	2	spinc	spinc	PROPN
ejpam-1949	54	3	structures	structure	NOUN
ejpam-1949	54	4	on	on	ADP
ejpam-1949	54	5	tw	tw	NOUN
ejpam-1949	54	6	and	and	CCONJ
ejpam-1949	54	7	h	h	NOUN
ejpam-1949	54	8	induce	induce	VERB
ejpam-1949	54	9	a	a	DET
ejpam-1949	54	10	spinc	spinc	NOUN
ejpam-1949	54	11	structure	structure	NOUN
ejpam-1949	54	12	on	on	ADP
ejpam-1949	54	13	tcw	tcw	PROPN
ejpam-1949	54	14	.	.	PUNCT
ejpam-1949	55	1	let	let	VERB
ejpam-1949	55	2	s	s	PRON
ejpam-1949	55	3	=	=	VERB
ejpam-1949	55	4	s−	s−	PROPN
ejpam-1949	55	5	⊕	⊕	PROPN
ejpam-1949	55	6	s+	s+	ADV
ejpam-1949	55	7	be	be	AUX
ejpam-1949	55	8	the	the	DET
ejpam-1949	55	9	z2	z2	NOUN
ejpam-1949	55	10	-	-	PUNCT
ejpam-1949	55	11	graded	grade	VERB
ejpam-1949	55	12	bundle	bundle	NOUN
ejpam-1949	55	13	of	of	ADP
ejpam-1949	55	14	clifford	clifford	PROPN
ejpam-1949	55	15	modules	module	NOUN
ejpam-1949	55	16	over	over	ADP
ejpam-1949	55	17	w	w	ADP
ejpam-1949	55	18	associated	associate	VERB
ejpam-1949	55	19	with	with	ADP
ejpam-1949	55	20	the	the	DET
ejpam-1949	55	21	spinc	spinc	ADJ
ejpam-1949	55	22	structure	structure	NOUN
ejpam-1949	55	23	on	on	ADP
ejpam-1949	55	24	h.	h.	PROPN
ejpam-1949	55	25	we	we	PRON
ejpam-1949	55	26	denote	denote	VERB
ejpam-1949	55	27	by	by	ADP
ejpam-1949	55	28	h0	h0	NOUN
ejpam-1949	55	29	and	and	CCONJ
ejpam-1949	55	30	h1	h1	VERB
ejpam-1949	55	31	the	the	DET
ejpam-1949	55	32	pullbacks	pullback	NOUN
ejpam-1949	55	33	of	of	ADP
ejpam-1949	55	34	s−	s−	PROPN
ejpam-1949	55	35	and	and	CCONJ
ejpam-1949	55	36	s+	s+	ADV
ejpam-1949	55	37	,	,	PUNCT
ejpam-1949	55	38	respectively	respectively	ADV
ejpam-1949	55	39	,	,	PUNCT
ejpam-1949	55	40	to	to	ADP
ejpam-1949	55	41	h	h	NOUN
ejpam-1949	55	42	by	by	ADP
ejpam-1949	55	43	the	the	DET
ejpam-1949	55	44	bundle	bundle	NOUN
ejpam-1949	55	45	projection	projection	NOUN
ejpam-1949	55	46	h	h	PROPN
ejpam-1949	55	47	→w	→w	PRON
ejpam-1949	55	48	.	.	PUNCT
ejpam-1949	56	1	then	then	ADV
ejpam-1949	56	2	h	h	NOUN
ejpam-1949	56	3	acts	act	VERB
ejpam-1949	56	4	on	on	ADP
ejpam-1949	56	5	h0	h0	NOUN
ejpam-1949	56	6	and	and	CCONJ
ejpam-1949	56	7	h1	h1	VERB
ejpam-1949	56	8	by	by	ADP
ejpam-1949	56	9	clifford	clifford	PROPN
ejpam-1949	56	10	multiplication	multiplication	NOUN
ejpam-1949	56	11	map	map	NOUN
ejpam-1949	56	12	:	:	PUNCT
ejpam-1949	56	13	h0	h0	NOUN
ejpam-1949	56	14	σ→	σ→	PROPN
ejpam-1949	56	15	h1	h1	PROPN
ejpam-1949	56	16	.	.	PUNCT
ejpam-1949	57	1	the	the	DET
ejpam-1949	57	2	manifold	manifold	ADJ
ejpam-1949	57	3	cw	cw	NOUN
ejpam-1949	57	4	can	can	AUX
ejpam-1949	57	5	be	be	AUX
ejpam-1949	57	6	thought	think	VERB
ejpam-1949	57	7	of	of	ADP
ejpam-1949	57	8	as	as	ADP
ejpam-1949	57	9	formed	form	VERB
ejpam-1949	57	10	of	of	ADP
ejpam-1949	57	11	two	two	NUM
ejpam-1949	57	12	copies	copy	NOUN
ejpam-1949	57	13	,	,	PUNCT
ejpam-1949	57	14	b0(h	b0(h	PROPN
ejpam-1949	57	15	)	)	PUNCT
ejpam-1949	57	16	and	and	CCONJ
ejpam-1949	57	17	b1(h	b1(h	PROPN
ejpam-1949	57	18	)	)	PUNCT
ejpam-1949	57	19	,	,	PUNCT
ejpam-1949	57	20	of	of	ADP
ejpam-1949	57	21	the	the	DET
ejpam-1949	57	22	unit	unit	NOUN
ejpam-1949	57	23	ball	ball	NOUN
ejpam-1949	57	24	bundle	bundle	NOUN
ejpam-1949	57	25	of	of	ADP
ejpam-1949	57	26	h	h	PROPN
ejpam-1949	57	27	(	(	PUNCT
ejpam-1949	57	28	carrying	carry	VERB
ejpam-1949	57	29	opposite	opposite	ADJ
ejpam-1949	57	30	spinc	spinc	PROPN
ejpam-1949	57	31	structures	structure	NOUN
ejpam-1949	57	32	)	)	PUNCT
ejpam-1949	57	33	glued	glue	VERB
ejpam-1949	57	34	together	together	ADV
ejpam-1949	57	35	by	by	ADP
ejpam-1949	57	36	the	the	DET
ejpam-1949	57	37	identity	identity	NOUN
ejpam-1949	57	38	map	map	NOUN
ejpam-1949	57	39	of	of	ADP
ejpam-1949	57	40	s(h	s(h	PROPN
ejpam-1949	57	41	):	):	PUNCT
ejpam-1949	57	42	cw	cw	NOUN
ejpam-1949	57	43	=	=	SYM
ejpam-1949	57	44	b0(h)∪s(h	b0(h)∪s(h	PROPN
ejpam-1949	57	45	)	)	PUNCT
ejpam-1949	57	46	b1(h	b1(h	PROPN
ejpam-1949	57	47	)	)	PUNCT
ejpam-1949	57	48	.	.	PUNCT
ejpam-1949	58	1	the	the	DET
ejpam-1949	58	2	vector	vector	PROPN
ejpam-1949	58	3	bundle	bundle	NOUN
ejpam-1949	58	4	bh	bh	PROPN
ejpam-1949	58	5	over	over	ADP
ejpam-1949	58	6	cw	cw	PROPN
ejpam-1949	58	7	is	be	AUX
ejpam-1949	58	8	obtained	obtain	VERB
ejpam-1949	58	9	by	by	ADP
ejpam-1949	58	10	putting	put	VERB
ejpam-1949	58	11	h0	h0	NOUN
ejpam-1949	58	12	over	over	ADP
ejpam-1949	58	13	b0(h	b0(h	PROPN
ejpam-1949	58	14	)	)	PUNCT
ejpam-1949	58	15	and	and	CCONJ
ejpam-1949	58	16	h1	h1	VERB
ejpam-1949	58	17	over	over	ADP
ejpam-1949	58	18	b1(h	b1(h	PROPN
ejpam-1949	58	19	)	)	PUNCT
ejpam-1949	58	20	and	and	CCONJ
ejpam-1949	58	21	then	then	ADV
ejpam-1949	58	22	clutching	clutch	VERB
ejpam-1949	58	23	these	these	DET
ejpam-1949	58	24	two	two	NUM
ejpam-1949	58	25	vector	vector	NOUN
ejpam-1949	58	26	bundles	bundle	NOUN
ejpam-1949	58	27	along	along	ADP
ejpam-1949	58	28	s(h	s(h	PROPN
ejpam-1949	58	29	)	)	PUNCT
ejpam-1949	58	30	by	by	ADP
ejpam-1949	58	31	the	the	DET
ejpam-1949	58	32	isomorphism	isomorphism	PROPN
ejpam-1949	58	33	σ	σ	PROPN
ejpam-1949	58	34	.	.	PUNCT
ejpam-1949	59	1	the	the	DET
ejpam-1949	59	2	process	process	NOUN
ejpam-1949	59	3	of	of	ADP
ejpam-1949	59	4	obtaining	obtain	VERB
ejpam-1949	59	5	the	the	DET
ejpam-1949	59	6	k	k	NOUN
ejpam-1949	59	7	-	-	NOUN
ejpam-1949	59	8	chain	chain	NOUN
ejpam-1949	59	9	(	(	PUNCT
ejpam-1949	59	10	cw	cw	NOUN
ejpam-1949	59	11	,	,	PUNCT
ejpam-1949	59	12	bh	bh	PROPN
ejpam-1949	59	13	⊗π∗ε	⊗π∗ε	PROPN
ejpam-1949	59	14	,	,	PUNCT
ejpam-1949	59	15	g	g	PROPN
ejpam-1949	59	16	◦	◦	NOUN
ejpam-1949	59	17	π	π	NOUN
ejpam-1949	59	18	)	)	PUNCT
ejpam-1949	59	19	from	from	ADP
ejpam-1949	59	20	(	(	PUNCT
ejpam-1949	59	21	w	w	PROPN
ejpam-1949	59	22	,	,	PUNCT
ejpam-1949	59	23	ε	ε	PROPN
ejpam-1949	59	24	,	,	PUNCT
ejpam-1949	59	25	g	g	NOUN
ejpam-1949	59	26	)	)	PUNCT
ejpam-1949	59	27	is	be	AUX
ejpam-1949	59	28	called	call	VERB
ejpam-1949	59	29	vector	vector	NOUN
ejpam-1949	59	30	bundle	bundle	NOUN
ejpam-1949	59	31	modification	modification	NOUN
ejpam-1949	59	32	.	.	PUNCT
ejpam-1949	60	1	note	note	VERB
ejpam-1949	60	2	that	that	PRON
ejpam-1949	60	3	∂	∂	ADJ
ejpam-1949	60	4	(	(	PUNCT
ejpam-1949	60	5	cw	cw	NOUN
ejpam-1949	60	6	,	,	PUNCT
ejpam-1949	60	7	bh	bh	PROPN
ejpam-1949	60	8	⊗π∗ε	⊗π∗ε	PROPN
ejpam-1949	60	9	,	,	PUNCT
ejpam-1949	60	10	g	g	PROPN
ejpam-1949	60	11	◦	◦	NOUN
ejpam-1949	60	12	π	π	NOUN
ejpam-1949	60	13	)	)	PUNCT
ejpam-1949	60	14	=	=	SYM
ejpam-1949	60	15	(	(	PUNCT
ejpam-1949	60	16	ô∂w	ô∂w	NOUN
ejpam-1949	60	17	,	,	PUNCT
ejpam-1949	60	18	×h|∂w	×h|∂w	ADP
ejpam-1949	60	19	⊗π∗(ε|∂w	⊗π∗(ε|∂w	NOUN
ejpam-1949	60	20	)	)	PUNCT
ejpam-1949	60	21	,	,	PUNCT
ejpam-1949	60	22	g|∂w	g|∂w	PROPN
ejpam-1949	60	23	◦	◦	PROPN
ejpam-1949	60	24	π|ô∂w	π|ô∂w	PROPN
ejpam-1949	60	25	)	)	PUNCT
ejpam-1949	60	26	.	.	PUNCT
ejpam-1949	61	1	definition	definition	NOUN
ejpam-1949	61	2	2	2	NUM
ejpam-1949	61	3	.	.	PUNCT
ejpam-1949	62	1	we	we	PRON
ejpam-1949	62	2	define	define	VERB
ejpam-1949	62	3	the	the	DET
ejpam-1949	62	4	set	set	ADJ
ejpam-1949	62	5	c∗(x	c∗(x	NOUN
ejpam-1949	62	6	)	)	PUNCT
ejpam-1949	62	7	as	as	ADP
ejpam-1949	62	8	the	the	DET
ejpam-1949	62	9	quotient	quotient	NOUN
ejpam-1949	62	10	of	of	ADP
ejpam-1949	62	11	the	the	DET
ejpam-1949	62	12	set	set	NOUN
ejpam-1949	62	13	of	of	ADP
ejpam-1949	62	14	isomorphism	isomorphism	NOUN
ejpam-1949	62	15	classes	class	NOUN
ejpam-1949	62	16	of	of	ADP
ejpam-1949	62	17	k	k	NOUN
ejpam-1949	62	18	-	-	NOUN
ejpam-1949	62	19	cycles	cycle	NOUN
ejpam-1949	62	20	over	over	ADP
ejpam-1949	62	21	x	x	PUNCT
ejpam-1949	62	22	by	by	ADP
ejpam-1949	62	23	the	the	DET
ejpam-1949	62	24	equivalence	equivalence	NOUN
ejpam-1949	62	25	relation	relation	NOUN
ejpam-1949	62	26	∼	∼	NOUN
ejpam-1949	62	27	generated	generate	VERB
ejpam-1949	62	28	by	by	ADP
ejpam-1949	62	29	the	the	DET
ejpam-1949	62	30	relations	relation	NOUN
ejpam-1949	62	31	of	of	ADP
ejpam-1949	62	32	•	•	NUM
ejpam-1949	62	33	direct	direct	ADJ
ejpam-1949	62	34	sum	sum	NOUN
ejpam-1949	62	35	:	:	PUNCT
ejpam-1949	62	36	if	if	SCONJ
ejpam-1949	62	37	e	e	PROPN
ejpam-1949	62	38	=	=	SYM
ejpam-1949	62	39	e1⊕	e1⊕	PROPN
ejpam-1949	62	40	e2	e2	PROPN
ejpam-1949	62	41	,	,	PUNCT
ejpam-1949	62	42	then	then	ADV
ejpam-1949	62	43	(	(	PUNCT
ejpam-1949	62	44	m	m	PROPN
ejpam-1949	62	45	,	,	PUNCT
ejpam-1949	62	46	e1	e1	PROPN
ejpam-1949	62	47	,	,	PUNCT
ejpam-1949	62	48	f	f	PROPN
ejpam-1949	62	49	)	)	PUNCT
ejpam-1949	62	50	t	t	PROPN
ejpam-1949	62	51	(	(	PUNCT
ejpam-1949	62	52	m	m	PROPN
ejpam-1949	62	53	,	,	PUNCT
ejpam-1949	62	54	e2	e2	PROPN
ejpam-1949	62	55	,	,	PUNCT
ejpam-1949	62	56	f	f	NOUN
ejpam-1949	62	57	)	)	PUNCT
ejpam-1949	62	58	∼	∼	NOUN
ejpam-1949	62	59	(	(	PUNCT
ejpam-1949	62	60	m	m	PROPN
ejpam-1949	62	61	,	,	PUNCT
ejpam-1949	62	62	e1⊕	e1⊕	PROPN
ejpam-1949	62	63	e2	e2	PROPN
ejpam-1949	62	64	,	,	PUNCT
ejpam-1949	62	65	f	f	PROPN
ejpam-1949	62	66	)	)	PUNCT
ejpam-1949	62	67	;	;	PUNCT
ejpam-1949	62	68	and	and	CCONJ
ejpam-1949	62	69	•	•	NUM
ejpam-1949	62	70	vector	vector	NOUN
ejpam-1949	62	71	bundle	bundle	NOUN
ejpam-1949	62	72	modification	modification	NOUN
ejpam-1949	62	73	.	.	PUNCT
ejpam-1949	63	1	an	an	DET
ejpam-1949	63	2	operation	operation	NOUN
ejpam-1949	63	3	on	on	ADP
ejpam-1949	63	4	c∗(x	c∗(x	NOUN
ejpam-1949	63	5	)	)	PUNCT
ejpam-1949	63	6	is	be	AUX
ejpam-1949	63	7	given	give	VERB
ejpam-1949	63	8	by	by	ADP
ejpam-1949	63	9	disjoint	disjoint	NOUN
ejpam-1949	63	10	union	union	NOUN
ejpam-1949	63	11	,	,	PUNCT
ejpam-1949	63	12	(	(	PUNCT
ejpam-1949	63	13	m	m	PROPN
ejpam-1949	63	14	,	,	PUNCT
ejpam-1949	63	15	e	e	PROPN
ejpam-1949	63	16	,	,	PUNCT
ejpam-1949	63	17	f	f	PROPN
ejpam-1949	63	18	)	)	PUNCT
ejpam-1949	63	19	t	t	PROPN
ejpam-1949	63	20	(	(	PUNCT
ejpam-1949	63	21	m	m	PROPN
ejpam-1949	63	22	′	′	NUM
ejpam-1949	63	23	,	,	PUNCT
ejpam-1949	63	24	e′	e′	PROPN
ejpam-1949	63	25	,	,	PUNCT
ejpam-1949	63	26	f	f	PROPN
ejpam-1949	63	27	′	′	NUM
ejpam-1949	63	28	)	)	PUNCT
ejpam-1949	63	29	:	:	PUNCT
ejpam-1949	64	1	=	=	SYM
ejpam-1949	64	2	(	(	PUNCT
ejpam-1949	64	3	m	m	VERB
ejpam-1949	64	4	tm	tm	NOUN
ejpam-1949	64	5	′	′	PROPN
ejpam-1949	64	6	,	,	PUNCT
ejpam-1949	64	7	e	e	PROPN
ejpam-1949	64	8	t	t	NOUN
ejpam-1949	64	9	e′	e′	PROPN
ejpam-1949	64	10	,	,	PUNCT
ejpam-1949	64	11	f	f	PROPN
ejpam-1949	64	12	t	t	PROPN
ejpam-1949	64	13	f	f	PROPN
ejpam-1949	64	14	′	′	NUM
ejpam-1949	64	15	)	)	PUNCT
ejpam-1949	64	16	.	.	PUNCT
ejpam-1949	65	1	this	this	DET
ejpam-1949	65	2	operation	operation	NOUN
ejpam-1949	65	3	turns	turn	VERB
ejpam-1949	65	4	c∗(x	c∗(x	NOUN
ejpam-1949	65	5	)	)	PUNCT
ejpam-1949	65	6	into	into	ADP
ejpam-1949	65	7	an	an	DET
ejpam-1949	65	8	abelian	abelian	ADJ
ejpam-1949	65	9	semigroup	semigroup	NOUN
ejpam-1949	65	10	.	.	PUNCT
ejpam-1949	66	1	since	since	SCONJ
ejpam-1949	66	2	the	the	DET
ejpam-1949	66	3	relation	relation	NOUN
ejpam-1949	66	4	∼	∼	NOUN
ejpam-1949	66	5	preserves	preserve	VERB
ejpam-1949	66	6	the	the	DET
ejpam-1949	66	7	parity	parity	NOUN
ejpam-1949	66	8	of	of	ADP
ejpam-1949	66	9	the	the	DET
ejpam-1949	66	10	dimension	dimension	NOUN
ejpam-1949	66	11	of	of	ADP
ejpam-1949	66	12	m	m	PROPN
ejpam-1949	66	13	in	in	ADP
ejpam-1949	66	14	k	k	NOUN
ejpam-1949	66	15	-	-	NOUN
ejpam-1949	66	16	cycles	cycle	NOUN
ejpam-1949	66	17	(	(	PUNCT
ejpam-1949	66	18	m	m	PROPN
ejpam-1949	66	19	,	,	PUNCT
ejpam-1949	66	20	e	e	PROPN
ejpam-1949	66	21	,	,	PUNCT
ejpam-1949	66	22	f	f	PROPN
ejpam-1949	66	23	)	)	PUNCT
ejpam-1949	66	24	,	,	PUNCT
ejpam-1949	66	25	one	one	PRON
ejpam-1949	66	26	can	can	AUX
ejpam-1949	66	27	define	define	VERB
ejpam-1949	66	28	the	the	DET
ejpam-1949	66	29	subsemigroup	subsemigroup	NOUN
ejpam-1949	66	30	c0(x	c0(x	PROPN
ejpam-1949	66	31	)	)	PUNCT
ejpam-1949	66	32	(	(	PUNCT
ejpam-1949	66	33	resp	resp	NOUN
ejpam-1949	66	34	.	.	PUNCT
ejpam-1949	67	1	a.	a.	NOUN
ejpam-1949	67	2	elmrabty	elmrabty	NOUN
ejpam-1949	67	3	,	,	PUNCT
ejpam-1949	67	4	m.	m.	NOUN
ejpam-1949	67	5	maghfoul	maghfoul	PROPN
ejpam-1949	67	6	/	/	SYM
ejpam-1949	67	7	eur	eur	PROPN
ejpam-1949	67	8	.	.	PUNCT
ejpam-1949	68	1	j.	j.	PROPN
ejpam-1949	68	2	pure	pure	PROPN
ejpam-1949	68	3	appl	appl	PROPN
ejpam-1949	68	4	.	.	PROPN
ejpam-1949	68	5	math	math	PROPN
ejpam-1949	68	6	,	,	PUNCT
ejpam-1949	68	7	7	7	NUM
ejpam-1949	68	8	(	(	PUNCT
ejpam-1949	68	9	2014	2014	NUM
ejpam-1949	68	10	)	)	PUNCT
ejpam-1949	68	11	,	,	PUNCT
ejpam-1949	68	12	65	65	NUM
ejpam-1949	68	13	-	-	SYM
ejpam-1949	68	14	76	76	NUM
ejpam-1949	68	15	68	68	NUM
ejpam-1949	68	16	c1(x	c1(x	NOUN
ejpam-1949	68	17	)	)	PUNCT
ejpam-1949	68	18	)	)	PUNCT
ejpam-1949	69	1	consisting	consist	VERB
ejpam-1949	69	2	of	of	ADP
ejpam-1949	69	3	classes	class	NOUN
ejpam-1949	69	4	of	of	ADP
ejpam-1949	69	5	k	k	NOUN
ejpam-1949	69	6	-	-	NOUN
ejpam-1949	69	7	cycles	cycle	NOUN
ejpam-1949	69	8	(	(	PUNCT
ejpam-1949	69	9	m	m	PROPN
ejpam-1949	69	10	,	,	PUNCT
ejpam-1949	69	11	e	e	PROPN
ejpam-1949	69	12	,	,	PUNCT
ejpam-1949	69	13	f	f	PROPN
ejpam-1949	69	14	)	)	PUNCT
ejpam-1949	69	15	for	for	ADP
ejpam-1949	69	16	which	which	PRON
ejpam-1949	69	17	all	all	DET
ejpam-1949	69	18	connected	connected	ADJ
ejpam-1949	69	19	components	component	NOUN
ejpam-1949	69	20	of	of	ADP
ejpam-1949	69	21	m	m	PROPN
ejpam-1949	69	22	are	be	AUX
ejpam-1949	69	23	of	of	ADP
ejpam-1949	69	24	even	even	ADV
ejpam-1949	69	25	(	(	PUNCT
ejpam-1949	69	26	resp	resp	NOUN
ejpam-1949	69	27	.	.	PUNCT
ejpam-1949	70	1	odd	odd	ADJ
ejpam-1949	70	2	)	)	PUNCT
ejpam-1949	70	3	dimension	dimension	NOUN
ejpam-1949	70	4	.	.	PUNCT
ejpam-1949	71	1	then	then	ADV
ejpam-1949	71	2	c∗(x	c∗(x	NOUN
ejpam-1949	71	3	)	)	PUNCT
ejpam-1949	72	1	=	=	PUNCT
ejpam-1949	72	2	c0(x	c0(x	NOUN
ejpam-1949	72	3	)	)	PUNCT
ejpam-1949	72	4	⊕	⊕	PROPN
ejpam-1949	72	5	c1(x	c1(x	PROPN
ejpam-1949	72	6	)	)	PUNCT
ejpam-1949	72	7	has	have	VERB
ejpam-1949	72	8	a	a	DET
ejpam-1949	72	9	natural	natural	ADJ
ejpam-1949	72	10	z2	z2	NOUN
ejpam-1949	72	11	-	-	PUNCT
ejpam-1949	72	12	grading	grade	VERB
ejpam-1949	72	13	.	.	PUNCT
ejpam-1949	73	1	bordism	bordism	NOUN
ejpam-1949	73	2	.	.	PUNCT
ejpam-1949	74	1	two	two	NUM
ejpam-1949	74	2	k	k	NOUN
ejpam-1949	74	3	-	-	PUNCT
ejpam-1949	74	4	cycles	cycle	NOUN
ejpam-1949	74	5	(	(	PUNCT
ejpam-1949	74	6	m	m	PROPN
ejpam-1949	74	7	,	,	PUNCT
ejpam-1949	74	8	e	e	PROPN
ejpam-1949	74	9	,	,	PUNCT
ejpam-1949	74	10	f	f	PROPN
ejpam-1949	74	11	)	)	PUNCT
ejpam-1949	74	12	and	and	CCONJ
ejpam-1949	74	13	(	(	PUNCT
ejpam-1949	74	14	m	m	PROPN
ejpam-1949	74	15	′	′	NUM
ejpam-1949	74	16	,	,	PUNCT
ejpam-1949	74	17	e′	e′	PROPN
ejpam-1949	74	18	,	,	PUNCT
ejpam-1949	74	19	f	f	PROPN
ejpam-1949	74	20	′	′	NOUN
ejpam-1949	74	21	)	)	PUNCT
ejpam-1949	74	22	over	over	ADV
ejpam-1949	74	23	x	x	SYM
ejpam-1949	74	24	are	be	AUX
ejpam-1949	74	25	bordant	bordant	ADJ
ejpam-1949	74	26	if	if	SCONJ
ejpam-1949	74	27	there	there	PRON
ejpam-1949	74	28	exists	exist	VERB
ejpam-1949	74	29	a	a	DET
ejpam-1949	74	30	k	k	NOUN
ejpam-1949	74	31	-	-	NOUN
ejpam-1949	74	32	chain	chain	NOUN
ejpam-1949	74	33	(	(	PUNCT
ejpam-1949	74	34	w	w	PROPN
ejpam-1949	74	35	,	,	PUNCT
ejpam-1949	74	36	ε	ε	PROPN
ejpam-1949	74	37	,	,	PUNCT
ejpam-1949	74	38	g	g	NOUN
ejpam-1949	74	39	)	)	PUNCT
ejpam-1949	74	40	such	such	ADJ
ejpam-1949	74	41	that	that	SCONJ
ejpam-1949	74	42	the	the	DET
ejpam-1949	74	43	two	two	NUM
ejpam-1949	74	44	k	k	ADJ
ejpam-1949	74	45	-	-	PUNCT
ejpam-1949	74	46	cycles	cycle	NOUN
ejpam-1949	74	47	∂	∂	NOUN
ejpam-1949	74	48	(	(	PUNCT
ejpam-1949	74	49	w	w	PROPN
ejpam-1949	74	50	,	,	PUNCT
ejpam-1949	74	51	ε	ε	PROPN
ejpam-1949	74	52	,	,	PUNCT
ejpam-1949	74	53	g	g	NOUN
ejpam-1949	74	54	)	)	PUNCT
ejpam-1949	74	55	and	and	CCONJ
ejpam-1949	74	56	(	(	PUNCT
ejpam-1949	74	57	m	m	PROPN
ejpam-1949	74	58	,	,	PUNCT
ejpam-1949	74	59	e	e	PROPN
ejpam-1949	74	60	,	,	PUNCT
ejpam-1949	74	61	f	f	PROPN
ejpam-1949	74	62	)	)	PUNCT
ejpam-1949	74	63	t	t	PROPN
ejpam-1949	74	64	(	(	PUNCT
ejpam-1949	74	65	−m	−m	NOUN
ejpam-1949	74	66	′	′	NUM
ejpam-1949	74	67	,	,	PUNCT
ejpam-1949	74	68	e′	e′	PROPN
ejpam-1949	74	69	,	,	PUNCT
ejpam-1949	74	70	f	f	PROPN
ejpam-1949	74	71	′	′	NUM
ejpam-1949	74	72	)	)	PUNCT
ejpam-1949	74	73	are	be	AUX
ejpam-1949	74	74	isomorphic	isomorphic	ADJ
ejpam-1949	74	75	,	,	PUNCT
ejpam-1949	74	76	where	where	SCONJ
ejpam-1949	74	77	−m	−m	ADJ
ejpam-1949	74	78	′	′	NUM
ejpam-1949	74	79	denotes	denote	NOUN
ejpam-1949	74	80	m	m	VERB
ejpam-1949	74	81	′	′	ADJ
ejpam-1949	74	82	with	with	ADP
ejpam-1949	74	83	the	the	DET
ejpam-1949	74	84	spinc	spinc	ADJ
ejpam-1949	74	85	structure	structure	NOUN
ejpam-1949	74	86	on	on	ADP
ejpam-1949	74	87	its	its	PRON
ejpam-1949	74	88	tangent	tangent	NOUN
ejpam-1949	74	89	bundle	bundle	PROPN
ejpam-1949	75	1	t	t	PROPN
ejpam-1949	75	2	m	m	AUX
ejpam-1949	75	3	′	′	NUM
ejpam-1949	75	4	reversed	reverse	VERB
ejpam-1949	75	5	[	[	X
ejpam-1949	75	6	1	1	NUM
ejpam-1949	75	7	]	]	PUNCT
ejpam-1949	75	8	.	.	PUNCT
ejpam-1949	76	1	the	the	DET
ejpam-1949	76	2	bordism	bordism	NOUN
ejpam-1949	76	3	relation	relation	NOUN
ejpam-1949	76	4	induces	induce	VERB
ejpam-1949	76	5	a	a	DET
ejpam-1949	76	6	well	well	ADV
ejpam-1949	76	7	-	-	PUNCT
ejpam-1949	76	8	defined	define	VERB
ejpam-1949	76	9	equivalence	equivalence	NOUN
ejpam-1949	76	10	relation	relation	NOUN
ejpam-1949	76	11	∼b	∼b	PROPN
ejpam-1949	76	12	on	on	ADP
ejpam-1949	76	13	c∗(x	c∗(x	NOUN
ejpam-1949	76	14	)	)	PUNCT
ejpam-1949	76	15	.	.	PUNCT
ejpam-1949	77	1	this	this	DET
ejpam-1949	77	2	relation	relation	NOUN
ejpam-1949	77	3	is	be	AUX
ejpam-1949	77	4	compatible	compatible	ADJ
ejpam-1949	77	5	with	with	ADP
ejpam-1949	77	6	the	the	DET
ejpam-1949	77	7	semigroup	semigroup	ADJ
ejpam-1949	77	8	structure	structure	NOUN
ejpam-1949	77	9	,	,	PUNCT
ejpam-1949	77	10	and	and	CCONJ
ejpam-1949	77	11	then	then	ADV
ejpam-1949	77	12	the	the	DET
ejpam-1949	77	13	quotient	quotient	NOUN
ejpam-1949	77	14	set	set	VERB
ejpam-1949	77	15	c∗(x	c∗(x	NOUN
ejpam-1949	77	16	)	)	PUNCT
ejpam-1949	77	17	/	/	SYM
ejpam-1949	78	1	∼b	∼b	PROPN
ejpam-1949	78	2	turns	turn	VERB
ejpam-1949	78	3	out	out	ADP
ejpam-1949	78	4	to	to	PART
ejpam-1949	78	5	be	be	AUX
ejpam-1949	78	6	an	an	DET
ejpam-1949	78	7	abelian	abelian	ADJ
ejpam-1949	78	8	semigroup	semigroup	NOUN
ejpam-1949	78	9	.	.	PUNCT
ejpam-1949	79	1	the	the	DET
ejpam-1949	79	2	abelian	abelian	PROPN
ejpam-1949	79	3	semigroup	semigroup	PROPN
ejpam-1949	79	4	c∗(x	c∗(x	PROPN
ejpam-1949	79	5	)	)	PUNCT
ejpam-1949	79	6	/∼b	/∼b	X
ejpam-1949	79	7	is	be	AUX
ejpam-1949	79	8	in	in	ADP
ejpam-1949	79	9	fact	fact	NOUN
ejpam-1949	79	10	an	an	DET
ejpam-1949	79	11	abelian	abelian	ADJ
ejpam-1949	79	12	group	group	NOUN
ejpam-1949	79	13	.	.	PUNCT
ejpam-1949	80	1	the	the	DET
ejpam-1949	80	2	additive	additive	ADJ
ejpam-1949	80	3	inverse	inverse	NOUN
ejpam-1949	80	4	of	of	ADP
ejpam-1949	80	5	the	the	DET
ejpam-1949	80	6	class	class	NOUN
ejpam-1949	80	7	of	of	ADP
ejpam-1949	80	8	a	a	DET
ejpam-1949	80	9	k	k	NOUN
ejpam-1949	80	10	-	-	NOUN
ejpam-1949	80	11	cycle	cycle	NOUN
ejpam-1949	80	12	is	be	AUX
ejpam-1949	80	13	obtained	obtain	VERB
ejpam-1949	80	14	by	by	ADP
ejpam-1949	80	15	reversing	reverse	VERB
ejpam-1949	80	16	the	the	DET
ejpam-1949	80	17	spinc	spinc	NOUN
ejpam-1949	80	18	structure	structure	NOUN
ejpam-1949	80	19	:	:	PUNCT
ejpam-1949	80	20	−[m	−[m	NOUN
ejpam-1949	80	21	,	,	PUNCT
ejpam-1949	80	22	e	e	PROPN
ejpam-1949	80	23	,	,	PUNCT
ejpam-1949	80	24	f	f	X
ejpam-1949	80	25	]	]	PUNCT
ejpam-1949	81	1	=	=	PUNCT
ejpam-1949	82	1	[	[	X
ejpam-1949	82	2	−m	−m	INTJ
ejpam-1949	82	3	,	,	PUNCT
ejpam-1949	82	4	e	e	PROPN
ejpam-1949	82	5	,	,	PUNCT
ejpam-1949	82	6	f	f	X
ejpam-1949	82	7	]	]	PUNCT
ejpam-1949	82	8	.	.	PUNCT
ejpam-1949	83	1	the	the	DET
ejpam-1949	83	2	neutral	neutral	ADJ
ejpam-1949	83	3	element	element	NOUN
ejpam-1949	83	4	is	be	AUX
ejpam-1949	83	5	represented	represent	VERB
ejpam-1949	83	6	by	by	ADP
ejpam-1949	83	7	the	the	DET
ejpam-1949	83	8	empty	empty	ADJ
ejpam-1949	83	9	manifold	manifold	NOUN
ejpam-1949	83	10	,	,	PUNCT
ejpam-1949	83	11	or	or	CCONJ
ejpam-1949	83	12	any	any	DET
ejpam-1949	83	13	k	k	ADJ
ejpam-1949	83	14	-	-	PUNCT
ejpam-1949	83	15	cycle	cycle	NOUN
ejpam-1949	83	16	bordant	bordant	NOUN
ejpam-1949	83	17	to	to	ADP
ejpam-1949	83	18	the	the	DET
ejpam-1949	83	19	empty	empty	ADJ
ejpam-1949	83	20	manifold	manifold	NOUN
ejpam-1949	83	21	.	.	PUNCT
ejpam-1949	84	1	definition	definition	NOUN
ejpam-1949	84	2	3	3	NUM
ejpam-1949	84	3	.	.	PUNCT
ejpam-1949	85	1	the	the	DET
ejpam-1949	85	2	quotient	quotient	NOUN
ejpam-1949	85	3	group	group	NOUN
ejpam-1949	85	4	c∗(x	c∗(x	PROPN
ejpam-1949	85	5	)	)	PUNCT
ejpam-1949	85	6	/	/	SYM
ejpam-1949	85	7	∼b	∼b	PROPN
ejpam-1949	85	8	is	be	AUX
ejpam-1949	85	9	denoted	denote	VERB
ejpam-1949	85	10	by	by	ADP
ejpam-1949	85	11	k∗(x	k∗(x	PROPN
ejpam-1949	85	12	)	)	PUNCT
ejpam-1949	85	13	and	and	CCONJ
ejpam-1949	85	14	called	call	VERB
ejpam-1949	85	15	the	the	DET
ejpam-1949	85	16	geometric	geometric	ADJ
ejpam-1949	85	17	khomology	khomology	NOUN
ejpam-1949	85	18	group	group	NOUN
ejpam-1949	85	19	of	of	ADP
ejpam-1949	85	20	x	x	X
ejpam-1949	85	21	.	.	PUNCT
ejpam-1949	86	1	it	it	PRON
ejpam-1949	86	2	has	have	VERB
ejpam-1949	86	3	a	a	DET
ejpam-1949	86	4	natural	natural	ADJ
ejpam-1949	86	5	z2	z2	NOUN
ejpam-1949	86	6	-	-	PUNCT
ejpam-1949	86	7	grading	grade	VERB
ejpam-1949	86	8	:	:	PUNCT
ejpam-1949	86	9	k∗(x	k∗(x	X
ejpam-1949	86	10	)	)	PUNCT
ejpam-1949	86	11	=	=	SYM
ejpam-1949	86	12	k0(x	k0(x	NOUN
ejpam-1949	86	13	)	)	PUNCT
ejpam-1949	86	14	⊕	⊕	PROPN
ejpam-1949	86	15	k1(x	k1(x	PROPN
ejpam-1949	86	16	)	)	PUNCT
ejpam-1949	86	17	.	.	PUNCT
ejpam-1949	87	1	the	the	DET
ejpam-1949	87	2	geometric	geometric	ADJ
ejpam-1949	87	3	construction	construction	NOUN
ejpam-1949	87	4	of	of	ADP
ejpam-1949	87	5	k	k	X
ejpam-1949	87	6	-	-	NOUN
ejpam-1949	87	7	homology	homology	NOUN
ejpam-1949	87	8	is	be	AUX
ejpam-1949	87	9	functorial	functorial	NOUN
ejpam-1949	87	10	.	.	PUNCT
ejpam-1949	88	1	if	if	SCONJ
ejpam-1949	88	2	ρ	ρ	PROPN
ejpam-1949	88	3	:	:	PUNCT
ejpam-1949	88	4	y	y	PROPN
ejpam-1949	88	5	→	→	PUNCT
ejpam-1949	88	6	x	x	X
ejpam-1949	88	7	is	be	AUX
ejpam-1949	88	8	a	a	DET
ejpam-1949	88	9	smooth	smooth	ADJ
ejpam-1949	88	10	map	map	NOUN
ejpam-1949	88	11	between	between	ADP
ejpam-1949	88	12	two	two	NUM
ejpam-1949	88	13	smooth	smooth	ADJ
ejpam-1949	88	14	compact	compact	ADJ
ejpam-1949	88	15	manifolds	manifold	NOUN
ejpam-1949	88	16	,	,	PUNCT
ejpam-1949	88	17	then	then	ADV
ejpam-1949	88	18	the	the	DET
ejpam-1949	88	19	induced	induced	ADJ
ejpam-1949	88	20	homomorphism	homomorphism	PROPN
ejpam-1949	88	21	ρ∗	ρ∗	PROPN
ejpam-1949	88	22	:	:	PUNCT
ejpam-1949	88	23	k∗(y	k∗(y	PROPN
ejpam-1949	88	24	)	)	PUNCT
ejpam-1949	88	25	→	→	SYM
ejpam-1949	88	26	k∗(x	k∗(x	NOUN
ejpam-1949	88	27	)	)	PUNCT
ejpam-1949	88	28	of	of	ADP
ejpam-1949	88	29	z2	z2	NOUN
ejpam-1949	88	30	-	-	PUNCT
ejpam-1949	88	31	graded	grade	VERB
ejpam-1949	88	32	abelian	abelian	ADJ
ejpam-1949	88	33	groups	group	NOUN
ejpam-1949	88	34	is	be	AUX
ejpam-1949	88	35	given	give	VERB
ejpam-1949	88	36	on	on	ADP
ejpam-1949	88	37	classes	class	NOUN
ejpam-1949	88	38	of	of	ADP
ejpam-1949	88	39	k	k	NOUN
ejpam-1949	88	40	-	-	NOUN
ejpam-1949	88	41	cycles	cycle	NOUN
ejpam-1949	88	42	[	[	X
ejpam-1949	88	43	m	m	X
ejpam-1949	88	44	,	,	PUNCT
ejpam-1949	88	45	e	e	PROPN
ejpam-1949	88	46	,	,	PUNCT
ejpam-1949	88	47	f	f	PROPN
ejpam-1949	88	48	]	]	PUNCT
ejpam-1949	88	49	∈	∈	PROPN
ejpam-1949	88	50	k∗(y	k∗(y	PROPN
ejpam-1949	88	51	)	)	PUNCT
ejpam-1949	88	52	by	by	ADP
ejpam-1949	88	53	ρ∗[m	ρ∗[m	NOUN
ejpam-1949	88	54	,	,	PUNCT
ejpam-1949	88	55	e	e	X
ejpam-1949	88	56	,	,	PUNCT
ejpam-1949	88	57	f	f	X
ejpam-1949	88	58	]	]	PUNCT
ejpam-1949	88	59	:	:	PUNCT
ejpam-1949	89	1	=	=	PUNCT
ejpam-1949	90	1	[	[	X
ejpam-1949	90	2	m	m	X
ejpam-1949	90	3	,	,	PUNCT
ejpam-1949	90	4	e	e	NOUN
ejpam-1949	90	5	,	,	PUNCT
ejpam-1949	90	6	ρ	ρ	PROPN
ejpam-1949	90	7	◦	◦	NOUN
ejpam-1949	90	8	f	f	X
ejpam-1949	90	9	]	]	X
ejpam-1949	90	10	.	.	PUNCT
ejpam-1949	91	1	since	since	SCONJ
ejpam-1949	91	2	vector	vector	NOUN
ejpam-1949	91	3	bundles	bundle	NOUN
ejpam-1949	91	4	over	over	ADP
ejpam-1949	91	5	m	m	VERB
ejpam-1949	91	6	extend	extend	VERB
ejpam-1949	91	7	to	to	ADP
ejpam-1949	91	8	vector	vector	NOUN
ejpam-1949	91	9	bundles	bundle	NOUN
ejpam-1949	91	10	over	over	ADP
ejpam-1949	91	11	m	m	NOUN
ejpam-1949	91	12	×	×	NOUN
ejpam-1949	91	13	[	[	X
ejpam-1949	91	14	0,1	0,1	NUM
ejpam-1949	91	15	]	]	PUNCT
ejpam-1949	91	16	,	,	PUNCT
ejpam-1949	91	17	it	it	PRON
ejpam-1949	91	18	follows	follow	VERB
ejpam-1949	91	19	by	by	ADP
ejpam-1949	91	20	bordism	bordism	NOUN
ejpam-1949	91	21	that	that	SCONJ
ejpam-1949	91	22	k∗(ρ	k∗(ρ	NOUN
ejpam-1949	91	23	)	)	PUNCT
ejpam-1949	91	24	:	:	PUNCT
ejpam-1949	92	1	=	=	SYM
ejpam-1949	92	2	ρ∗	ρ∗	PROPN
ejpam-1949	92	3	depend	depend	VERB
ejpam-1949	92	4	only	only	ADV
ejpam-1949	92	5	on	on	ADP
ejpam-1949	92	6	the	the	DET
ejpam-1949	92	7	smooth	smooth	ADJ
ejpam-1949	92	8	homotopy	homotopy	NOUN
ejpam-1949	92	9	classes	class	NOUN
ejpam-1949	92	10	of	of	ADP
ejpam-1949	92	11	ρ	ρ	PROPN
ejpam-1949	92	12	.	.	PUNCT
ejpam-1949	93	1	let	let	VERB
ejpam-1949	93	2	x	x	PRON
ejpam-1949	93	3	be	be	AUX
ejpam-1949	93	4	a	a	DET
ejpam-1949	93	5	smooth	smooth	ADJ
ejpam-1949	93	6	compact	compact	ADJ
ejpam-1949	93	7	manifold	manifold	NOUN
ejpam-1949	93	8	.	.	PUNCT
ejpam-1949	94	1	let	let	AUX
ejpam-1949	94	2	l∗(x	l∗(x	ADV
ejpam-1949	94	3	)	)	PUNCT
ejpam-1949	94	4	be	be	AUX
ejpam-1949	94	5	the	the	DET
ejpam-1949	94	6	quotient	quotient	NOUN
ejpam-1949	94	7	of	of	ADP
ejpam-1949	94	8	the	the	DET
ejpam-1949	94	9	set	set	NOUN
ejpam-1949	94	10	of	of	ADP
ejpam-1949	94	11	isomorphism	isomorphism	NOUN
ejpam-1949	94	12	classes	class	NOUN
ejpam-1949	94	13	of	of	ADP
ejpam-1949	94	14	k	k	NOUN
ejpam-1949	94	15	-	-	PUNCT
ejpam-1949	94	16	chains	chain	NOUN
ejpam-1949	94	17	over	over	ADP
ejpam-1949	94	18	x	x	PUNCT
ejpam-1949	94	19	by	by	ADP
ejpam-1949	94	20	∼.	∼.	PROPN
ejpam-1949	94	21	note	note	NOUN
ejpam-1949	94	22	that	that	SCONJ
ejpam-1949	94	23	the	the	DET
ejpam-1949	94	24	boundary	boundary	ADJ
ejpam-1949	94	25	map	map	NOUN
ejpam-1949	94	26	on	on	ADP
ejpam-1949	94	27	the	the	DET
ejpam-1949	94	28	set	set	NOUN
ejpam-1949	94	29	of	of	ADP
ejpam-1949	94	30	k	k	NOUN
ejpam-1949	94	31	-	-	PUNCT
ejpam-1949	94	32	chains	chain	NOUN
ejpam-1949	94	33	over	over	ADP
ejpam-1949	94	34	x	x	PUNCT
ejpam-1949	94	35	descends	descend	VERB
ejpam-1949	94	36	to	to	ADP
ejpam-1949	94	37	a	a	DET
ejpam-1949	94	38	boundary	boundary	ADJ
ejpam-1949	94	39	map	map	NOUN
ejpam-1949	94	40	∂	∂	NOUN
ejpam-1949	94	41	:	:	PUNCT
ejpam-1949	94	42	l∗(x	l∗(x	ADP
ejpam-1949	94	43	)	)	PUNCT
ejpam-1949	94	44	→	→	SYM
ejpam-1949	94	45	c∗−1(x	c∗−1(x	NOUN
ejpam-1949	94	46	)	)	PUNCT
ejpam-1949	94	47	⊂	⊂	PROPN
ejpam-1949	94	48	l∗−1(x	l∗−1(x	NUM
ejpam-1949	94	49	)	)	PUNCT
ejpam-1949	94	50	.	.	PUNCT
ejpam-1949	95	1	let	let	VERB
ejpam-1949	95	2	ω∗(x	ω∗(x	NOUN
ejpam-1949	95	3	)	)	PUNCT
ejpam-1949	95	4	be	be	AUX
ejpam-1949	95	5	the	the	DET
ejpam-1949	95	6	graded	grade	VERB
ejpam-1949	95	7	algebra	algebra	NOUN
ejpam-1949	95	8	of	of	ADP
ejpam-1949	95	9	real	real	ADV
ejpam-1949	95	10	-	-	PUNCT
ejpam-1949	95	11	valued	value	VERB
ejpam-1949	95	12	differential	differential	NOUN
ejpam-1949	95	13	forms	form	NOUN
ejpam-1949	95	14	on	on	ADP
ejpam-1949	95	15	x	x	X
ejpam-1949	95	16	.	.	PUNCT
ejpam-1949	96	1	let	let	VERB
ejpam-1949	96	2	ϕ	ϕ	NOUN
ejpam-1949	96	3	:	:	PUNCT
ejpam-1949	96	4	ω∗(x	ω∗(x	NOUN
ejpam-1949	96	5	)	)	PUNCT
ejpam-1949	96	6	→	→	SYM
ejpam-1949	96	7	hom(l∗(x	hom(l∗(x	PROPN
ejpam-1949	96	8	)	)	PUNCT
ejpam-1949	96	9	,	,	PUNCT
ejpam-1949	96	10	r	r	X
ejpam-1949	96	11	)	)	PUNCT
ejpam-1949	96	12	be	be	VERB
ejpam-1949	96	13	the	the	DET
ejpam-1949	96	14	map	map	NOUN
ejpam-1949	96	15	defined	define	VERB
ejpam-1949	96	16	by	by	ADP
ejpam-1949	96	17	ϕw(w	ϕw(w	NUM
ejpam-1949	96	18	,	,	PUNCT
ejpam-1949	96	19	ε	ε	PROPN
ejpam-1949	96	20	,	,	PUNCT
ejpam-1949	96	21	g	g	NOUN
ejpam-1949	96	22	)	)	PUNCT
ejpam-1949	96	23	:	:	PUNCT
ejpam-1949	97	1	=	=	PUNCT
ejpam-1949	97	2	∫	∫	PROPN
ejpam-1949	97	3	w	w	PROPN
ejpam-1949	97	4	g∗(w)ch(ε)t	g∗(w)ch(ε)t	PROPN
ejpam-1949	97	5	d(w	d(w	PROPN
ejpam-1949	97	6	)	)	PUNCT
ejpam-1949	97	7	,	,	PUNCT
ejpam-1949	97	8	where	where	SCONJ
ejpam-1949	97	9	ch(ε	ch(ε	NOUN
ejpam-1949	97	10	)	)	PUNCT
ejpam-1949	97	11	is	be	AUX
ejpam-1949	97	12	the	the	DET
ejpam-1949	97	13	chern	chern	ADJ
ejpam-1949	97	14	form	form	NOUN
ejpam-1949	97	15	of	of	ADP
ejpam-1949	97	16	the	the	DET
ejpam-1949	97	17	connection	connection	NOUN
ejpam-1949	98	1	∇ε	∇ε	VERB
ejpam-1949	98	2	on	on	ADP
ejpam-1949	98	3	ε	ε	PROPN
ejpam-1949	98	4	and	and	CCONJ
ejpam-1949	98	5	t	t	PROPN
ejpam-1949	98	6	d(w	d(w	PROPN
ejpam-1949	98	7	)	)	PUNCT
ejpam-1949	98	8	is	be	AUX
ejpam-1949	98	9	the	the	DET
ejpam-1949	98	10	todd	todd	ADJ
ejpam-1949	98	11	form	form	NOUN
ejpam-1949	98	12	of	of	ADP
ejpam-1949	98	13	the	the	DET
ejpam-1949	98	14	tangent	tangent	ADJ
ejpam-1949	98	15	bundle	bundle	NOUN
ejpam-1949	98	16	of	of	ADP
ejpam-1949	98	17	w	w	PROPN
ejpam-1949	98	18	.	.	PUNCT
ejpam-1949	99	1	the	the	DET
ejpam-1949	99	2	set	set	NOUN
ejpam-1949	99	3	of	of	ADP
ejpam-1949	99	4	k	k	NOUN
ejpam-1949	99	5	-	-	PUNCT
ejpam-1949	99	6	periods	period	NOUN
ejpam-1949	99	7	of	of	ADP
ejpam-1949	99	8	a	a	DET
ejpam-1949	99	9	real	real	ADV
ejpam-1949	99	10	-	-	PUNCT
ejpam-1949	99	11	valued	value	VERB
ejpam-1949	99	12	differential	differential	NOUN
ejpam-1949	99	13	form	form	NOUN
ejpam-1949	99	14	w	w	NOUN
ejpam-1949	99	15	∈	∈	NOUN
ejpam-1949	99	16	ω∗(x	ω∗(x	NOUN
ejpam-1949	99	17	)	)	PUNCT
ejpam-1949	99	18	is	be	AUX
ejpam-1949	99	19	the	the	DET
ejpam-1949	99	20	a.	a.	NOUN
ejpam-1949	99	21	elmrabty	elmrabty	NOUN
ejpam-1949	99	22	,	,	PUNCT
ejpam-1949	99	23	m.	m.	NOUN
ejpam-1949	99	24	maghfoul	maghfoul	PROPN
ejpam-1949	99	25	/	/	SYM
ejpam-1949	99	26	eur	eur	PROPN
ejpam-1949	99	27	.	.	PUNCT
ejpam-1949	100	1	j.	j.	PROPN
ejpam-1949	100	2	pure	pure	PROPN
ejpam-1949	100	3	appl	appl	PROPN
ejpam-1949	100	4	.	.	PROPN
ejpam-1949	100	5	math	math	PROPN
ejpam-1949	100	6	,	,	PUNCT
ejpam-1949	100	7	7	7	NUM
ejpam-1949	100	8	(	(	PUNCT
ejpam-1949	100	9	2014	2014	NUM
ejpam-1949	100	10	)	)	PUNCT
ejpam-1949	100	11	,	,	PUNCT
ejpam-1949	100	12	65	65	NUM
ejpam-1949	100	13	-	-	SYM
ejpam-1949	100	14	76	76	NUM
ejpam-1949	100	15	69	69	NUM
ejpam-1949	100	16	subset	subset	NOUN
ejpam-1949	100	17	ϕw(c∗(x	ϕw(c∗(x	NOUN
ejpam-1949	100	18	)	)	PUNCT
ejpam-1949	100	19	)	)	PUNCT
ejpam-1949	100	20	of	of	ADP
ejpam-1949	100	21	r.	r.	PROPN
ejpam-1949	100	22	the	the	DET
ejpam-1949	100	23	abelian	abelian	PROPN
ejpam-1949	100	24	group	group	NOUN
ejpam-1949	100	25	of	of	ADP
ejpam-1949	100	26	closed	closed	ADJ
ejpam-1949	100	27	real	real	ADV
ejpam-1949	100	28	-	-	PUNCT
ejpam-1949	100	29	valued	value	VERB
ejpam-1949	100	30	differential	differential	NOUN
ejpam-1949	100	31	forms	form	NOUN
ejpam-1949	100	32	on	on	ADP
ejpam-1949	100	33	x	x	PUNCT
ejpam-1949	100	34	with	with	ADP
ejpam-1949	100	35	integer	integer	NOUN
ejpam-1949	100	36	k	k	NOUN
ejpam-1949	100	37	-	-	PUNCT
ejpam-1949	100	38	periods	period	NOUN
ejpam-1949	100	39	is	be	AUX
ejpam-1949	100	40	denoted	denote	VERB
ejpam-1949	100	41	by	by	ADP
ejpam-1949	100	42	ω∗0(x	ω∗0(x	PROPN
ejpam-1949	100	43	)	)	PUNCT
ejpam-1949	100	44	.	.	PUNCT
ejpam-1949	101	1	it	it	PRON
ejpam-1949	101	2	has	have	VERB
ejpam-1949	101	3	a	a	DET
ejpam-1949	101	4	natural	natural	ADJ
ejpam-1949	101	5	z2	z2	NOUN
ejpam-1949	101	6	-	-	PUNCT
ejpam-1949	101	7	grading	grading	NOUN
ejpam-1949	101	8	:	:	PUNCT
ejpam-1949	101	9	ω∗0(x	ω∗0(x	PROPN
ejpam-1949	101	10	)	)	PUNCT
ejpam-1949	102	1	=	=	PUNCT
ejpam-1949	102	2	ω	ω	NUM
ejpam-1949	102	3	even	even	ADV
ejpam-1949	102	4	0	0	NUM
ejpam-1949	102	5	(	(	PUNCT
ejpam-1949	102	6	x	x	X
ejpam-1949	102	7	)	)	PUNCT
ejpam-1949	102	8	⊕ωodd	⊕ωodd	NOUN
ejpam-1949	102	9	0	0	NUM
ejpam-1949	102	10	(	(	PUNCT
ejpam-1949	102	11	x	x	NOUN
ejpam-1949	102	12	)	)	PUNCT
ejpam-1949	102	13	.	.	PUNCT
ejpam-1949	103	1	example	example	NOUN
ejpam-1949	104	1	1	1	X
ejpam-1949	104	2	.	.	PUNCT
ejpam-1949	105	1	let	let	VERB
ejpam-1949	105	2	x	x	PRON
ejpam-1949	105	3	be	be	AUX
ejpam-1949	105	4	a	a	DET
ejpam-1949	105	5	smooth	smooth	ADJ
ejpam-1949	105	6	compact	compact	ADJ
ejpam-1949	105	7	manifold	manifold	NOUN
ejpam-1949	105	8	.	.	PUNCT
ejpam-1949	106	1	let	let	VERB
ejpam-1949	106	2	f	f	PRON
ejpam-1949	106	3	be	be	AUX
ejpam-1949	106	4	a	a	DET
ejpam-1949	106	5	hermitian	hermitian	ADJ
ejpam-1949	106	6	vector	vector	NOUN
ejpam-1949	106	7	bundle	bundle	NOUN
ejpam-1949	106	8	over	over	ADP
ejpam-1949	106	9	x	x	PUNCT
ejpam-1949	106	10	with	with	ADP
ejpam-1949	106	11	a	a	DET
ejpam-1949	106	12	hermitian	hermitian	ADJ
ejpam-1949	106	13	connection	connection	NOUN
ejpam-1949	106	14	∇.	∇.	VERB
ejpam-1949	106	15	an	an	DET
ejpam-1949	106	16	example	example	NOUN
ejpam-1949	106	17	of	of	ADP
ejpam-1949	106	18	a	a	DET
ejpam-1949	106	19	form	form	NOUN
ejpam-1949	106	20	with	with	ADP
ejpam-1949	106	21	integer	integer	NOUN
ejpam-1949	106	22	k	k	NOUN
ejpam-1949	106	23	-	-	PUNCT
ejpam-1949	106	24	periods	period	NOUN
ejpam-1949	106	25	is	be	AUX
ejpam-1949	106	26	given	give	VERB
ejpam-1949	106	27	by	by	ADP
ejpam-1949	106	28	the	the	DET
ejpam-1949	106	29	atiyah	atiyah	NOUN
ejpam-1949	106	30	-	-	PUNCT
ejpam-1949	106	31	singer	singer	NOUN
ejpam-1949	106	32	index	index	NOUN
ejpam-1949	106	33	theorem	theorem	NOUN
ejpam-1949	106	34	applied	apply	VERB
ejpam-1949	106	35	to	to	ADP
ejpam-1949	106	36	the	the	DET
ejpam-1949	106	37	positive	positive	ADJ
ejpam-1949	106	38	part	part	NOUN
ejpam-1949	106	39	of	of	ADP
ejpam-1949	106	40	the	the	DET
ejpam-1949	106	41	dirac	dirac	NOUN
ejpam-1949	106	42	operator	operator	NOUN
ejpam-1949	106	43	associated	associate	VERB
ejpam-1949	106	44	to	to	ADP
ejpam-1949	106	45	the	the	DET
ejpam-1949	106	46	spinc	spinc	NOUN
ejpam-1949	106	47	structure	structure	NOUN
ejpam-1949	106	48	on	on	ADP
ejpam-1949	106	49	a	a	DET
ejpam-1949	106	50	spinc	spinc	ADJ
ejpam-1949	106	51	compact	compact	ADJ
ejpam-1949	106	52	manifold	manifold	ADJ
ejpam-1949	106	53	m	m	VERB
ejpam-1949	106	54	in	in	ADP
ejpam-1949	106	55	k	k	NOUN
ejpam-1949	106	56	-	-	NOUN
ejpam-1949	106	57	cycles	cycle	NOUN
ejpam-1949	106	58	(	(	PUNCT
ejpam-1949	106	59	m	m	PROPN
ejpam-1949	106	60	,	,	PUNCT
ejpam-1949	106	61	e	e	PROPN
ejpam-1949	106	62	,	,	PUNCT
ejpam-1949	106	63	f	f	PROPN
ejpam-1949	106	64	)	)	PUNCT
ejpam-1949	106	65	with	with	ADP
ejpam-1949	106	66	coefficients	coefficient	NOUN
ejpam-1949	106	67	in	in	ADP
ejpam-1949	106	68	e⊗	e⊗	PROPN
ejpam-1949	106	69	f	f	PROPN
ejpam-1949	106	70	∗f	∗f	PROPN
ejpam-1949	106	71	:	:	PUNCT
ejpam-1949	107	1	ind([d+(e	ind([d+(e	NUM
ejpam-1949	107	2	⊗	⊗	PROPN
ejpam-1949	107	3	f	f	PROPN
ejpam-1949	107	4	∗f	∗f	PROPN
ejpam-1949	107	5	)	)	PUNCT
ejpam-1949	107	6	]	]	PUNCT
ejpam-1949	107	7	)	)	PUNCT
ejpam-1949	108	1	=	=	SYM
ejpam-1949	109	1	∫	∫	PROPN
ejpam-1949	109	2	m	m	PROPN
ejpam-1949	109	3	f	f	PROPN
ejpam-1949	109	4	∗(ch(∇))ch(e)t	∗(ch(∇))ch(e)t	PROPN
ejpam-1949	109	5	d(m	d(m	PROPN
ejpam-1949	109	6	)	)	PUNCT
ejpam-1949	109	7	∈	∈	PROPN
ejpam-1949	109	8	z.	z.	PROPN
ejpam-1949	109	9	definition	definition	NOUN
ejpam-1949	109	10	4	4	NUM
ejpam-1949	109	11	.	.	PUNCT
ejpam-1949	110	1	(	(	PUNCT
ejpam-1949	110	2	i	i	NOUN
ejpam-1949	110	3	)	)	PUNCT
ejpam-1949	110	4	let	let	VERB
ejpam-1949	110	5	x	x	PRON
ejpam-1949	110	6	be	be	AUX
ejpam-1949	110	7	a	a	DET
ejpam-1949	110	8	smooth	smooth	ADJ
ejpam-1949	110	9	compact	compact	ADJ
ejpam-1949	110	10	manifold	manifold	NOUN
ejpam-1949	110	11	.	.	PUNCT
ejpam-1949	111	1	a	a	DET
ejpam-1949	111	2	differential	differential	ADJ
ejpam-1949	111	3	k	k	NOUN
ejpam-1949	111	4	-	-	NOUN
ejpam-1949	111	5	character	character	NOUN
ejpam-1949	111	6	on	on	ADP
ejpam-1949	111	7	x	x	SYM
ejpam-1949	111	8	is	be	AUX
ejpam-1949	111	9	a	a	DET
ejpam-1949	111	10	homomorphism	homomorphism	NOUN
ejpam-1949	111	11	of	of	ADP
ejpam-1949	111	12	semigroups	semigroup	NOUN
ejpam-1949	111	13	h	h	NOUN
ejpam-1949	111	14	:	:	PUNCT
ejpam-1949	111	15	c∗(x	c∗(x	NOUN
ejpam-1949	111	16	)	)	PUNCT
ejpam-1949	111	17	→	→	SYM
ejpam-1949	111	18	r	r	X
ejpam-1949	111	19	/	/	SYM
ejpam-1949	111	20	z	z	NOUN
ejpam-1949	111	21	such	such	ADJ
ejpam-1949	111	22	that	that	SCONJ
ejpam-1949	111	23	its	its	PRON
ejpam-1949	111	24	restriction	restriction	NOUN
ejpam-1949	111	25	to	to	ADP
ejpam-1949	111	26	the	the	DET
ejpam-1949	111	27	boundaries	boundary	NOUN
ejpam-1949	111	28	is	be	AUX
ejpam-1949	111	29	given	give	VERB
ejpam-1949	111	30	by	by	ADP
ejpam-1949	111	31	the	the	DET
ejpam-1949	111	32	following	follow	VERB
ejpam-1949	111	33	formula	formula	NOUN
ejpam-1949	111	34	:	:	PUNCT
ejpam-1949	111	35	h(∂	h(∂	PROPN
ejpam-1949	111	36	(	(	PUNCT
ejpam-1949	111	37	w	w	PROPN
ejpam-1949	111	38	,	,	PUNCT
ejpam-1949	111	39	ε	ε	PROPN
ejpam-1949	111	40	,	,	PUNCT
ejpam-1949	111	41	g	g	NOUN
ejpam-1949	111	42	)	)	PUNCT
ejpam-1949	111	43	)	)	PUNCT
ejpam-1949	111	44	:	:	PUNCT
ejpam-1949	112	1	=	=	PUNCT
ejpam-1949	112	2	∫	∫	PROPN
ejpam-1949	112	3	w	w	PROPN
ejpam-1949	112	4	g∗(w)ch(ε)t	g∗(w)ch(ε)t	PROPN
ejpam-1949	112	5	d(w	d(w	PROPN
ejpam-1949	112	6	)	)	PUNCT
ejpam-1949	112	7	mod	mod	PROPN
ejpam-1949	113	1	z	z	PROPN
ejpam-1949	113	2	,	,	PUNCT
ejpam-1949	113	3	where	where	SCONJ
ejpam-1949	113	4	w	w	NOUN
ejpam-1949	113	5	is	be	AUX
ejpam-1949	113	6	a	a	DET
ejpam-1949	113	7	closed	closed	ADJ
ejpam-1949	113	8	real	real	ADV
ejpam-1949	113	9	-	-	PUNCT
ejpam-1949	113	10	valued	value	VERB
ejpam-1949	113	11	differential	differential	NOUN
ejpam-1949	113	12	form	form	NOUN
ejpam-1949	113	13	on	on	ADP
ejpam-1949	113	14	x	x	PUNCT
ejpam-1949	113	15	with	with	ADP
ejpam-1949	113	16	integer	integer	PROPN
ejpam-1949	113	17	k	k	NOUN
ejpam-1949	113	18	-	-	PUNCT
ejpam-1949	113	19	periods	period	NOUN
ejpam-1949	113	20	.	.	PUNCT
ejpam-1949	114	1	(	(	PUNCT
ejpam-1949	114	2	ii	ii	NOUN
ejpam-1949	114	3	)	)	PUNCT
ejpam-1949	114	4	the	the	DET
ejpam-1949	114	5	set	set	NOUN
ejpam-1949	114	6	of	of	ADP
ejpam-1949	114	7	differential	differential	ADJ
ejpam-1949	114	8	k	k	NOUN
ejpam-1949	114	9	-	-	NOUN
ejpam-1949	114	10	characters	character	NOUN
ejpam-1949	114	11	on	on	ADP
ejpam-1949	114	12	x	x	VERB
ejpam-1949	114	13	is	be	AUX
ejpam-1949	114	14	denoted	denote	VERB
ejpam-1949	114	15	by	by	ADP
ejpam-1949	114	16	k̂∗(x	k̂∗(x	NOUN
ejpam-1949	114	17	)	)	PUNCT
ejpam-1949	114	18	.	.	PUNCT
ejpam-1949	115	1	it	it	PRON
ejpam-1949	115	2	is	be	AUX
ejpam-1949	115	3	an	an	DET
ejpam-1949	115	4	abelian	abelian	ADJ
ejpam-1949	115	5	group	group	NOUN
ejpam-1949	115	6	which	which	PRON
ejpam-1949	115	7	has	have	VERB
ejpam-1949	115	8	a	a	DET
ejpam-1949	115	9	natural	natural	ADJ
ejpam-1949	115	10	z2	z2	NOUN
ejpam-1949	115	11	-	-	PUNCT
ejpam-1949	115	12	grading	grade	VERB
ejpam-1949	115	13	:	:	PUNCT
ejpam-1949	115	14	k̂∗(x	k̂∗(x	ADJ
ejpam-1949	115	15	)	)	PUNCT
ejpam-1949	115	16	=	=	SYM
ejpam-1949	115	17	k̂0(x	k̂0(x	NOUN
ejpam-1949	115	18	)	)	PUNCT
ejpam-1949	115	19	⊕	⊕	PROPN
ejpam-1949	115	20	k̂1(x	k̂1(x	PROPN
ejpam-1949	115	21	)	)	PUNCT
ejpam-1949	115	22	.	.	PUNCT
ejpam-1949	116	1	the	the	DET
ejpam-1949	116	2	differential	differential	ADJ
ejpam-1949	116	3	form	form	NOUN
ejpam-1949	116	4	w	w	AUX
ejpam-1949	116	5	associated	associate	VERB
ejpam-1949	116	6	to	to	ADP
ejpam-1949	116	7	h	h	NUM
ejpam-1949	116	8	,	,	PUNCT
ejpam-1949	116	9	indicated	indicate	VERB
ejpam-1949	116	10	above	above	ADV
ejpam-1949	116	11	,	,	PUNCT
ejpam-1949	116	12	is	be	AUX
ejpam-1949	116	13	unique	unique	ADJ
ejpam-1949	116	14	.	.	PUNCT
ejpam-1949	117	1	it	it	PRON
ejpam-1949	117	2	will	will	AUX
ejpam-1949	117	3	be	be	AUX
ejpam-1949	117	4	denoted	denote	VERB
ejpam-1949	117	5	by	by	ADP
ejpam-1949	117	6	δ0(h	δ0(h	PROPN
ejpam-1949	117	7	)	)	PUNCT
ejpam-1949	117	8	.	.	PUNCT
ejpam-1949	118	1	thus	thus	ADV
ejpam-1949	118	2	we	we	PRON
ejpam-1949	118	3	have	have	VERB
ejpam-1949	118	4	a	a	DET
ejpam-1949	118	5	homomorphism	homomorphism	NOUN
ejpam-1949	118	6	δ0	δ0	NOUN
ejpam-1949	118	7	:	:	PUNCT
ejpam-1949	118	8	k̂∗(x	k̂∗(x	ADJ
ejpam-1949	118	9	)	)	PUNCT
ejpam-1949	118	10	→	→	SYM
ejpam-1949	118	11	ω∗+1	ω∗+1	NOUN
ejpam-1949	118	12	0	0	PUNCT
ejpam-1949	118	13	(	(	PUNCT
ejpam-1949	118	14	x	x	NOUN
ejpam-1949	118	15	)	)	PUNCT
ejpam-1949	118	16	.	.	PUNCT
ejpam-1949	119	1	note	note	VERB
ejpam-1949	119	2	that	that	SCONJ
ejpam-1949	119	3	a	a	DET
ejpam-1949	119	4	differential	differential	ADJ
ejpam-1949	119	5	form	form	NOUN
ejpam-1949	119	6	v	v	ADP
ejpam-1949	119	7	∈	∈	NOUN
ejpam-1949	119	8	ω∗(x	ω∗(x	NOUN
ejpam-1949	119	9	)	)	PUNCT
ejpam-1949	119	10	determines	determine	VERB
ejpam-1949	119	11	a	a	DET
ejpam-1949	119	12	differential	differential	ADJ
ejpam-1949	119	13	k	k	ADJ
ejpam-1949	119	14	-	-	ADJ
ejpam-1949	119	15	character	character	NOUN
ejpam-1949	119	16	fϕv	fϕv	NOUN
ejpam-1949	119	17	on	on	ADP
ejpam-1949	119	18	x	x	PUNCT
ejpam-1949	119	19	by	by	ADP
ejpam-1949	119	20	setting	set	VERB
ejpam-1949	119	21	fϕv(m	fϕv(m	PROPN
ejpam-1949	119	22	,	,	PUNCT
ejpam-1949	119	23	e	e	PROPN
ejpam-1949	119	24	,	,	PUNCT
ejpam-1949	119	25	f	f	PROPN
ejpam-1949	119	26	)	)	PUNCT
ejpam-1949	119	27	:	:	PUNCT
ejpam-1949	120	1	=	=	PUNCT
ejpam-1949	120	2	∫	∫	PROPN
ejpam-1949	121	1	m	m	PROPN
ejpam-1949	121	2	f	f	PROPN
ejpam-1949	121	3	∗(v)ch(e)t	∗(v)ch(e)t	PROPN
ejpam-1949	121	4	d(m	d(m	PROPN
ejpam-1949	121	5	)	)	PUNCT
ejpam-1949	122	1	mod	mod	PROPN
ejpam-1949	122	2	z.	z.	PROPN
ejpam-1949	122	3	it	it	PRON
ejpam-1949	122	4	is	be	AUX
ejpam-1949	122	5	easy	easy	ADJ
ejpam-1949	122	6	to	to	PART
ejpam-1949	122	7	see	see	VERB
ejpam-1949	122	8	that	that	DET
ejpam-1949	122	9	δ0(fϕv	δ0(fϕv	NOUN
ejpam-1949	122	10	)	)	PUNCT
ejpam-1949	123	1	=	=	SYM
ejpam-1949	123	2	dv	dv	PROPN
ejpam-1949	123	3	.	.	PUNCT
ejpam-1949	124	1	we	we	PRON
ejpam-1949	124	2	can	can	AUX
ejpam-1949	124	3	measure	measure	VERB
ejpam-1949	124	4	the	the	DET
ejpam-1949	124	5	size	size	NOUN
ejpam-1949	124	6	of	of	ADP
ejpam-1949	124	7	k̂∗	k̂∗	NOUN
ejpam-1949	124	8	by	by	ADP
ejpam-1949	124	9	inserting	insert	VERB
ejpam-1949	124	10	it	it	PRON
ejpam-1949	124	11	in	in	ADP
ejpam-1949	124	12	a	a	DET
ejpam-1949	124	13	certain	certain	ADJ
ejpam-1949	124	14	exact	exact	ADJ
ejpam-1949	124	15	sequence	sequence	NOUN
ejpam-1949	124	16	.	.	PUNCT
ejpam-1949	125	1	we	we	PRON
ejpam-1949	125	2	have	have	VERB
ejpam-1949	125	3	the	the	DET
ejpam-1949	125	4	short	short	ADJ
ejpam-1949	125	5	exact	exact	ADJ
ejpam-1949	125	6	sequence	sequence	NOUN
ejpam-1949	125	7	0→	0→	PROPN
ejpam-1949	125	8	hom(k∗(x	hom(k∗(x	ADP
ejpam-1949	125	9	)	)	PUNCT
ejpam-1949	125	10	,	,	PUNCT
ejpam-1949	125	11	r	r	NOUN
ejpam-1949	125	12	/	/	SYM
ejpam-1949	125	13	z	z	NOUN
ejpam-1949	125	14	)	)	PUNCT
ejpam-1949	125	15	,	,	PUNCT
ejpam-1949	125	16	→	→	SYM
ejpam-1949	125	17	k̂∗(x	k̂∗(x	ADJ
ejpam-1949	125	18	)	)	PUNCT
ejpam-1949	125	19	δ0→	δ0→	NOUN
ejpam-1949	125	20	ω∗+1	ω∗+1	NOUN
ejpam-1949	125	21	0	0	PUNCT
ejpam-1949	125	22	(	(	PUNCT
ejpam-1949	125	23	x	x	NOUN
ejpam-1949	125	24	)	)	PUNCT
ejpam-1949	125	25	→	→	SYM
ejpam-1949	125	26	0	0	X
ejpam-1949	125	27	.	.	PUNCT
ejpam-1949	126	1	this	this	PRON
ejpam-1949	126	2	,	,	PUNCT
ejpam-1949	126	3	together	together	ADV
ejpam-1949	126	4	with	with	ADP
ejpam-1949	126	5	the	the	DET
ejpam-1949	126	6	fact	fact	NOUN
ejpam-1949	126	7	that	that	SCONJ
ejpam-1949	126	8	the	the	DET
ejpam-1949	126	9	only	only	ADJ
ejpam-1949	126	10	k	k	NOUN
ejpam-1949	126	11	-	-	NOUN
ejpam-1949	126	12	cycles	cycle	NOUN
ejpam-1949	126	13	on	on	ADP
ejpam-1949	126	14	pt	pt	X
ejpam-1949	126	15	are	be	AUX
ejpam-1949	126	16	(	(	PUNCT
ejpam-1949	126	17	pt	pt	INTJ
ejpam-1949	126	18	,	,	PUNCT
ejpam-1949	126	19	ck	ck	ADJ
ejpam-1949	126	20	,	,	PUNCT
ejpam-1949	126	21	idpt	idpt	NOUN
ejpam-1949	126	22	)	)	PUNCT
ejpam-1949	126	23	,	,	PUNCT
ejpam-1949	126	24	implies	imply	VERB
ejpam-1949	126	25	that	that	SCONJ
ejpam-1949	126	26	k̂0(pt)∼=	k̂0(pt)∼=	NUM
ejpam-1949	126	27	r	r	NOUN
ejpam-1949	126	28	/	/	SYM
ejpam-1949	126	29	z	z	NOUN
ejpam-1949	126	30	and	and	CCONJ
ejpam-1949	126	31	k̂1(pt)∼=	k̂1(pt)∼=	PROPN
ejpam-1949	126	32	z.	z.	PROPN
ejpam-1949	126	33	a.	a.	NOUN
ejpam-1949	126	34	elmrabty	elmrabty	NOUN
ejpam-1949	126	35	,	,	PUNCT
ejpam-1949	126	36	m.	m.	NOUN
ejpam-1949	126	37	maghfoul	maghfoul	PROPN
ejpam-1949	126	38	/	/	SYM
ejpam-1949	126	39	eur	eur	PROPN
ejpam-1949	126	40	.	.	PUNCT
ejpam-1949	127	1	j.	j.	PROPN
ejpam-1949	127	2	pure	pure	PROPN
ejpam-1949	127	3	appl	appl	PROPN
ejpam-1949	127	4	.	.	PROPN
ejpam-1949	127	5	math	math	PROPN
ejpam-1949	127	6	,	,	PUNCT
ejpam-1949	127	7	7	7	NUM
ejpam-1949	127	8	(	(	PUNCT
ejpam-1949	127	9	2014	2014	NUM
ejpam-1949	127	10	)	)	PUNCT
ejpam-1949	127	11	,	,	PUNCT
ejpam-1949	127	12	65	65	NUM
ejpam-1949	127	13	-	-	SYM
ejpam-1949	127	14	76	76	NUM
ejpam-1949	127	15	70	70	NUM
ejpam-1949	127	16	the	the	DET
ejpam-1949	127	17	construction	construction	NOUN
ejpam-1949	127	18	of	of	ADP
ejpam-1949	127	19	k̂∗(x	k̂∗(x	PROPN
ejpam-1949	127	20	)	)	PUNCT
ejpam-1949	127	21	is	be	AUX
ejpam-1949	127	22	functorial	functorial	NOUN
ejpam-1949	127	23	.	.	PUNCT
ejpam-1949	128	1	if	if	SCONJ
ejpam-1949	128	2	ρ	ρ	PROPN
ejpam-1949	128	3	:	:	PUNCT
ejpam-1949	128	4	y	y	PROPN
ejpam-1949	128	5	→	→	PUNCT
ejpam-1949	128	6	x	x	X
ejpam-1949	128	7	is	be	AUX
ejpam-1949	128	8	a	a	DET
ejpam-1949	128	9	smooth	smooth	ADJ
ejpam-1949	128	10	map	map	NOUN
ejpam-1949	128	11	between	between	ADP
ejpam-1949	128	12	two	two	NUM
ejpam-1949	128	13	smooth	smooth	ADJ
ejpam-1949	128	14	compact	compact	ADJ
ejpam-1949	128	15	manifolds	manifold	NOUN
ejpam-1949	128	16	,	,	PUNCT
ejpam-1949	128	17	then	then	ADV
ejpam-1949	128	18	the	the	DET
ejpam-1949	128	19	induced	induced	ADJ
ejpam-1949	128	20	homomorphism	homomorphism	PROPN
ejpam-1949	128	21	ρ∗	ρ∗	PROPN
ejpam-1949	128	22	:	:	PUNCT
ejpam-1949	128	23	k̂∗(x	k̂∗(x	ADJ
ejpam-1949	128	24	)	)	PUNCT
ejpam-1949	128	25	→	→	SYM
ejpam-1949	128	26	k̂∗(y	k̂∗(y	PROPN
ejpam-1949	128	27	)	)	PUNCT
ejpam-1949	128	28	of	of	ADP
ejpam-1949	128	29	z2	z2	NOUN
ejpam-1949	128	30	-	-	PUNCT
ejpam-1949	128	31	graded	grade	VERB
ejpam-1949	128	32	abelian	abelian	ADJ
ejpam-1949	128	33	groups	group	NOUN
ejpam-1949	128	34	is	be	AUX
ejpam-1949	128	35	given	give	VERB
ejpam-1949	128	36	on	on	ADP
ejpam-1949	128	37	differential	differential	ADJ
ejpam-1949	128	38	k	k	NOUN
ejpam-1949	128	39	-	-	NOUN
ejpam-1949	128	40	characters	character	NOUN
ejpam-1949	128	41	on	on	ADP
ejpam-1949	128	42	x	x	PUNCT
ejpam-1949	128	43	by	by	ADP
ejpam-1949	128	44	ρ∗(h)(m	ρ∗(h)(m	NUM
ejpam-1949	128	45	,	,	PUNCT
ejpam-1949	128	46	e	e	PROPN
ejpam-1949	128	47	,	,	PUNCT
ejpam-1949	128	48	f	f	PROPN
ejpam-1949	128	49	)	)	PUNCT
ejpam-1949	128	50	:	:	PUNCT
ejpam-1949	129	1	=	=	SYM
ejpam-1949	129	2	h(ρ∗(m	h(ρ∗(m	NOUN
ejpam-1949	129	3	,	,	PUNCT
ejpam-1949	129	4	e	e	PROPN
ejpam-1949	129	5	,	,	PUNCT
ejpam-1949	129	6	f	f	PROPN
ejpam-1949	129	7	)	)	PUNCT
ejpam-1949	129	8	)	)	PUNCT
ejpam-1949	129	9	for	for	ADP
ejpam-1949	129	10	all	all	PRON
ejpam-1949	129	11	(	(	PUNCT
ejpam-1949	129	12	m	m	PROPN
ejpam-1949	129	13	,	,	PUNCT
ejpam-1949	129	14	e	e	NOUN
ejpam-1949	129	15	,	,	PUNCT
ejpam-1949	129	16	f	f	PROPN
ejpam-1949	129	17	)	)	PUNCT
ejpam-1949	129	18	∈	∈	PROPN
ejpam-1949	129	19	c∗(x	c∗(x	NOUN
ejpam-1949	129	20	)	)	PUNCT
ejpam-1949	129	21	.	.	PUNCT
ejpam-1949	130	1	it	it	PRON
ejpam-1949	130	2	is	be	AUX
ejpam-1949	130	3	obvious	obvious	ADJ
ejpam-1949	130	4	that	that	SCONJ
ejpam-1949	130	5	δ0(ρ∗(h	δ0(ρ∗(h	NOUN
ejpam-1949	130	6	)	)	PUNCT
ejpam-1949	130	7	)	)	PUNCT
ejpam-1949	130	8	=	=	SYM
ejpam-1949	130	9	ρ∗(δ0(h	ρ∗(δ0(h	X
ejpam-1949	130	10	)	)	PUNCT
ejpam-1949	130	11	)	)	PUNCT
ejpam-1949	130	12	.	.	PUNCT
ejpam-1949	131	1	let	let	VERB
ejpam-1949	131	2	x	x	PRON
ejpam-1949	131	3	be	be	AUX
ejpam-1949	131	4	a	a	DET
ejpam-1949	131	5	smooth	smooth	ADJ
ejpam-1949	131	6	compact	compact	ADJ
ejpam-1949	131	7	manifold	manifold	NOUN
ejpam-1949	131	8	.	.	PUNCT
ejpam-1949	132	1	let	let	VERB
ejpam-1949	132	2	i	i	PRON
ejpam-1949	132	3	be	be	AUX
ejpam-1949	132	4	the	the	DET
ejpam-1949	132	5	inclusion	inclusion	NOUN
ejpam-1949	132	6	pt	pt	NOUN
ejpam-1949	132	7	,	,	PUNCT
ejpam-1949	132	8	→	→	SYM
ejpam-1949	132	9	x	x	X
ejpam-1949	132	10	.	.	PUNCT
ejpam-1949	133	1	set	set	VERB
ejpam-1949	133	2	k̃∗(x	k̃∗(x	ADV
ejpam-1949	133	3	)	)	PUNCT
ejpam-1949	133	4	:	:	PUNCT
ejpam-1949	133	5	=	=	SYM
ejpam-1949	133	6	ker[k̂∗(x	ker[k̂∗(x	NOUN
ejpam-1949	133	7	)	)	PUNCT
ejpam-1949	133	8	i∗→	i∗→	PUNCT
ejpam-1949	134	1	k̂∗(pt	k̂∗(pt	PROPN
ejpam-1949	134	2	)	)	PUNCT
ejpam-1949	134	3	]	]	PUNCT
ejpam-1949	134	4	.	.	PUNCT
ejpam-1949	135	1	since	since	SCONJ
ejpam-1949	135	2	the	the	DET
ejpam-1949	135	3	short	short	ADJ
ejpam-1949	135	4	exact	exact	ADJ
ejpam-1949	135	5	sequence	sequence	NOUN
ejpam-1949	135	6	0→	0→	NOUN
ejpam-1949	135	7	k̃∗(x	k̃∗(x	NOUN
ejpam-1949	135	8	)	)	PUNCT
ejpam-1949	135	9	,	,	PUNCT
ejpam-1949	135	10	→	→	SYM
ejpam-1949	135	11	k̂∗(x	k̂∗(x	X
ejpam-1949	135	12	)	)	PUNCT
ejpam-1949	135	13	i∗→	i∗→	PROPN
ejpam-1949	136	1	k̂∗(pt)→	k̂∗(pt)→	NOUN
ejpam-1949	136	2	0	0	NUM
ejpam-1949	136	3	is	be	AUX
ejpam-1949	136	4	split	split	VERB
ejpam-1949	136	5	,	,	PUNCT
ejpam-1949	136	6	we	we	PRON
ejpam-1949	136	7	obtain	obtain	VERB
ejpam-1949	136	8	isomorphisms	isomorphisms	PROPN
ejpam-1949	136	9	k̂0(x	k̂0(x	NOUN
ejpam-1949	136	10	)	)	PUNCT
ejpam-1949	136	11	∼=	∼=	PROPN
ejpam-1949	136	12	k̃0(x	k̃0(x	NOUN
ejpam-1949	136	13	)	)	PUNCT
ejpam-1949	136	14	⊕r	⊕r	NOUN
ejpam-1949	136	15	/	/	SYM
ejpam-1949	136	16	z	z	PROPN
ejpam-1949	136	17	and	and	CCONJ
ejpam-1949	136	18	k̂1(x	k̂1(x	NOUN
ejpam-1949	136	19	)	)	PUNCT
ejpam-1949	136	20	∼=	∼=	PROPN
ejpam-1949	136	21	k̃1(x	k̃1(x	NOUN
ejpam-1949	136	22	)	)	PUNCT
ejpam-1949	136	23	⊕z	⊕z	NOUN
ejpam-1949	136	24	.	.	PUNCT
ejpam-1949	137	1	3	3	X
ejpam-1949	137	2	.	.	X
ejpam-1949	137	3	relative	relative	ADJ
ejpam-1949	137	4	differential	differential	PROPN
ejpam-1949	137	5	k	k	NOUN
ejpam-1949	137	6	-	-	NOUN
ejpam-1949	137	7	theory	theory	NOUN
ejpam-1949	137	8	in	in	ADP
ejpam-1949	137	9	this	this	DET
ejpam-1949	137	10	section	section	NOUN
ejpam-1949	137	11	,	,	PUNCT
ejpam-1949	137	12	we	we	PRON
ejpam-1949	137	13	define	define	VERB
ejpam-1949	137	14	the	the	DET
ejpam-1949	137	15	relative	relative	ADJ
ejpam-1949	137	16	differential	differential	NOUN
ejpam-1949	137	17	k	k	NOUN
ejpam-1949	137	18	-	-	NOUN
ejpam-1949	137	19	theory	theory	NOUN
ejpam-1949	137	20	of	of	ADP
ejpam-1949	137	21	a	a	DET
ejpam-1949	137	22	smooth	smooth	ADJ
ejpam-1949	137	23	map	map	NOUN
ejpam-1949	137	24	between	between	ADP
ejpam-1949	137	25	two	two	NUM
ejpam-1949	137	26	smooth	smooth	ADJ
ejpam-1949	137	27	compact	compact	ADJ
ejpam-1949	137	28	manifolds	manifold	NOUN
ejpam-1949	137	29	and	and	CCONJ
ejpam-1949	137	30	show	show	VERB
ejpam-1949	137	31	that	that	SCONJ
ejpam-1949	137	32	it	it	PRON
ejpam-1949	137	33	fits	fit	VERB
ejpam-1949	137	34	into	into	ADP
ejpam-1949	137	35	a	a	DET
ejpam-1949	137	36	six	six	NUM
ejpam-1949	137	37	-	-	PUNCT
ejpam-1949	137	38	term	term	NOUN
ejpam-1949	137	39	exact	exact	ADJ
ejpam-1949	137	40	sequence	sequence	NOUN
ejpam-1949	137	41	.	.	PUNCT
ejpam-1949	138	1	let	let	VERB
ejpam-1949	138	2	x	x	PRON
ejpam-1949	138	3	be	be	AUX
ejpam-1949	138	4	a	a	DET
ejpam-1949	138	5	smooth	smooth	ADJ
ejpam-1949	138	6	compact	compact	ADJ
ejpam-1949	138	7	manifold	manifold	NOUN
ejpam-1949	138	8	.	.	PUNCT
ejpam-1949	139	1	let	let	VERB
ejpam-1949	139	2	a⊆	a⊆	VERB
ejpam-1949	139	3	r	r	NOUN
ejpam-1949	139	4	be	be	AUX
ejpam-1949	139	5	a	a	DET
ejpam-1949	139	6	subring	subring	NOUN
ejpam-1949	139	7	of	of	ADP
ejpam-1949	139	8	the	the	DET
ejpam-1949	139	9	reals	real	NOUN
ejpam-1949	139	10	.	.	PUNCT
ejpam-1949	140	1	a	a	DET
ejpam-1949	140	2	k	k	NOUN
ejpam-1949	140	3	-	-	NOUN
ejpam-1949	140	4	cochain	cochain	NOUN
ejpam-1949	140	5	over	over	ADP
ejpam-1949	140	6	x	x	PUNCT
ejpam-1949	140	7	with	with	ADP
ejpam-1949	140	8	coefficients	coefficient	NOUN
ejpam-1949	140	9	in	in	ADP
ejpam-1949	140	10	a	a	PRON
ejpam-1949	140	11	is	be	AUX
ejpam-1949	140	12	a	a	DET
ejpam-1949	140	13	semigroup	semigroup	ADJ
ejpam-1949	140	14	homomorphism	homomorphism	NOUN
ejpam-1949	140	15	from	from	ADP
ejpam-1949	140	16	l∗(x	l∗(x	ADV
ejpam-1949	140	17	)	)	PUNCT
ejpam-1949	140	18	to	to	PART
ejpam-1949	140	19	a.	a.	VERB
ejpam-1949	140	20	the	the	DET
ejpam-1949	140	21	set	set	NOUN
ejpam-1949	140	22	of	of	ADP
ejpam-1949	140	23	k	k	PROPN
ejpam-1949	140	24	-	-	PUNCT
ejpam-1949	140	25	cochains	cochain	NOUN
ejpam-1949	140	26	over	over	ADP
ejpam-1949	140	27	x	x	PUNCT
ejpam-1949	140	28	with	with	SCONJ
ejpam-1949	140	29	coefficients	coefficient	NOUN
ejpam-1949	140	30	in	in	ADP
ejpam-1949	140	31	a	a	PRON
ejpam-1949	140	32	is	be	AUX
ejpam-1949	140	33	denoted	denote	VERB
ejpam-1949	140	34	by	by	ADP
ejpam-1949	140	35	l∗(x	l∗(x	PROPN
ejpam-1949	140	36	,	,	PUNCT
ejpam-1949	140	37	a	a	PRON
ejpam-1949	140	38	)	)	PUNCT
ejpam-1949	140	39	.	.	PUNCT
ejpam-1949	141	1	the	the	DET
ejpam-1949	141	2	set	set	NOUN
ejpam-1949	141	3	l∗(x	l∗(x	ADP
ejpam-1949	141	4	,	,	PUNCT
ejpam-1949	141	5	a	a	PRON
ejpam-1949	141	6	)	)	PUNCT
ejpam-1949	141	7	is	be	AUX
ejpam-1949	141	8	an	an	DET
ejpam-1949	141	9	abelian	abelian	ADJ
ejpam-1949	141	10	group	group	NOUN
ejpam-1949	141	11	and	and	CCONJ
ejpam-1949	141	12	a	a	DET
ejpam-1949	141	13	coboundary	coboundary	ADJ
ejpam-1949	141	14	map	map	NOUN
ejpam-1949	141	15	on	on	ADP
ejpam-1949	141	16	l∗(x	l∗(x	ADP
ejpam-1949	141	17	,	,	PUNCT
ejpam-1949	141	18	a	a	PRON
ejpam-1949	141	19	)	)	PUNCT
ejpam-1949	141	20	is	be	AUX
ejpam-1949	141	21	defined	define	VERB
ejpam-1949	141	22	by	by	ADP
ejpam-1949	141	23	transposition	transposition	NOUN
ejpam-1949	141	24	:	:	PUNCT
ejpam-1949	141	25	δh(w	δh(w	NUM
ejpam-1949	141	26	,	,	PUNCT
ejpam-1949	141	27	ε	ε	PROPN
ejpam-1949	141	28	,	,	PUNCT
ejpam-1949	141	29	g	g	NOUN
ejpam-1949	141	30	)	)	PUNCT
ejpam-1949	141	31	:	:	PUNCT
ejpam-1949	142	1	=	=	SYM
ejpam-1949	142	2	h(∂	h(∂	PROPN
ejpam-1949	142	3	(	(	PUNCT
ejpam-1949	142	4	w	w	PROPN
ejpam-1949	142	5	,	,	PUNCT
ejpam-1949	142	6	ε	ε	PROPN
ejpam-1949	142	7	,	,	PUNCT
ejpam-1949	142	8	g	g	NOUN
ejpam-1949	142	9	)	)	PUNCT
ejpam-1949	142	10	)	)	PUNCT
ejpam-1949	142	11	.	.	PUNCT
ejpam-1949	143	1	we	we	PRON
ejpam-1949	143	2	set	set	VERB
ejpam-1949	143	3	ľ∗(x	ľ∗(x	X
ejpam-1949	143	4	)	)	PUNCT
ejpam-1949	144	1	=	=	SYM
ejpam-1949	144	2	l∗(x	l∗(x	PROPN
ejpam-1949	144	3	,	,	PUNCT
ejpam-1949	144	4	z)×	z)×	NUM
ejpam-1949	144	5	l∗−1(x	l∗−1(x	NOUN
ejpam-1949	144	6	,	,	PUNCT
ejpam-1949	144	7	r)×ω∗0(x	r)×ω∗0(x	PROPN
ejpam-1949	144	8	)	)	PUNCT
ejpam-1949	144	9	,	,	PUNCT
ejpam-1949	144	10	and	and	CCONJ
ejpam-1949	144	11	define	define	VERB
ejpam-1949	144	12	a	a	DET
ejpam-1949	144	13	coboundary	coboundary	ADJ
ejpam-1949	144	14	map	map	NOUN
ejpam-1949	144	15	δ̂	δ̂	NOUN
ejpam-1949	144	16	:	:	PUNCT
ejpam-1949	144	17	ľ∗(x	ľ∗(x	NUM
ejpam-1949	144	18	)	)	PUNCT
ejpam-1949	144	19	→	→	SYM
ejpam-1949	144	20	ľ∗+1(x	ľ∗+1(x	PROPN
ejpam-1949	144	21	)	)	PUNCT
ejpam-1949	144	22	by	by	ADP
ejpam-1949	144	23	the	the	DET
ejpam-1949	144	24	formula	formula	NOUN
ejpam-1949	144	25	:	:	PUNCT
ejpam-1949	144	26	δ̂(c	δ̂(c	ADJ
ejpam-1949	144	27	,	,	PUNCT
ejpam-1949	144	28	h	h	NOUN
ejpam-1949	144	29	,	,	PUNCT
ejpam-1949	144	30	w	w	PROPN
ejpam-1949	144	31	)	)	PUNCT
ejpam-1949	144	32	:	:	PUNCT
ejpam-1949	144	33	=	=	SYM
ejpam-1949	144	34	(	(	PUNCT
ejpam-1949	144	35	−δc,−ϕw	−δc,−ϕw	NOUN
ejpam-1949	144	36	+	+	CCONJ
ejpam-1949	144	37	c+δh	c+δh	NOUN
ejpam-1949	144	38	,	,	PUNCT
ejpam-1949	144	39	0	0	NUM
ejpam-1949	144	40	)	)	PUNCT
ejpam-1949	144	41	.	.	PUNCT
ejpam-1949	145	1	let	let	VERB
ejpam-1949	145	2	ρ	ρ	NOUN
ejpam-1949	145	3	:	:	PUNCT
ejpam-1949	145	4	y	y	PROPN
ejpam-1949	145	5	→	→	PUNCT
ejpam-1949	145	6	x	x	PUNCT
ejpam-1949	145	7	be	be	AUX
ejpam-1949	145	8	a	a	DET
ejpam-1949	145	9	smooth	smooth	ADJ
ejpam-1949	145	10	map	map	NOUN
ejpam-1949	145	11	between	between	ADP
ejpam-1949	145	12	two	two	NUM
ejpam-1949	145	13	smooth	smooth	ADJ
ejpam-1949	145	14	compact	compact	ADJ
ejpam-1949	145	15	manifolds	manifold	NOUN
ejpam-1949	145	16	.	.	PUNCT
ejpam-1949	146	1	we	we	PRON
ejpam-1949	146	2	define	define	VERB
ejpam-1949	146	3	the	the	DET
ejpam-1949	146	4	set	set	NOUN
ejpam-1949	146	5	of	of	ADP
ejpam-1949	146	6	relative	relative	ADJ
ejpam-1949	146	7	k	k	PROPN
ejpam-1949	146	8	-	-	PUNCT
ejpam-1949	146	9	cochains	cochain	NOUN
ejpam-1949	146	10	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	146	11	)	)	PUNCT
ejpam-1949	146	12	as	as	ADP
ejpam-1949	146	13	the	the	DET
ejpam-1949	146	14	direct	direct	ADJ
ejpam-1949	146	15	product	product	NOUN
ejpam-1949	146	16	ľ∗(x	ľ∗(x	X
ejpam-1949	146	17	)	)	PUNCT
ejpam-1949	146	18	×	×	PROPN
ejpam-1949	146	19	ľ∗−1(y	ľ∗−1(y	PROPN
ejpam-1949	146	20	)	)	PUNCT
ejpam-1949	146	21	.	.	PUNCT
ejpam-1949	147	1	a	a	DET
ejpam-1949	147	2	coboundary	coboundary	ADJ
ejpam-1949	147	3	map	map	NOUN
ejpam-1949	147	4	δ̌	δ̌	X
ejpam-1949	147	5	:	:	PUNCT
ejpam-1949	147	6	ľ∗(ρ)→	ľ∗(ρ)→	PROPN
ejpam-1949	147	7	ľ∗+1(ρ	ľ∗+1(ρ	PROPN
ejpam-1949	147	8	)	)	PUNCT
ejpam-1949	147	9	is	be	AUX
ejpam-1949	147	10	given	give	VERB
ejpam-1949	147	11	by	by	ADP
ejpam-1949	147	12	setting	set	VERB
ejpam-1949	147	13	δ̌(s	δ̌(s	NOUN
ejpam-1949	147	14	,	,	PUNCT
ejpam-1949	147	15	t	t	PROPN
ejpam-1949	147	16	)	)	PUNCT
ejpam-1949	147	17	:	:	PUNCT
ejpam-1949	148	1	=	=	SYM
ejpam-1949	148	2	(	(	PUNCT
ejpam-1949	148	3	δ̂s	δ̂s	PROPN
ejpam-1949	148	4	,	,	PUNCT
ejpam-1949	148	5	ρ∗s−	ρ∗s−	NUM
ejpam-1949	148	6	δ̂t	δ̂t	X
ejpam-1949	148	7	)	)	PUNCT
ejpam-1949	148	8	.	.	PUNCT
ejpam-1949	149	1	elements	element	NOUN
ejpam-1949	149	2	of	of	ADP
ejpam-1949	149	3	ker	ker	PROPN
ejpam-1949	149	4	[	[	PUNCT
ejpam-1949	149	5	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	149	6	)	)	PUNCT
ejpam-1949	149	7	δ̌→	δ̌→	NOUN
ejpam-1949	149	8	ľ∗+1(ρ	ľ∗+1(ρ	PROPN
ejpam-1949	149	9	)	)	PUNCT
ejpam-1949	149	10	]	]	PUNCT
ejpam-1949	149	11	are	be	AUX
ejpam-1949	149	12	called	call	VERB
ejpam-1949	149	13	k	k	NOUN
ejpam-1949	149	14	-	-	NOUN
ejpam-1949	149	15	cocycles	cocycle	NOUN
ejpam-1949	149	16	and	and	CCONJ
ejpam-1949	149	17	those	those	PRON
ejpam-1949	149	18	of	of	ADP
ejpam-1949	149	19	img	img	PROPN
ejpam-1949	149	20	[	[	PUNCT
ejpam-1949	149	21	ľ∗−1(ρ	ľ∗−1(ρ	PROPN
ejpam-1949	149	22	)	)	PUNCT
ejpam-1949	149	23	δ̌→	δ̌→	NOUN
ejpam-1949	149	24	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	149	25	)	)	PUNCT
ejpam-1949	149	26	]	]	PUNCT
ejpam-1949	149	27	are	be	AUX
ejpam-1949	149	28	called	call	VERB
ejpam-1949	149	29	k	k	NOUN
ejpam-1949	149	30	-	-	NOUN
ejpam-1949	149	31	coboundaries	coboundarie	NOUN
ejpam-1949	149	32	.	.	PUNCT
ejpam-1949	150	1	let	let	AUX
ejpam-1949	150	2	ž∗(ρ	ž∗(ρ	NUM
ejpam-1949	150	3	)	)	PUNCT
ejpam-1949	150	4	be	be	AUX
ejpam-1949	150	5	the	the	DET
ejpam-1949	150	6	set	set	NOUN
ejpam-1949	150	7	of	of	ADP
ejpam-1949	150	8	k	k	NOUN
ejpam-1949	150	9	-	-	NOUN
ejpam-1949	150	10	cocycles	cocycle	NOUN
ejpam-1949	150	11	and	and	CCONJ
ejpam-1949	150	12	b̌∗(ρ	b̌∗(ρ	NUM
ejpam-1949	150	13	)	)	PUNCT
ejpam-1949	150	14	the	the	DET
ejpam-1949	150	15	set	set	NOUN
ejpam-1949	150	16	of	of	ADP
ejpam-1949	150	17	k	k	NOUN
ejpam-1949	150	18	-	-	NOUN
ejpam-1949	150	19	coboundaries	coboundarie	NOUN
ejpam-1949	150	20	.	.	PUNCT
ejpam-1949	151	1	a.	a.	NOUN
ejpam-1949	151	2	elmrabty	elmrabty	NOUN
ejpam-1949	151	3	,	,	PUNCT
ejpam-1949	151	4	m.	m.	NOUN
ejpam-1949	151	5	maghfoul	maghfoul	PROPN
ejpam-1949	151	6	/	/	SYM
ejpam-1949	151	7	eur	eur	PROPN
ejpam-1949	151	8	.	.	PUNCT
ejpam-1949	152	1	j.	j.	PROPN
ejpam-1949	152	2	pure	pure	PROPN
ejpam-1949	152	3	appl	appl	PROPN
ejpam-1949	152	4	.	.	PROPN
ejpam-1949	152	5	math	math	PROPN
ejpam-1949	152	6	,	,	PUNCT
ejpam-1949	152	7	7	7	NUM
ejpam-1949	152	8	(	(	PUNCT
ejpam-1949	152	9	2014	2014	NUM
ejpam-1949	152	10	)	)	PUNCT
ejpam-1949	152	11	,	,	PUNCT
ejpam-1949	152	12	65	65	NUM
ejpam-1949	152	13	-	-	SYM
ejpam-1949	152	14	76	76	NUM
ejpam-1949	152	15	71	71	NUM
ejpam-1949	152	16	definition	definition	NOUN
ejpam-1949	152	17	5	5	NUM
ejpam-1949	152	18	.	.	PUNCT
ejpam-1949	153	1	we	we	PRON
ejpam-1949	153	2	define	define	VERB
ejpam-1949	153	3	the	the	DET
ejpam-1949	153	4	relative	relative	ADJ
ejpam-1949	153	5	differential	differential	NOUN
ejpam-1949	153	6	k	k	PROPN
ejpam-1949	153	7	-	-	ADJ
ejpam-1949	153	8	theory	theory	NOUN
ejpam-1949	153	9	group	group	NOUN
ejpam-1949	153	10	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	153	11	)	)	PUNCT
ejpam-1949	153	12	as	as	ADP
ejpam-1949	153	13	the	the	DET
ejpam-1949	153	14	quotient	quotient	NOUN
ejpam-1949	153	15	group	group	NOUN
ejpam-1949	153	16	ž∗(ρ)/b̌∗(ρ	ž∗(ρ)/b̌∗(ρ	NOUN
ejpam-1949	153	17	)	)	PUNCT
ejpam-1949	153	18	.	.	PUNCT
ejpam-1949	154	1	the	the	DET
ejpam-1949	154	2	construction	construction	NOUN
ejpam-1949	154	3	of	of	ADP
ejpam-1949	154	4	relative	relative	ADJ
ejpam-1949	154	5	differential	differential	NOUN
ejpam-1949	154	6	k	k	NOUN
ejpam-1949	154	7	-	-	NOUN
ejpam-1949	154	8	theory	theory	NOUN
ejpam-1949	154	9	is	be	AUX
ejpam-1949	154	10	functorial	functorial	NOUN
ejpam-1949	154	11	.	.	PUNCT
ejpam-1949	155	1	if	if	SCONJ
ejpam-1949	155	2	y	y	PROPN
ejpam-1949	155	3	′	′	PROPN
ejpam-1949	155	4	ρ′	ρ′	PUNCT
ejpam-1949	155	5	//	//	SYM
ejpam-1949	155	6	g	g	PROPN
ejpam-1949	155	7	�	�	PROPN
ejpam-1949	155	8	�	�	PROPN
ejpam-1949	155	9	�	�	PROPN
ejpam-1949	155	10	x	x	SYM
ejpam-1949	155	11	′	′	NUM
ejpam-1949	155	12	f	f	PROPN
ejpam-1949	155	13	�	�	PROPN
ejpam-1949	155	14	�	�	PROPN
ejpam-1949	155	15	y	y	PROPN
ejpam-1949	155	16	ρ	ρ	PROPN
ejpam-1949	155	17	//	//	PROPN
ejpam-1949	155	18	x	x	PROPN
ejpam-1949	155	19	is	be	AUX
ejpam-1949	155	20	a	a	DET
ejpam-1949	155	21	commutative	commutative	ADJ
ejpam-1949	155	22	diagram	diagram	NOUN
ejpam-1949	155	23	of	of	ADP
ejpam-1949	155	24	smooth	smooth	ADJ
ejpam-1949	155	25	maps	map	NOUN
ejpam-1949	155	26	between	between	ADP
ejpam-1949	155	27	smooth	smooth	ADJ
ejpam-1949	155	28	compact	compact	ADJ
ejpam-1949	155	29	manifolds	manifold	NOUN
ejpam-1949	155	30	,	,	PUNCT
ejpam-1949	155	31	then	then	ADV
ejpam-1949	155	32	the	the	DET
ejpam-1949	155	33	homomorphism	homomorphism	NOUN
ejpam-1949	155	34	(	(	PUNCT
ejpam-1949	155	35	f	f	X
ejpam-1949	155	36	,	,	PUNCT
ejpam-1949	155	37	g)∗	g)∗	PROPN
ejpam-1949	155	38	:	:	PUNCT
ejpam-1949	155	39	ǩ∗(ρ)→	ǩ∗(ρ)→	PROPN
ejpam-1949	155	40	ǩ∗(ρ′	ǩ∗(ρ′	PROPN
ejpam-1949	155	41	)	)	PUNCT
ejpam-1949	155	42	of	of	ADP
ejpam-1949	155	43	z2	z2	NOUN
ejpam-1949	155	44	-	-	PUNCT
ejpam-1949	155	45	graded	grade	VERB
ejpam-1949	155	46	abelian	abelian	ADJ
ejpam-1949	155	47	groups	group	NOUN
ejpam-1949	155	48	is	be	AUX
ejpam-1949	155	49	given	give	VERB
ejpam-1949	155	50	on	on	ADP
ejpam-1949	155	51	classes	class	NOUN
ejpam-1949	155	52	of	of	ADP
ejpam-1949	155	53	k	k	NOUN
ejpam-1949	155	54	-	-	NOUN
ejpam-1949	155	55	cocycles	cocycle	NOUN
ejpam-1949	155	56	[	[	X
ejpam-1949	155	57	s	s	X
ejpam-1949	155	58	,	,	PUNCT
ejpam-1949	155	59	t	t	PROPN
ejpam-1949	155	60	]	]	PUNCT
ejpam-1949	155	61	∈	∈	PROPN
ejpam-1949	155	62	ǩ∗(ρ′	ǩ∗(ρ′	PROPN
ejpam-1949	155	63	)	)	PUNCT
ejpam-1949	155	64	by	by	ADP
ejpam-1949	155	65	(	(	PUNCT
ejpam-1949	155	66	f	f	PROPN
ejpam-1949	155	67	,	,	PUNCT
ejpam-1949	155	68	g)∗([s	g)∗([s	PROPN
ejpam-1949	155	69	,	,	PUNCT
ejpam-1949	155	70	t	t	PROPN
ejpam-1949	155	71	]	]	PUNCT
ejpam-1949	155	72	)	)	PUNCT
ejpam-1949	155	73	:	:	PUNCT
ejpam-1949	156	1	=	=	PUNCT
ejpam-1949	156	2	[	[	PUNCT
ejpam-1949	156	3	f	f	X
ejpam-1949	156	4	∗s	∗s	PROPN
ejpam-1949	156	5	,	,	PUNCT
ejpam-1949	156	6	g∗t	g∗t	NOUN
ejpam-1949	156	7	]	]	X
ejpam-1949	156	8	.	.	PUNCT
ejpam-1949	157	1	exact	exact	ADJ
ejpam-1949	157	2	sequence	sequence	NOUN
ejpam-1949	157	3	let	let	VERB
ejpam-1949	157	4	(	(	PUNCT
ejpam-1949	157	5	s	s	X
ejpam-1949	157	6	,	,	PUNCT
ejpam-1949	157	7	t	t	NOUN
ejpam-1949	157	8	)	)	PUNCT
ejpam-1949	157	9	∈	∈	PROPN
ejpam-1949	157	10	ž∗(ρ	ž∗(ρ	NUM
ejpam-1949	157	11	)	)	PUNCT
ejpam-1949	157	12	.	.	PUNCT
ejpam-1949	158	1	if	if	SCONJ
ejpam-1949	158	2	we	we	PRON
ejpam-1949	158	3	set	set	VERB
ejpam-1949	158	4	s	s	VERB
ejpam-1949	158	5	=	=	PUNCT
ejpam-1949	158	6	(	(	PUNCT
ejpam-1949	158	7	cx	cx	PROPN
ejpam-1949	158	8	,	,	PUNCT
ejpam-1949	158	9	hx	hx	PROPN
ejpam-1949	158	10	,	,	PUNCT
ejpam-1949	158	11	wx	wx	PROPN
ejpam-1949	158	12	)	)	PUNCT
ejpam-1949	158	13	and	and	CCONJ
ejpam-1949	158	14	t	t	NOUN
ejpam-1949	158	15	=	=	SYM
ejpam-1949	158	16	(	(	PUNCT
ejpam-1949	158	17	cy	cy	PROPN
ejpam-1949	158	18	,	,	PUNCT
ejpam-1949	158	19	hy	hy	PROPN
ejpam-1949	158	20	,	,	PUNCT
ejpam-1949	158	21	w	w	PROPN
ejpam-1949	158	22	y	y	PROPN
ejpam-1949	158	23	)	)	PUNCT
ejpam-1949	158	24	,	,	PUNCT
ejpam-1949	158	25	then	then	ADV
ejpam-1949	158	26	the	the	DET
ejpam-1949	158	27	equality	equality	NOUN
ejpam-1949	158	28	δ̌(s	δ̌(s	NOUN
ejpam-1949	158	29	,	,	PUNCT
ejpam-1949	158	30	t	t	NOUN
ejpam-1949	158	31	)	)	PUNCT
ejpam-1949	159	1	=	=	SYM
ejpam-1949	159	2	0	0	NUM
ejpam-1949	159	3	implies	imply	VERB
ejpam-1949	159	4	that	that	SCONJ
ejpam-1949	159	5	:	:	PUNCT
ejpam-1949	159	6	¨	¨	NOUN
ejpam-1949	159	7	δcx	δcx	X
ejpam-1949	159	8	=	=	SYM
ejpam-1949	159	9	0	0	NUM
ejpam-1949	159	10	ϕwx	ϕwx	NOUN
ejpam-1949	160	1	=	=	PRON
ejpam-1949	160	2	δhx	δhx	PROPN
ejpam-1949	160	3	+	+	CCONJ
ejpam-1949	161	1	cx	cx	PROPN
ejpam-1949	162	1	and	and	CCONJ
ejpam-1949	162	2			VERB
ejpam-1949	162	3			PROPN
ejpam-1949	162	4			NOUN
ejpam-1949	162	5	ρ∗cx	ρ∗cx	PROPN
ejpam-1949	163	1	=	=	NOUN
ejpam-1949	164	1	−δcy	−δcy	X
ejpam-1949	164	2	ρ∗hx	ρ∗hx	NOUN
ejpam-1949	164	3	=	=	NOUN
ejpam-1949	164	4	−ϕw	−ϕw	NOUN
ejpam-1949	164	5	y	y	PROPN
ejpam-1949	164	6	+	+	PROPN
ejpam-1949	164	7	δhy	δhy	NOUN
ejpam-1949	164	8	+	+	X
ejpam-1949	164	9	cy	cy	ADP
ejpam-1949	164	10	ρ∗wx	ρ∗wx	NOUN
ejpam-1949	164	11	=	=	PUNCT
ejpam-1949	164	12	0	0	NUM
ejpam-1949	165	1	it	it	PRON
ejpam-1949	165	2	follows	follow	VERB
ejpam-1949	165	3	that	that	SCONJ
ejpam-1949	165	4	the	the	DET
ejpam-1949	165	5	natural	natural	ADJ
ejpam-1949	165	6	homomorphism	homomorphism	NOUN
ejpam-1949	165	7	r	r	NOUN
ejpam-1949	165	8	∼→	∼→	PROPN
ejpam-1949	165	9	r	r	NOUN
ejpam-1949	165	10	/	/	SYM
ejpam-1949	165	11	z	z	PROPN
ejpam-1949	165	12	composed	compose	VERB
ejpam-1949	165	13	with	with	ADP
ejpam-1949	165	14	the	the	DET
ejpam-1949	165	15	restriction	restriction	NOUN
ejpam-1949	165	16	of	of	ADP
ejpam-1949	165	17	hx	hx	PROPN
ejpam-1949	165	18	to	to	ADP
ejpam-1949	165	19	c∗−1(x	c∗−1(x	PROPN
ejpam-1949	165	20	)	)	PUNCT
ejpam-1949	165	21	,	,	PUNCT
ejpam-1949	165	22	denoted	denote	VERB
ejpam-1949	165	23	by	by	ADP
ejpam-1949	165	24	hx	hx	PROPN
ejpam-1949	165	25	,	,	PUNCT
ejpam-1949	165	26	is	be	AUX
ejpam-1949	165	27	a	a	DET
ejpam-1949	165	28	differential	differential	ADJ
ejpam-1949	165	29	k	k	NOUN
ejpam-1949	165	30	-	-	NOUN
ejpam-1949	165	31	character	character	NOUN
ejpam-1949	165	32	on	on	ADP
ejpam-1949	165	33	x	x	X
ejpam-1949	165	34	.	.	PUNCT
ejpam-1949	166	1	let	let	VERB
ejpam-1949	166	2	j	j	NOUN
ejpam-1949	166	3	:	:	PUNCT
ejpam-1949	166	4	ž∗(ρ	ž∗(ρ	NUM
ejpam-1949	166	5	)	)	PUNCT
ejpam-1949	166	6	→	→	SYM
ejpam-1949	166	7	k̂∗−1(x	k̂∗−1(x	NOUN
ejpam-1949	166	8	)	)	PUNCT
ejpam-1949	166	9	be	be	AUX
ejpam-1949	166	10	the	the	DET
ejpam-1949	166	11	map	map	NOUN
ejpam-1949	166	12	given	give	VERB
ejpam-1949	166	13	by	by	ADP
ejpam-1949	166	14	j(s	j(s	PROPN
ejpam-1949	166	15	,	,	PUNCT
ejpam-1949	166	16	t	t	PROPN
ejpam-1949	166	17	)	)	PUNCT
ejpam-1949	166	18	:	:	PUNCT
ejpam-1949	167	1	=	=	NOUN
ejpam-1949	167	2	hx	hx	INTJ
ejpam-1949	167	3	.	.	PUNCT
ejpam-1949	168	1	it	it	PRON
ejpam-1949	168	2	is	be	AUX
ejpam-1949	168	3	obvious	obvious	ADJ
ejpam-1949	168	4	that	that	SCONJ
ejpam-1949	168	5	j(δ̌(s	j(δ̌(s	NOUN
ejpam-1949	168	6	,	,	PUNCT
ejpam-1949	168	7	t	t	NOUN
ejpam-1949	168	8	)	)	PUNCT
ejpam-1949	168	9	)	)	PUNCT
ejpam-1949	169	1	=	=	PUNCT
ejpam-1949	169	2	0	0	X
ejpam-1949	169	3	.	.	PUNCT
ejpam-1949	170	1	then	then	ADV
ejpam-1949	170	2	we	we	PRON
ejpam-1949	170	3	obtain	obtain	VERB
ejpam-1949	170	4	a	a	DET
ejpam-1949	170	5	homomorphism	homomorphism	NOUN
ejpam-1949	170	6	from	from	ADP
ejpam-1949	170	7	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	170	8	)	)	PUNCT
ejpam-1949	170	9	to	to	ADP
ejpam-1949	170	10	k̂∗−1(x	k̂∗−1(x	NOUN
ejpam-1949	170	11	)	)	PUNCT
ejpam-1949	170	12	,	,	PUNCT
ejpam-1949	170	13	also	also	ADV
ejpam-1949	170	14	denoted	denote	VERB
ejpam-1949	170	15	by	by	ADP
ejpam-1949	170	16	j.	j.	PROPN
ejpam-1949	170	17	now	now	ADV
ejpam-1949	170	18	,	,	PUNCT
ejpam-1949	170	19	let	let	VERB
ejpam-1949	170	20	h	h	PROPN
ejpam-1949	170	21	∈	∈	PROPN
ejpam-1949	170	22	k̂∗(y	k̂∗(y	PROPN
ejpam-1949	170	23	)	)	PUNCT
ejpam-1949	170	24	.	.	PUNCT
ejpam-1949	171	1	since	since	SCONJ
ejpam-1949	171	2	r	r	NOUN
ejpam-1949	171	3	is	be	AUX
ejpam-1949	171	4	divisible	divisible	ADJ
ejpam-1949	171	5	,	,	PUNCT
ejpam-1949	171	6	there	there	PRON
ejpam-1949	171	7	is	be	VERB
ejpam-1949	171	8	a	a	DET
ejpam-1949	171	9	real	real	ADJ
ejpam-1949	171	10	k	k	NOUN
ejpam-1949	171	11	-	-	PUNCT
ejpam-1949	171	12	cochain	cochain	NOUN
ejpam-1949	171	13	h′	h′	PROPN
ejpam-1949	171	14	with	with	ADP
ejpam-1949	171	15	h′	h′	PROPN
ejpam-1949	171	16	=	=	SYM
ejpam-1949	171	17	h.	h.	PROPN
ejpam-1949	171	18	set	set	VERB
ejpam-1949	171	19	uh′	uh′	PROPN
ejpam-1949	172	1	=	=	PRON
ejpam-1949	172	2	ϕδ0(h)−δh′.	ϕδ0(h)−δh′.	PROPN
ejpam-1949	172	3	it	it	PRON
ejpam-1949	172	4	is	be	AUX
ejpam-1949	172	5	obvious	obvious	ADJ
ejpam-1949	172	6	that	that	SCONJ
ejpam-1949	172	7	uh′	uh′	PROPN
ejpam-1949	172	8	∈	∈	PROPN
ejpam-1949	172	9	l∗−1(y	l∗−1(y	PROPN
ejpam-1949	172	10	,	,	PUNCT
ejpam-1949	172	11	z	z	NOUN
ejpam-1949	172	12	)	)	PUNCT
ejpam-1949	172	13	.	.	PUNCT
ejpam-1949	173	1	on	on	ADP
ejpam-1949	173	2	the	the	DET
ejpam-1949	173	3	other	other	ADJ
ejpam-1949	173	4	hand	hand	NOUN
ejpam-1949	173	5	,	,	PUNCT
ejpam-1949	173	6	we	we	PRON
ejpam-1949	173	7	have	have	VERB
ejpam-1949	173	8	δuh′	δuh′	NOUN
ejpam-1949	173	9	=	=	SYM
ejpam-1949	173	10	ϕdδ0(h)−	ϕdδ0(h)−	NOUN
ejpam-1949	173	11	(	(	PUNCT
ejpam-1949	173	12	δ	δ	NOUN
ejpam-1949	173	13	◦	◦	NOUN
ejpam-1949	173	14	δ)h	δ)h	PUNCT
ejpam-1949	173	15	′	′	NUM
ejpam-1949	174	1	=	=	SYM
ejpam-1949	175	1	0	0	X
ejpam-1949	175	2	.	.	PUNCT
ejpam-1949	176	1	therefore	therefore	ADV
ejpam-1949	176	2	,	,	PUNCT
ejpam-1949	176	3	[	[	X
ejpam-1949	176	4	0	0	NUM
ejpam-1949	176	5	,	,	PUNCT
ejpam-1949	176	6	(	(	PUNCT
ejpam-1949	176	7	uh′	uh′	NOUN
ejpam-1949	176	8	,	,	PUNCT
ejpam-1949	176	9	h′,δ0(h	h′,δ0(h	NUM
ejpam-1949	176	10	)	)	PUNCT
ejpam-1949	176	11	)	)	PUNCT
ejpam-1949	176	12	]	]	PUNCT
ejpam-1949	176	13	∈	∈	PROPN
ejpam-1949	176	14	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	176	15	)	)	PUNCT
ejpam-1949	176	16	.	.	PUNCT
ejpam-1949	177	1	we	we	PRON
ejpam-1949	177	2	claim	claim	VERB
ejpam-1949	177	3	that	that	SCONJ
ejpam-1949	177	4	[	[	X
ejpam-1949	177	5	0	0	NUM
ejpam-1949	177	6	,	,	PUNCT
ejpam-1949	177	7	(	(	PUNCT
ejpam-1949	177	8	uh′	uh′	NOUN
ejpam-1949	177	9	,	,	PUNCT
ejpam-1949	177	10	h′,δ0(h	h′,δ0(h	NUM
ejpam-1949	177	11	)	)	PUNCT
ejpam-1949	177	12	)	)	PUNCT
ejpam-1949	177	13	]	]	PUNCT
ejpam-1949	177	14	is	be	AUX
ejpam-1949	177	15	independent	independent	ADJ
ejpam-1949	177	16	of	of	ADP
ejpam-1949	177	17	the	the	DET
ejpam-1949	177	18	choice	choice	NOUN
ejpam-1949	177	19	of	of	ADP
ejpam-1949	177	20	h′.	h′.	PROPN
ejpam-1949	177	21	in	in	ADP
ejpam-1949	177	22	fact	fact	NOUN
ejpam-1949	177	23	if	if	SCONJ
ejpam-1949	177	24	h′′	h′′	PROPN
ejpam-1949	177	25	is	be	AUX
ejpam-1949	177	26	another	another	DET
ejpam-1949	177	27	lift	lift	NOUN
ejpam-1949	177	28	of	of	ADP
ejpam-1949	177	29	h	h	NOUN
ejpam-1949	177	30	,	,	PUNCT
ejpam-1949	177	31	then	then	ADV
ejpam-1949	177	32	h′′−h′	h′′−h′	PROPN
ejpam-1949	177	33	=	=	PROPN
ejpam-1949	177	34	0	0	PUNCT
ejpam-1949	178	1	so	so	SCONJ
ejpam-1949	178	2	that	that	SCONJ
ejpam-1949	178	3	h′′	h′′	NOUN
ejpam-1949	178	4	=	=	PUNCT
ejpam-1949	178	5	h′+	h′+	NOUN
ejpam-1949	178	6	c+δγ	c+δγ	NOUN
ejpam-1949	178	7	for	for	ADP
ejpam-1949	178	8	same	same	ADJ
ejpam-1949	178	9	c	c	PROPN
ejpam-1949	178	10	∈	∈	PROPN
ejpam-1949	178	11	l∗(y	l∗(y	PROPN
ejpam-1949	178	12	,	,	PUNCT
ejpam-1949	178	13	z	z	PROPN
ejpam-1949	178	14	)	)	PUNCT
ejpam-1949	178	15	and	and	CCONJ
ejpam-1949	178	16	γ	γ	X
ejpam-1949	178	17	∈	∈	PROPN
ejpam-1949	178	18	l∗−1(y	l∗−1(y	PROPN
ejpam-1949	178	19	,	,	PUNCT
ejpam-1949	178	20	r	r	NOUN
ejpam-1949	178	21	)	)	PUNCT
ejpam-1949	178	22	.	.	PUNCT
ejpam-1949	179	1	thus	thus	ADV
ejpam-1949	179	2	we	we	PRON
ejpam-1949	179	3	finally	finally	ADV
ejpam-1949	179	4	get	get	VERB
ejpam-1949	179	5	(	(	PUNCT
ejpam-1949	179	6	0	0	NUM
ejpam-1949	179	7	,	,	PUNCT
ejpam-1949	179	8	(	(	PUNCT
ejpam-1949	179	9	uh′′	uh′′	NOUN
ejpam-1949	179	10	,	,	PUNCT
ejpam-1949	179	11	h′′,δ0(h	h′′,δ0(h	PROPN
ejpam-1949	179	12	)	)	PUNCT
ejpam-1949	179	13	)	)	PUNCT
ejpam-1949	179	14	)	)	PUNCT
ejpam-1949	180	1	=	=	PUNCT
ejpam-1949	180	2	(	(	PUNCT
ejpam-1949	180	3	0	0	NUM
ejpam-1949	180	4	,	,	PUNCT
ejpam-1949	180	5	(	(	PUNCT
ejpam-1949	180	6	uh′	uh′	NOUN
ejpam-1949	180	7	,	,	PUNCT
ejpam-1949	180	8	h′,δ0(h)))−	h′,δ0(h)))−	NOUN
ejpam-1949	180	9	δ̌(0	δ̌(0	NOUN
ejpam-1949	180	10	,	,	PUNCT
ejpam-1949	180	11	(	(	PUNCT
ejpam-1949	180	12	c	c	X
ejpam-1949	180	13	,	,	PUNCT
ejpam-1949	180	14	γ	γ	X
ejpam-1949	180	15	,	,	PUNCT
ejpam-1949	180	16	0	0	NUM
ejpam-1949	180	17	)	)	PUNCT
ejpam-1949	180	18	)	)	PUNCT
ejpam-1949	180	19	.	.	PUNCT
ejpam-1949	181	1	we	we	PRON
ejpam-1949	181	2	define	define	VERB
ejpam-1949	181	3	a	a	DET
ejpam-1949	181	4	homomorphism	homomorphism	NOUN
ejpam-1949	181	5	θ	θ	NOUN
ejpam-1949	181	6	:	:	PUNCT
ejpam-1949	181	7	k̂∗(y	k̂∗(y	PROPN
ejpam-1949	181	8	)	)	PUNCT
ejpam-1949	181	9	→	→	SYM
ejpam-1949	181	10	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	181	11	)	)	PUNCT
ejpam-1949	181	12	by	by	ADP
ejpam-1949	181	13	setting	set	VERB
ejpam-1949	181	14	θ(h	θ(h	PROPN
ejpam-1949	181	15	)	)	PUNCT
ejpam-1949	181	16	:	:	PUNCT
ejpam-1949	182	1	=	=	PUNCT
ejpam-1949	183	1	[	[	X
ejpam-1949	183	2	0	0	NUM
ejpam-1949	183	3	,	,	PUNCT
ejpam-1949	183	4	(	(	PUNCT
ejpam-1949	183	5	uh′	uh′	NOUN
ejpam-1949	183	6	,	,	PUNCT
ejpam-1949	183	7	h′,δ0(h	h′,δ0(h	NUM
ejpam-1949	183	8	)	)	PUNCT
ejpam-1949	183	9	)	)	PUNCT
ejpam-1949	183	10	]	]	PUNCT
ejpam-1949	183	11	.	.	PUNCT
ejpam-1949	184	1	a.	a.	NOUN
ejpam-1949	184	2	elmrabty	elmrabty	NOUN
ejpam-1949	184	3	,	,	PUNCT
ejpam-1949	184	4	m.	m.	NOUN
ejpam-1949	184	5	maghfoul	maghfoul	PROPN
ejpam-1949	184	6	/	/	SYM
ejpam-1949	184	7	eur	eur	PROPN
ejpam-1949	184	8	.	.	PUNCT
ejpam-1949	185	1	j.	j.	PROPN
ejpam-1949	185	2	pure	pure	PROPN
ejpam-1949	185	3	appl	appl	PROPN
ejpam-1949	185	4	.	.	PROPN
ejpam-1949	185	5	math	math	PROPN
ejpam-1949	185	6	,	,	PUNCT
ejpam-1949	185	7	7	7	NUM
ejpam-1949	185	8	(	(	PUNCT
ejpam-1949	185	9	2014	2014	NUM
ejpam-1949	185	10	)	)	PUNCT
ejpam-1949	185	11	,	,	PUNCT
ejpam-1949	185	12	65	65	NUM
ejpam-1949	185	13	-	-	SYM
ejpam-1949	185	14	76	76	NUM
ejpam-1949	185	15	72	72	NUM
ejpam-1949	185	16	theorem	theorem	NOUN
ejpam-1949	185	17	1	1	NUM
ejpam-1949	185	18	.	.	PUNCT
ejpam-1949	186	1	the	the	DET
ejpam-1949	186	2	following	follow	VERB
ejpam-1949	186	3	six	six	NUM
ejpam-1949	186	4	-	-	PUNCT
ejpam-1949	186	5	term	term	NOUN
ejpam-1949	186	6	sequence	sequence	NOUN
ejpam-1949	186	7	k̂0(x	k̂0(x	NOUN
ejpam-1949	186	8	)	)	PUNCT
ejpam-1949	186	9	ρ∗	ρ∗	PROPN
ejpam-1949	186	10	//	//	SYM
ejpam-1949	186	11	k̂0(y	k̂0(y	PROPN
ejpam-1949	186	12	)	)	PUNCT
ejpam-1949	186	13	θ	θ	PROPN
ejpam-1949	186	14	//	//	SYM
ejpam-1949	186	15	ǩ0(ρ	ǩ0(ρ	PROPN
ejpam-1949	186	16	)	)	PUNCT
ejpam-1949	186	17	j	j	PROPN
ejpam-1949	186	18	�	�	PROPN
ejpam-1949	186	19	�	�	PROPN
ejpam-1949	186	20	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	186	21	)	)	PUNCT
ejpam-1949	186	22	j	j	PROPN
ejpam-1949	186	23	oo	oo	PROPN
ejpam-1949	186	24	k̂1(y	k̂1(y	PROPN
ejpam-1949	186	25	)	)	PUNCT
ejpam-1949	186	26	θoo	θoo	PROPN
ejpam-1949	186	27	k̂1(x	k̂1(x	PROPN
ejpam-1949	186	28	)	)	PUNCT
ejpam-1949	186	29	ρ∗oo	ρ∗oo	PROPN
ejpam-1949	186	30	is	be	AUX
ejpam-1949	186	31	exact	exact	ADJ
ejpam-1949	186	32	.	.	PUNCT
ejpam-1949	187	1	proof	proof	NOUN
ejpam-1949	187	2	.	.	PUNCT
ejpam-1949	188	1	exactness	exactness	NOUN
ejpam-1949	188	2	at	at	ADP
ejpam-1949	188	3	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	188	4	)	)	PUNCT
ejpam-1949	188	5	.	.	PUNCT
ejpam-1949	189	1	it	it	PRON
ejpam-1949	189	2	is	be	AUX
ejpam-1949	189	3	evident	evident	ADJ
ejpam-1949	189	4	that	that	SCONJ
ejpam-1949	189	5	j	j	PROPN
ejpam-1949	189	6	◦	◦	NOUN
ejpam-1949	189	7	θ	θ	PROPN
ejpam-1949	189	8	=	=	SYM
ejpam-1949	189	9	0	0	X
ejpam-1949	189	10	.	.	PUNCT
ejpam-1949	190	1	let	let	VERB
ejpam-1949	190	2	[	[	X
ejpam-1949	190	3	s	s	X
ejpam-1949	190	4	,	,	PUNCT
ejpam-1949	190	5	t	t	PROPN
ejpam-1949	190	6	]	]	X
ejpam-1949	190	7	∈	∈	PROPN
ejpam-1949	190	8	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	190	9	)	)	PUNCT
ejpam-1949	190	10	with	with	ADP
ejpam-1949	190	11	s	s	NOUN
ejpam-1949	190	12	=	=	PUNCT
ejpam-1949	190	13	(	(	PUNCT
ejpam-1949	190	14	cx	cx	PROPN
ejpam-1949	190	15	,	,	PUNCT
ejpam-1949	190	16	hx	hx	PROPN
ejpam-1949	190	17	,	,	PUNCT
ejpam-1949	190	18	wx	wx	PROPN
ejpam-1949	190	19	)	)	PUNCT
ejpam-1949	190	20	and	and	CCONJ
ejpam-1949	190	21	t	t	NOUN
ejpam-1949	191	1	=	=	SYM
ejpam-1949	191	2	(	(	PUNCT
ejpam-1949	191	3	cy	cy	PROPN
ejpam-1949	191	4	,	,	PUNCT
ejpam-1949	191	5	hy	hy	PROPN
ejpam-1949	191	6	,	,	PUNCT
ejpam-1949	191	7	w	w	PROPN
ejpam-1949	191	8	y	y	NOUN
ejpam-1949	191	9	)	)	PUNCT
ejpam-1949	191	10	.	.	PUNCT
ejpam-1949	192	1	assume	assume	VERB
ejpam-1949	192	2	that	that	SCONJ
ejpam-1949	192	3	j[s	j[s	PROPN
ejpam-1949	192	4	,	,	PUNCT
ejpam-1949	192	5	t	t	PROPN
ejpam-1949	192	6	]	]	X
ejpam-1949	192	7	=	=	SYM
ejpam-1949	192	8	0	0	X
ejpam-1949	192	9	.	.	PUNCT
ejpam-1949	193	1	then	then	ADV
ejpam-1949	193	2	we	we	PRON
ejpam-1949	193	3	have	have	VERB
ejpam-1949	193	4	wx	wx	PROPN
ejpam-1949	193	5	=	=	SYM
ejpam-1949	193	6	0	0	PROPN
ejpam-1949	193	7	,	,	PUNCT
ejpam-1949	193	8	cx	cx	NOUN
ejpam-1949	193	9	=	=	PUNCT
ejpam-1949	193	10	−δhx	−δhx	NOUN
ejpam-1949	193	11	,	,	PUNCT
ejpam-1949	193	12	and	and	CCONJ
ejpam-1949	193	13	there	there	PRON
ejpam-1949	193	14	exist	exist	VERB
ejpam-1949	193	15	g	g	PROPN
ejpam-1949	193	16	∈	∈	PROPN
ejpam-1949	193	17	l1(x	l1(x	PROPN
ejpam-1949	193	18	,	,	PUNCT
ejpam-1949	193	19	r	r	NOUN
ejpam-1949	193	20	)	)	PUNCT
ejpam-1949	193	21	and	and	CCONJ
ejpam-1949	193	22	u	u	PROPN
ejpam-1949	193	23	∈	∈	PROPN
ejpam-1949	193	24	l0(x	l0(x	X
ejpam-1949	193	25	,	,	PUNCT
ejpam-1949	193	26	z	z	NOUN
ejpam-1949	193	27	)	)	PUNCT
ejpam-1949	193	28	such	such	ADJ
ejpam-1949	193	29	that	that	SCONJ
ejpam-1949	193	30	hx	hx	NOUN
ejpam-1949	193	31	=	=	PUNCT
ejpam-1949	193	32	δg	δg	PROPN
ejpam-1949	193	33	+	+	CCONJ
ejpam-1949	193	34	u.	u.	VERB
ejpam-1949	193	35	since	since	SCONJ
ejpam-1949	193	36	(	(	PUNCT
ejpam-1949	193	37	s	s	PROPN
ejpam-1949	193	38	,	,	PUNCT
ejpam-1949	193	39	t	t	NOUN
ejpam-1949	193	40	)	)	PUNCT
ejpam-1949	193	41	=	=	PUNCT
ejpam-1949	194	1	(	(	PUNCT
ejpam-1949	194	2	0	0	NUM
ejpam-1949	194	3	,	,	PUNCT
ejpam-1949	194	4	(	(	PUNCT
ejpam-1949	194	5	cy	cy	PROPN
ejpam-1949	194	6	−ρ∗u	−ρ∗u	PROPN
ejpam-1949	194	7	,	,	PUNCT
ejpam-1949	194	8	hy	hy	PROPN
ejpam-1949	194	9	−ρ∗g	−ρ∗g	PROPN
ejpam-1949	194	10	,	,	PUNCT
ejpam-1949	194	11	w	w	PROPN
ejpam-1949	194	12	y	y	NOUN
ejpam-1949	194	13	)	)	PUNCT
ejpam-1949	194	14	)	)	PUNCT
ejpam-1949	195	1	+	+	CCONJ
ejpam-1949	195	2	δ̌((u	δ̌((u	NOUN
ejpam-1949	195	3	,	,	PUNCT
ejpam-1949	195	4	g	g	NOUN
ejpam-1949	195	5	,	,	PUNCT
ejpam-1949	195	6	0	0	NUM
ejpam-1949	195	7	)	)	PUNCT
ejpam-1949	195	8	,	,	PUNCT
ejpam-1949	195	9	0	0	NUM
ejpam-1949	195	10	)	)	PUNCT
ejpam-1949	195	11	and	and	CCONJ
ejpam-1949	195	12	[	[	X
ejpam-1949	195	13	0	0	NUM
ejpam-1949	195	14	,	,	PUNCT
ejpam-1949	195	15	(	(	PUNCT
ejpam-1949	195	16	cy	cy	PROPN
ejpam-1949	195	17	−ρ∗u	−ρ∗u	PROPN
ejpam-1949	195	18	,	,	PUNCT
ejpam-1949	195	19	hy	hy	PROPN
ejpam-1949	195	20	−ρ∗g	−ρ∗g	PROPN
ejpam-1949	195	21	,	,	PUNCT
ejpam-1949	195	22	w	w	PROPN
ejpam-1949	195	23	y	y	PROPN
ejpam-1949	195	24	)	)	PUNCT
ejpam-1949	195	25	]	]	PUNCT
ejpam-1949	195	26	lies	lie	VERB
ejpam-1949	195	27	in	in	ADP
ejpam-1949	195	28	the	the	DET
ejpam-1949	195	29	image	image	NOUN
ejpam-1949	195	30	of	of	ADP
ejpam-1949	195	31	θ	θ	PROPN
ejpam-1949	195	32	,	,	PUNCT
ejpam-1949	195	33	we	we	PRON
ejpam-1949	195	34	get	get	VERB
ejpam-1949	195	35	[	[	X
ejpam-1949	195	36	s	s	X
ejpam-1949	195	37	,	,	PUNCT
ejpam-1949	195	38	t	t	PROPN
ejpam-1949	195	39	]	]	X
ejpam-1949	195	40	∈	∈	PROPN
ejpam-1949	195	41	img(θ	img(θ	PROPN
ejpam-1949	195	42	)	)	PUNCT
ejpam-1949	195	43	.	.	PUNCT
ejpam-1949	196	1	exactness	exactness	NOUN
ejpam-1949	196	2	at	at	ADP
ejpam-1949	196	3	k̂1(x	k̂1(x	PROPN
ejpam-1949	196	4	)	)	PUNCT
ejpam-1949	196	5	.	.	PUNCT
ejpam-1949	197	1	for	for	ADP
ejpam-1949	197	2	any	any	DET
ejpam-1949	197	3	[	[	X
ejpam-1949	197	4	s	s	X
ejpam-1949	197	5	,	,	PUNCT
ejpam-1949	197	6	t	t	PROPN
ejpam-1949	197	7	]	]	X
ejpam-1949	197	8	∈	∈	PROPN
ejpam-1949	197	9	ǩ0(ρ	ǩ0(ρ	PROPN
ejpam-1949	197	10	)	)	PUNCT
ejpam-1949	197	11	with	with	ADP
ejpam-1949	197	12	(	(	PUNCT
ejpam-1949	197	13	s	s	PROPN
ejpam-1949	197	14	,	,	PUNCT
ejpam-1949	197	15	t	t	NOUN
ejpam-1949	197	16	)	)	PUNCT
ejpam-1949	197	17	=	=	PUNCT
ejpam-1949	197	18	(	(	PUNCT
ejpam-1949	197	19	(	(	PUNCT
ejpam-1949	197	20	cx	cx	INTJ
ejpam-1949	197	21	,	,	PUNCT
ejpam-1949	197	22	hx	hx	PROPN
ejpam-1949	197	23	,	,	PUNCT
ejpam-1949	197	24	wx	wx	PROPN
ejpam-1949	197	25	)	)	PUNCT
ejpam-1949	197	26	,	,	PUNCT
ejpam-1949	197	27	(	(	PUNCT
ejpam-1949	197	28	cy	cy	PROPN
ejpam-1949	197	29	,	,	PUNCT
ejpam-1949	197	30	hy	hy	PROPN
ejpam-1949	197	31	,	,	PUNCT
ejpam-1949	197	32	w	w	PROPN
ejpam-1949	197	33	y	y	PROPN
ejpam-1949	197	34	)	)	PUNCT
ejpam-1949	197	35	)	)	PUNCT
ejpam-1949	197	36	,	,	PUNCT
ejpam-1949	197	37	the	the	DET
ejpam-1949	197	38	equality	equality	NOUN
ejpam-1949	197	39	δ̌(s	δ̌(s	NOUN
ejpam-1949	197	40	,	,	PUNCT
ejpam-1949	197	41	t	t	NOUN
ejpam-1949	197	42	)	)	PUNCT
ejpam-1949	198	1	=	=	SYM
ejpam-1949	198	2	0	0	NUM
ejpam-1949	198	3	,	,	PUNCT
ejpam-1949	198	4	together	together	ADV
ejpam-1949	198	5	with	with	ADP
ejpam-1949	198	6	the	the	DET
ejpam-1949	198	7	fact	fact	NOUN
ejpam-1949	198	8	that	that	SCONJ
ejpam-1949	198	9	w	w	PROPN
ejpam-1949	198	10	y	y	PROPN
ejpam-1949	198	11	∈	∈	PROPN
ejpam-1949	198	12	ωodd	ωodd	NOUN
ejpam-1949	198	13	0	0	NUM
ejpam-1949	199	1	(	(	PUNCT
ejpam-1949	199	2	y	y	PROPN
ejpam-1949	199	3	)	)	PUNCT
ejpam-1949	199	4	,	,	PUNCT
ejpam-1949	199	5	implies	imply	VERB
ejpam-1949	199	6	that	that	SCONJ
ejpam-1949	199	7	ρ∗	ρ∗	PROPN
ejpam-1949	199	8	◦	◦	NOUN
ejpam-1949	199	9	j[s	j[s	PROPN
ejpam-1949	199	10	,	,	PUNCT
ejpam-1949	199	11	t](σ	t](σ	ADV
ejpam-1949	199	12	)	)	PUNCT
ejpam-1949	200	1	=	=	NOUN
ejpam-1949	200	2	−ϕw	−ϕw	ADP
ejpam-1949	200	3	y	y	PROPN
ejpam-1949	200	4	(	(	PUNCT
ejpam-1949	200	5	σ	σ	PROPN
ejpam-1949	200	6	)	)	PUNCT
ejpam-1949	200	7	+	+	CCONJ
ejpam-1949	200	8	hy(∂	hy(∂	PROPN
ejpam-1949	200	9	σ	σ	PROPN
ejpam-1949	200	10	)	)	PUNCT
ejpam-1949	200	11	=	=	SYM
ejpam-1949	200	12	0	0	NUM
ejpam-1949	200	13	for	for	ADP
ejpam-1949	200	14	all	all	DET
ejpam-1949	200	15	σ	σ	NOUN
ejpam-1949	200	16	∈	∈	PROPN
ejpam-1949	200	17	c1(y	c1(y	PROPN
ejpam-1949	200	18	)	)	PUNCT
ejpam-1949	200	19	.	.	PUNCT
ejpam-1949	201	1	now	now	ADV
ejpam-1949	201	2	,	,	PUNCT
ejpam-1949	201	3	let	let	VERB
ejpam-1949	201	4	h	h	PRON
ejpam-1949	201	5	∈	∈	PROPN
ejpam-1949	201	6	ker[k̂0(x	ker[k̂0(x	PROPN
ejpam-1949	201	7	)	)	PUNCT
ejpam-1949	201	8	ρ∗	ρ∗	PROPN
ejpam-1949	201	9	→	→	SYM
ejpam-1949	201	10	k̂0(y	k̂0(y	PROPN
ejpam-1949	201	11	)	)	PUNCT
ejpam-1949	201	12	]	]	PUNCT
ejpam-1949	201	13	.	.	PUNCT
ejpam-1949	202	1	first	first	ADV
ejpam-1949	202	2	,	,	PUNCT
ejpam-1949	202	3	we	we	PRON
ejpam-1949	202	4	have	have	VERB
ejpam-1949	202	5	ρ∗(δ0(h	ρ∗(δ0(h	ADV
ejpam-1949	202	6	)	)	PUNCT
ejpam-1949	202	7	)	)	PUNCT
ejpam-1949	203	1	=	=	PUNCT
ejpam-1949	203	2	0	0	X
ejpam-1949	203	3	.	.	PUNCT
ejpam-1949	204	1	furthermore	furthermore	ADV
ejpam-1949	204	2	,	,	PUNCT
ejpam-1949	204	3	we	we	PRON
ejpam-1949	204	4	can	can	AUX
ejpam-1949	204	5	find	find	VERB
ejpam-1949	204	6	f	f	X
ejpam-1949	204	7	∈	∈	PROPN
ejpam-1949	204	8	l1(y	l1(y	PROPN
ejpam-1949	204	9	,	,	PUNCT
ejpam-1949	204	10	r	r	NOUN
ejpam-1949	204	11	)	)	PUNCT
ejpam-1949	204	12	and	and	CCONJ
ejpam-1949	204	13	c	c	NOUN
ejpam-1949	204	14	∈	∈	PROPN
ejpam-1949	204	15	l0(y	l0(y	X
ejpam-1949	204	16	,	,	PUNCT
ejpam-1949	204	17	z	z	NOUN
ejpam-1949	204	18	)	)	PUNCT
ejpam-1949	204	19	such	such	ADJ
ejpam-1949	204	20	that	that	SCONJ
ejpam-1949	204	21	ρ∗h′	ρ∗h′	PROPN
ejpam-1949	204	22	=	=	SYM
ejpam-1949	204	23	δ	δ	X
ejpam-1949	204	24	f	f	PROPN
ejpam-1949	204	25	+	+	CCONJ
ejpam-1949	204	26	c	c	NOUN
ejpam-1949	204	27	and	and	CCONJ
ejpam-1949	204	28	ρ∗uh′	ρ∗uh′	NOUN
ejpam-1949	204	29	=	=	NOUN
ejpam-1949	204	30	−δc	−δc	NOUN
ejpam-1949	204	31	.	.	PUNCT
ejpam-1949	205	1	it	it	PRON
ejpam-1949	205	2	is	be	AUX
ejpam-1949	205	3	easy	easy	ADJ
ejpam-1949	205	4	to	to	PART
ejpam-1949	205	5	check	check	VERB
ejpam-1949	205	6	that	that	DET
ejpam-1949	205	7	r	r	NOUN
ejpam-1949	205	8	:	:	PUNCT
ejpam-1949	205	9	=	=	SYM
ejpam-1949	205	10	(	(	PUNCT
ejpam-1949	205	11	(	(	PUNCT
ejpam-1949	205	12	uh′	uh′	ADJ
ejpam-1949	205	13	,	,	PUNCT
ejpam-1949	205	14	h′,δ0(h	h′,δ0(h	NUM
ejpam-1949	205	15	)	)	PUNCT
ejpam-1949	205	16	)	)	PUNCT
ejpam-1949	205	17	,	,	PUNCT
ejpam-1949	205	18	(	(	PUNCT
ejpam-1949	205	19	c	c	X
ejpam-1949	205	20	,	,	PUNCT
ejpam-1949	205	21	f	f	PROPN
ejpam-1949	205	22	,	,	PUNCT
ejpam-1949	205	23	0	0	NUM
ejpam-1949	205	24	)	)	PUNCT
ejpam-1949	205	25	)	)	PUNCT
ejpam-1949	205	26	defines	define	VERB
ejpam-1949	205	27	an	an	DET
ejpam-1949	205	28	element	element	NOUN
ejpam-1949	205	29	in	in	ADP
ejpam-1949	205	30	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	205	31	)	)	PUNCT
ejpam-1949	205	32	with	with	ADP
ejpam-1949	205	33	j([r	j([r	PROPN
ejpam-1949	205	34	]	]	PUNCT
ejpam-1949	205	35	)	)	PUNCT
ejpam-1949	206	1	=	=	SYM
ejpam-1949	206	2	h.	h.	NOUN
ejpam-1949	206	3	exactness	exactness	NOUN
ejpam-1949	206	4	at	at	ADP
ejpam-1949	206	5	k̂0(y	k̂0(y	PROPN
ejpam-1949	206	6	)	)	PUNCT
ejpam-1949	206	7	.	.	PUNCT
ejpam-1949	207	1	for	for	ADP
ejpam-1949	207	2	every	every	DET
ejpam-1949	207	3	h	h	NOUN
ejpam-1949	207	4	∈	∈	PROPN
ejpam-1949	207	5	k̂0(x	k̂0(x	NOUN
ejpam-1949	207	6	)	)	PUNCT
ejpam-1949	207	7	,	,	PUNCT
ejpam-1949	207	8	θ	θ	PROPN
ejpam-1949	207	9	◦	◦	NOUN
ejpam-1949	207	10	ρ∗(h	ρ∗(h	PROPN
ejpam-1949	207	11	)	)	PUNCT
ejpam-1949	208	1	=	=	PUNCT
ejpam-1949	209	1	[	[	X
ejpam-1949	209	2	0	0	NUM
ejpam-1949	209	3	,	,	PUNCT
ejpam-1949	209	4	(	(	PUNCT
ejpam-1949	209	5	uρ∗h′	uρ∗h′	NOUN
ejpam-1949	209	6	,	,	PUNCT
ejpam-1949	209	7	ρ	ρ	PROPN
ejpam-1949	209	8	∗h′,ρ∗δ0(h	∗h′,ρ∗δ0(h	PROPN
ejpam-1949	209	9	)	)	PUNCT
ejpam-1949	209	10	)	)	PUNCT
ejpam-1949	209	11	]	]	PUNCT
ejpam-1949	210	1	=	=	PUNCT
ejpam-1949	211	1	[	[	X
ejpam-1949	211	2	δ̌((uh′	δ̌((uh′	PROPN
ejpam-1949	211	3	,	,	PUNCT
ejpam-1949	211	4	h′,δ0(h	h′,δ0(h	NUM
ejpam-1949	211	5	)	)	PUNCT
ejpam-1949	211	6	)	)	PUNCT
ejpam-1949	211	7	,	,	PUNCT
ejpam-1949	211	8	0	0	NUM
ejpam-1949	211	9	)	)	PUNCT
ejpam-1949	211	10	]	]	PUNCT
ejpam-1949	212	1	=	=	PUNCT
ejpam-1949	212	2	0	0	X
ejpam-1949	212	3	.	.	PUNCT
ejpam-1949	213	1	if	if	SCONJ
ejpam-1949	213	2	f	f	PROPN
ejpam-1949	213	3	∈	∈	PROPN
ejpam-1949	213	4	k̂0(y	k̂0(y	PROPN
ejpam-1949	213	5	)	)	PUNCT
ejpam-1949	214	1	such	such	ADJ
ejpam-1949	214	2	that	that	SCONJ
ejpam-1949	214	3	θ	θ	PROPN
ejpam-1949	214	4	(	(	PUNCT
ejpam-1949	214	5	f	f	NOUN
ejpam-1949	214	6	)	)	PUNCT
ejpam-1949	214	7	=	=	SYM
ejpam-1949	214	8	0	0	NUM
ejpam-1949	214	9	,	,	PUNCT
ejpam-1949	214	10	then	then	ADV
ejpam-1949	214	11	there	there	PRON
ejpam-1949	214	12	exists	exist	VERB
ejpam-1949	214	13	(	(	PUNCT
ejpam-1949	214	14	(	(	PUNCT
ejpam-1949	214	15	cx	cx	INTJ
ejpam-1949	214	16	,	,	PUNCT
ejpam-1949	214	17	hx	hx	PROPN
ejpam-1949	214	18	,	,	PUNCT
ejpam-1949	214	19	wx	wx	PROPN
ejpam-1949	214	20	)	)	PUNCT
ejpam-1949	214	21	,	,	PUNCT
ejpam-1949	214	22	(	(	PUNCT
ejpam-1949	214	23	cy	cy	PROPN
ejpam-1949	214	24	,	,	PUNCT
ejpam-1949	214	25	hy	hy	PROPN
ejpam-1949	214	26	,	,	PUNCT
ejpam-1949	214	27	w	w	PROPN
ejpam-1949	214	28	y	y	NOUN
ejpam-1949	214	29	)	)	PUNCT
ejpam-1949	214	30	)	)	PUNCT
ejpam-1949	215	1	∈	∈	PROPN
ejpam-1949	215	2	ľ1(ρ	ľ1(ρ	PROPN
ejpam-1949	215	3	)	)	PUNCT
ejpam-1949	215	4	with	with	ADP
ejpam-1949	215	5	coboundary	coboundary	ADJ
ejpam-1949	215	6	(	(	PUNCT
ejpam-1949	215	7	0	0	NUM
ejpam-1949	215	8	,	,	PUNCT
ejpam-1949	215	9	(	(	PUNCT
ejpam-1949	215	10	u	u	NOUN
ejpam-1949	215	11	f	f	NOUN
ejpam-1949	215	12	′	′	NUM
ejpam-1949	215	13	,	,	PUNCT
ejpam-1949	215	14	f	f	PROPN
ejpam-1949	215	15	′,δ0	′,δ0	NOUN
ejpam-1949	215	16	(	(	PUNCT
ejpam-1949	215	17	f	f	PROPN
ejpam-1949	215	18	)	)	PUNCT
ejpam-1949	215	19	)	)	PUNCT
ejpam-1949	215	20	)	)	PUNCT
ejpam-1949	215	21	.	.	PUNCT
ejpam-1949	216	1	therefore	therefore	ADV
ejpam-1949	216	2	,	,	PUNCT
ejpam-1949	216	3	we	we	PRON
ejpam-1949	216	4	have	have	VERB
ejpam-1949	216	5	the	the	DET
ejpam-1949	216	6	equations	equation	NOUN
ejpam-1949	216	7	¨	¨	NOUN
ejpam-1949	216	8	δcx	δcx	PROPN
ejpam-1949	216	9	=	=	SYM
ejpam-1949	216	10	0	0	NUM
ejpam-1949	216	11	ϕwx	ϕwx	NOUN
ejpam-1949	217	1	=	=	PRON
ejpam-1949	217	2	δhx	δhx	PROPN
ejpam-1949	217	3	+	+	CCONJ
ejpam-1949	218	1	cx	cx	PROPN
ejpam-1949	219	1	and	and	CCONJ
ejpam-1949	219	2			VERB
ejpam-1949	219	3			PROPN
ejpam-1949	219	4			NOUN
ejpam-1949	219	5	ρ∗cx	ρ∗cx	PROPN
ejpam-1949	220	1	+	+	PROPN
ejpam-1949	220	2	δcy	δcy	NOUN
ejpam-1949	220	3	=	=	SYM
ejpam-1949	220	4	u	u	NOUN
ejpam-1949	220	5	f	f	NOUN
ejpam-1949	220	6	′	′	NUM
ejpam-1949	220	7	ρ∗hx	ρ∗hx	NUM
ejpam-1949	221	1	+	+	PROPN
ejpam-1949	221	2	ϕw	ϕw	ADJ
ejpam-1949	221	3	y	y	NOUN
ejpam-1949	221	4	−δhy	−δhy	NOUN
ejpam-1949	221	5	−	−	PROPN
ejpam-1949	222	1	cy	cy	INTJ
ejpam-1949	222	2	=	=	SYM
ejpam-1949	222	3	f	f	PROPN
ejpam-1949	222	4	′	′	NUM
ejpam-1949	222	5	ρ∗wx	ρ∗wx	PROPN
ejpam-1949	223	1	=	=	SYM
ejpam-1949	223	2	δ0	δ0	NOUN
ejpam-1949	223	3	(	(	PUNCT
ejpam-1949	223	4	f	f	PROPN
ejpam-1949	223	5	)	)	PUNCT
ejpam-1949	223	6	which	which	PRON
ejpam-1949	223	7	imply	imply	VERB
ejpam-1949	223	8	that	that	SCONJ
ejpam-1949	223	9	hx	hx	PROPN
ejpam-1949	223	10	is	be	AUX
ejpam-1949	223	11	a	a	DET
ejpam-1949	223	12	differential	differential	ADJ
ejpam-1949	223	13	k	k	NOUN
ejpam-1949	223	14	-	-	NOUN
ejpam-1949	223	15	character	character	NOUN
ejpam-1949	223	16	on	on	ADP
ejpam-1949	223	17	x	x	PUNCT
ejpam-1949	223	18	with	with	ADP
ejpam-1949	223	19	δ0(hx	δ0(hx	PROPN
ejpam-1949	223	20	)	)	PUNCT
ejpam-1949	223	21	=	=	SYM
ejpam-1949	223	22	wx	wx	PROPN
ejpam-1949	223	23	and	and	CCONJ
ejpam-1949	223	24	ρ∗(hx	ρ∗(hx	PROPN
ejpam-1949	223	25	)	)	PUNCT
ejpam-1949	223	26	=	=	SYM
ejpam-1949	224	1	f	f	PROPN
ejpam-1949	224	2	.	.	PUNCT
ejpam-1949	225	1	remark	remark	PROPN
ejpam-1949	225	2	1	1	NUM
ejpam-1949	225	3	.	.	PUNCT
ejpam-1949	226	1	let	let	VERB
ejpam-1949	226	2	x	x	PRON
ejpam-1949	226	3	be	be	AUX
ejpam-1949	226	4	a	a	DET
ejpam-1949	226	5	smooth	smooth	ADJ
ejpam-1949	226	6	compact	compact	ADJ
ejpam-1949	226	7	manifold	manifold	NOUN
ejpam-1949	226	8	.	.	PUNCT
ejpam-1949	227	1	let	let	VERB
ejpam-1949	227	2	i	i	PRON
ejpam-1949	227	3	be	be	AUX
ejpam-1949	227	4	the	the	DET
ejpam-1949	227	5	inclusion	inclusion	NOUN
ejpam-1949	227	6	pt	pt	NOUN
ejpam-1949	227	7	,	,	PUNCT
ejpam-1949	227	8	→	→	SYM
ejpam-1949	227	9	x	x	X
ejpam-1949	227	10	.	.	PUNCT
ejpam-1949	228	1	the	the	DET
ejpam-1949	228	2	above	above	ADJ
ejpam-1949	228	3	exact	exact	ADJ
ejpam-1949	228	4	sequence	sequence	NOUN
ejpam-1949	228	5	,	,	PUNCT
ejpam-1949	228	6	together	together	ADV
ejpam-1949	228	7	with	with	ADP
ejpam-1949	228	8	the	the	DET
ejpam-1949	228	9	fact	fact	NOUN
ejpam-1949	228	10	that	that	SCONJ
ejpam-1949	228	11	i∗	i∗	NOUN
ejpam-1949	228	12	:	:	PUNCT
ejpam-1949	228	13	k̂∗−1(x	k̂∗−1(x	NOUN
ejpam-1949	228	14	)	)	PUNCT
ejpam-1949	228	15	→	→	SYM
ejpam-1949	228	16	k̂∗−1(pt	k̂∗−1(pt	NOUN
ejpam-1949	228	17	)	)	PUNCT
ejpam-1949	228	18	is	be	AUX
ejpam-1949	228	19	surjective	surjective	ADJ
ejpam-1949	228	20	,	,	PUNCT
ejpam-1949	228	21	implies	imply	VERB
ejpam-1949	228	22	that	that	SCONJ
ejpam-1949	228	23	j	j	PROPN
ejpam-1949	228	24	:	:	PUNCT
ejpam-1949	228	25	ǩ∗(i)→	ǩ∗(i)→	ADJ
ejpam-1949	228	26	k̂∗−1(x	k̂∗−1(x	NOUN
ejpam-1949	228	27	)	)	PUNCT
ejpam-1949	228	28	is	be	AUX
ejpam-1949	228	29	injective	injective	ADJ
ejpam-1949	228	30	with	with	ADP
ejpam-1949	228	31	img	img	PROPN
ejpam-1949	228	32	(	(	PUNCT
ejpam-1949	228	33	j	j	NOUN
ejpam-1949	228	34	)	)	PUNCT
ejpam-1949	228	35	=	=	PUNCT
ejpam-1949	228	36	ker(i∗	ker(i∗	X
ejpam-1949	228	37	)	)	PUNCT
ejpam-1949	228	38	.	.	PUNCT
ejpam-1949	229	1	thus	thus	ADV
ejpam-1949	229	2	we	we	PRON
ejpam-1949	229	3	get	get	VERB
ejpam-1949	229	4	an	an	DET
ejpam-1949	229	5	isomorphism	isomorphism	NOUN
ejpam-1949	229	6	ǩ∗(i)∼=	ǩ∗(i)∼=	PUNCT
ejpam-1949	229	7	k̃∗−1(x	k̃∗−1(x	NOUN
ejpam-1949	229	8	)	)	PUNCT
ejpam-1949	229	9	.	.	PUNCT
ejpam-1949	230	1	a.	a.	NOUN
ejpam-1949	230	2	elmrabty	elmrabty	NOUN
ejpam-1949	230	3	,	,	PUNCT
ejpam-1949	230	4	m.	m.	NOUN
ejpam-1949	230	5	maghfoul	maghfoul	PROPN
ejpam-1949	230	6	/	/	SYM
ejpam-1949	230	7	eur	eur	PROPN
ejpam-1949	230	8	.	.	PUNCT
ejpam-1949	231	1	j.	j.	PROPN
ejpam-1949	231	2	pure	pure	PROPN
ejpam-1949	231	3	appl	appl	PROPN
ejpam-1949	231	4	.	.	PROPN
ejpam-1949	231	5	math	math	PROPN
ejpam-1949	231	6	,	,	PUNCT
ejpam-1949	231	7	7	7	NUM
ejpam-1949	231	8	(	(	PUNCT
ejpam-1949	231	9	2014	2014	NUM
ejpam-1949	231	10	)	)	PUNCT
ejpam-1949	231	11	,	,	PUNCT
ejpam-1949	231	12	65	65	NUM
ejpam-1949	231	13	-	-	SYM
ejpam-1949	231	14	76	76	NUM
ejpam-1949	231	15	73	73	NUM
ejpam-1949	231	16	4	4	NUM
ejpam-1949	231	17	.	.	PUNCT
ejpam-1949	232	1	r	r	X
ejpam-1949	232	2	/	/	SYM
ejpam-1949	232	3	z	z	NOUN
ejpam-1949	232	4	relative	relative	ADJ
ejpam-1949	232	5	k	k	NOUN
ejpam-1949	232	6	-	-	NOUN
ejpam-1949	232	7	theory	theory	NOUN
ejpam-1949	232	8	this	this	DET
ejpam-1949	232	9	section	section	NOUN
ejpam-1949	232	10	is	be	AUX
ejpam-1949	232	11	concerned	concern	VERB
ejpam-1949	232	12	with	with	ADP
ejpam-1949	232	13	the	the	DET
ejpam-1949	232	14	definition	definition	NOUN
ejpam-1949	232	15	of	of	ADP
ejpam-1949	232	16	the	the	DET
ejpam-1949	232	17	k	k	NOUN
ejpam-1949	232	18	-	-	NOUN
ejpam-1949	232	19	theory	theory	NOUN
ejpam-1949	232	20	of	of	ADP
ejpam-1949	232	21	a	a	DET
ejpam-1949	232	22	smooth	smooth	ADJ
ejpam-1949	232	23	map	map	NOUN
ejpam-1949	232	24	ρ	ρ	NOUN
ejpam-1949	232	25	:	:	PUNCT
ejpam-1949	232	26	y	y	PROPN
ejpam-1949	232	27	→	→	PUNCT
ejpam-1949	232	28	x	x	X
ejpam-1949	232	29	with	with	ADP
ejpam-1949	232	30	r	r	NOUN
ejpam-1949	232	31	/	/	SYM
ejpam-1949	232	32	z	z	NOUN
ejpam-1949	232	33	coefficients	coefficient	NOUN
ejpam-1949	232	34	and	and	CCONJ
ejpam-1949	232	35	the	the	DET
ejpam-1949	232	36	construction	construction	NOUN
ejpam-1949	232	37	of	of	ADP
ejpam-1949	232	38	an	an	DET
ejpam-1949	232	39	isomorphism	isomorphism	NOUN
ejpam-1949	232	40	between	between	ADP
ejpam-1949	232	41	this	this	DET
ejpam-1949	232	42	group	group	NOUN
ejpam-1949	232	43	and	and	CCONJ
ejpam-1949	232	44	the	the	DET
ejpam-1949	232	45	group	group	NOUN
ejpam-1949	232	46	of	of	ADP
ejpam-1949	232	47	homomorphisms	homomorphism	NOUN
ejpam-1949	232	48	from	from	ADP
ejpam-1949	232	49	the	the	DET
ejpam-1949	232	50	relative	relative	ADJ
ejpam-1949	232	51	k	k	NOUN
ejpam-1949	232	52	-	-	NOUN
ejpam-1949	232	53	homology	homology	NOUN
ejpam-1949	232	54	of	of	ADP
ejpam-1949	232	55	ρ	ρ	PROPN
ejpam-1949	233	1	[	[	X
ejpam-1949	233	2	8	8	NUM
ejpam-1949	233	3	]	]	PUNCT
ejpam-1949	233	4	to	to	ADP
ejpam-1949	233	5	r	r	PROPN
ejpam-1949	233	6	/	/	SYM
ejpam-1949	233	7	z.	z.	PROPN
ejpam-1949	233	8	let	let	VERB
ejpam-1949	233	9	ρ	ρ	NOUN
ejpam-1949	233	10	:	:	PUNCT
ejpam-1949	233	11	y	y	PROPN
ejpam-1949	233	12	→	→	PUNCT
ejpam-1949	233	13	x	x	PUNCT
ejpam-1949	233	14	be	be	AUX
ejpam-1949	233	15	a	a	DET
ejpam-1949	233	16	smooth	smooth	ADJ
ejpam-1949	233	17	map	map	NOUN
ejpam-1949	233	18	between	between	ADP
ejpam-1949	233	19	two	two	NUM
ejpam-1949	233	20	smooth	smooth	ADJ
ejpam-1949	233	21	compact	compact	ADJ
ejpam-1949	233	22	manifolds	manifold	NOUN
ejpam-1949	233	23	.	.	PUNCT
ejpam-1949	234	1	we	we	PRON
ejpam-1949	234	2	write	write	VERB
ejpam-1949	234	3	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	234	4	,	,	PUNCT
ejpam-1949	234	5	r	r	NOUN
ejpam-1949	234	6	/	/	SYM
ejpam-1949	234	7	z	z	NOUN
ejpam-1949	234	8	)	)	PUNCT
ejpam-1949	234	9	for	for	ADP
ejpam-1949	234	10	the	the	DET
ejpam-1949	234	11	set	set	NOUN
ejpam-1949	234	12	of	of	ADP
ejpam-1949	234	13	relative	relative	ADJ
ejpam-1949	234	14	k	k	NOUN
ejpam-1949	234	15	-	-	PUNCT
ejpam-1949	234	16	cochains	cochain	NOUN
ejpam-1949	234	17	of	of	ADP
ejpam-1949	234	18	the	the	DET
ejpam-1949	234	19	form	form	NOUN
ejpam-1949	234	20	(	(	PUNCT
ejpam-1949	234	21	(	(	PUNCT
ejpam-1949	234	22	cx	cx	INTJ
ejpam-1949	234	23	,	,	PUNCT
ejpam-1949	234	24	hx	hx	PROPN
ejpam-1949	234	25	,	,	PUNCT
ejpam-1949	234	26	0	0	NUM
ejpam-1949	234	27	)	)	PUNCT
ejpam-1949	234	28	,	,	PUNCT
ejpam-1949	234	29	(	(	PUNCT
ejpam-1949	234	30	cy	cy	PROPN
ejpam-1949	234	31	,	,	PUNCT
ejpam-1949	234	32	hy	hy	PROPN
ejpam-1949	234	33	,	,	PUNCT
ejpam-1949	234	34	0	0	NUM
ejpam-1949	234	35	)	)	PUNCT
ejpam-1949	234	36	)	)	PUNCT
ejpam-1949	234	37	.	.	PUNCT
ejpam-1949	235	1	the	the	DET
ejpam-1949	235	2	set	set	NOUN
ejpam-1949	235	3	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	235	4	,	,	PUNCT
ejpam-1949	235	5	r	r	NOUN
ejpam-1949	235	6	/	/	SYM
ejpam-1949	235	7	z	z	NOUN
ejpam-1949	235	8	)	)	PUNCT
ejpam-1949	235	9	is	be	AUX
ejpam-1949	235	10	in	in	ADP
ejpam-1949	235	11	fact	fact	NOUN
ejpam-1949	235	12	an	an	DET
ejpam-1949	235	13	abelian	abelian	ADJ
ejpam-1949	235	14	subgroup	subgroup	NOUN
ejpam-1949	235	15	of	of	ADP
ejpam-1949	235	16	ľ∗(ρ	ľ∗(ρ	PROPN
ejpam-1949	235	17	)	)	PUNCT
ejpam-1949	235	18	.	.	PUNCT
ejpam-1949	236	1	note	note	VERB
ejpam-1949	236	2	that	that	SCONJ
ejpam-1949	236	3	the	the	DET
ejpam-1949	236	4	image	image	NOUN
ejpam-1949	236	5	of	of	ADP
ejpam-1949	236	6	the	the	DET
ejpam-1949	236	7	restriction	restriction	NOUN
ejpam-1949	236	8	of	of	ADP
ejpam-1949	236	9	δ̌	δ̌	NOUN
ejpam-1949	236	10	:	:	PUNCT
ejpam-1949	236	11	ľ∗(ρ)→	ľ∗(ρ)→	PROPN
ejpam-1949	236	12	ľ∗+1(ρ	ľ∗+1(ρ	PROPN
ejpam-1949	236	13	)	)	PUNCT
ejpam-1949	236	14	to	to	ADP
ejpam-1949	236	15	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	236	16	,	,	PUNCT
ejpam-1949	236	17	r	r	NOUN
ejpam-1949	236	18	/	/	SYM
ejpam-1949	236	19	z	z	NOUN
ejpam-1949	236	20	)	)	PUNCT
ejpam-1949	236	21	is	be	AUX
ejpam-1949	236	22	included	include	VERB
ejpam-1949	236	23	in	in	ADP
ejpam-1949	236	24	ľ∗+1(ρ	ľ∗+1(ρ	PROPN
ejpam-1949	236	25	,	,	PUNCT
ejpam-1949	236	26	r	r	NOUN
ejpam-1949	236	27	/	/	SYM
ejpam-1949	236	28	z	z	NOUN
ejpam-1949	236	29	)	)	PUNCT
ejpam-1949	236	30	.	.	PUNCT
ejpam-1949	237	1	the	the	DET
ejpam-1949	237	2	kernel	kernel	NOUN
ejpam-1949	237	3	of	of	ADP
ejpam-1949	237	4	δ̌	δ̌	PROPN
ejpam-1949	237	5	:	:	PUNCT
ejpam-1949	237	6	ľ∗(ρ	ľ∗(ρ	NOUN
ejpam-1949	237	7	,	,	PUNCT
ejpam-1949	237	8	r	r	NOUN
ejpam-1949	237	9	/	/	SYM
ejpam-1949	237	10	z	z	NOUN
ejpam-1949	237	11	)	)	PUNCT
ejpam-1949	237	12	→	→	SYM
ejpam-1949	237	13	ľ∗+1(ρ	ľ∗+1(ρ	PROPN
ejpam-1949	237	14	,	,	PUNCT
ejpam-1949	237	15	r	r	NOUN
ejpam-1949	237	16	/	/	SYM
ejpam-1949	237	17	z	z	NOUN
ejpam-1949	237	18	)	)	PUNCT
ejpam-1949	237	19	is	be	AUX
ejpam-1949	237	20	denoted	denote	VERB
ejpam-1949	237	21	by	by	ADP
ejpam-1949	237	22	ž∗(ρ	ž∗(ρ	NOUN
ejpam-1949	237	23	,	,	PUNCT
ejpam-1949	237	24	r	r	NOUN
ejpam-1949	237	25	/	/	SYM
ejpam-1949	237	26	z	z	NOUN
ejpam-1949	237	27	)	)	PUNCT
ejpam-1949	237	28	and	and	CCONJ
ejpam-1949	237	29	the	the	DET
ejpam-1949	237	30	image	image	NOUN
ejpam-1949	237	31	of	of	ADP
ejpam-1949	237	32	δ̌	δ̌	NOUN
ejpam-1949	237	33	:	:	PUNCT
ejpam-1949	237	34	ľ∗−1(ρ	ľ∗−1(ρ	PROPN
ejpam-1949	237	35	,	,	PUNCT
ejpam-1949	237	36	r	r	NOUN
ejpam-1949	237	37	/	/	SYM
ejpam-1949	237	38	z)→	z)→	NOUN
ejpam-1949	237	39	ľ∗(ρ	ľ∗(ρ	PROPN
ejpam-1949	237	40	,	,	PUNCT
ejpam-1949	237	41	r	r	NOUN
ejpam-1949	237	42	/	/	SYM
ejpam-1949	237	43	z	z	NOUN
ejpam-1949	237	44	)	)	PUNCT
ejpam-1949	237	45	is	be	AUX
ejpam-1949	237	46	denoted	denote	VERB
ejpam-1949	237	47	by	by	ADP
ejpam-1949	237	48	b̌∗(ρ	b̌∗(ρ	NOUN
ejpam-1949	237	49	,	,	PUNCT
ejpam-1949	237	50	r	r	NOUN
ejpam-1949	237	51	/	/	SYM
ejpam-1949	237	52	z	z	NOUN
ejpam-1949	237	53	)	)	PUNCT
ejpam-1949	237	54	.	.	PUNCT
ejpam-1949	238	1	definition	definition	NOUN
ejpam-1949	238	2	6	6	NUM
ejpam-1949	238	3	.	.	PUNCT
ejpam-1949	239	1	we	we	PRON
ejpam-1949	239	2	define	define	VERB
ejpam-1949	239	3	the	the	DET
ejpam-1949	239	4	relative	relative	ADJ
ejpam-1949	239	5	k	k	NOUN
ejpam-1949	239	6	-	-	NOUN
ejpam-1949	239	7	theory	theory	NOUN
ejpam-1949	239	8	of	of	ADP
ejpam-1949	239	9	ρ	ρ	PROPN
ejpam-1949	239	10	with	with	ADP
ejpam-1949	239	11	r	r	NOUN
ejpam-1949	239	12	/	/	SYM
ejpam-1949	239	13	z	z	NOUN
ejpam-1949	239	14	coefficients	coefficient	NOUN
ejpam-1949	239	15	,	,	PUNCT
ejpam-1949	239	16	denoted	denote	VERB
ejpam-1949	239	17	by	by	ADP
ejpam-1949	239	18	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	239	19	,	,	PUNCT
ejpam-1949	239	20	r	r	NOUN
ejpam-1949	239	21	/	/	SYM
ejpam-1949	239	22	z	z	NOUN
ejpam-1949	239	23	)	)	PUNCT
ejpam-1949	239	24	,	,	PUNCT
ejpam-1949	239	25	as	as	ADP
ejpam-1949	239	26	the	the	DET
ejpam-1949	239	27	quotient	quotient	NOUN
ejpam-1949	239	28	group	group	PROPN
ejpam-1949	239	29	ž∗(ρ	ž∗(ρ	PROPN
ejpam-1949	239	30	,	,	PUNCT
ejpam-1949	239	31	r	r	NOUN
ejpam-1949	239	32	/	/	SYM
ejpam-1949	239	33	z)/b̌∗(ρ	z)/b̌∗(ρ	NOUN
ejpam-1949	239	34	,	,	PUNCT
ejpam-1949	239	35	r	r	NOUN
ejpam-1949	239	36	/	/	SYM
ejpam-1949	239	37	z	z	NOUN
ejpam-1949	239	38	)	)	PUNCT
ejpam-1949	239	39	.	.	PUNCT
ejpam-1949	240	1	it	it	PRON
ejpam-1949	240	2	is	be	AUX
ejpam-1949	240	3	obvious	obvious	ADJ
ejpam-1949	240	4	that	that	SCONJ
ejpam-1949	240	5	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	240	6	,	,	PUNCT
ejpam-1949	240	7	r	r	NOUN
ejpam-1949	240	8	/	/	SYM
ejpam-1949	240	9	z	z	NOUN
ejpam-1949	240	10	)	)	PUNCT
ejpam-1949	240	11	is	be	AUX
ejpam-1949	240	12	an	an	DET
ejpam-1949	240	13	abelian	abelian	ADJ
ejpam-1949	240	14	subgroup	subgroup	NOUN
ejpam-1949	240	15	of	of	ADP
ejpam-1949	240	16	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	240	17	)	)	PUNCT
ejpam-1949	240	18	.	.	PUNCT
ejpam-1949	241	1	let	let	VERB
ejpam-1949	241	2	us	we	PRON
ejpam-1949	241	3	recall	recall	VERB
ejpam-1949	241	4	the	the	DET
ejpam-1949	241	5	six	six	NUM
ejpam-1949	241	6	-	-	PUNCT
ejpam-1949	241	7	term	term	NOUN
ejpam-1949	241	8	exact	exact	ADJ
ejpam-1949	241	9	sequence	sequence	NOUN
ejpam-1949	241	10	in	in	ADP
ejpam-1949	241	11	section	section	NOUN
ejpam-1949	241	12	3	3	NUM
ejpam-1949	241	13	:	:	PUNCT
ejpam-1949	241	14	k̂0(x	k̂0(x	NOUN
ejpam-1949	241	15	)	)	PUNCT
ejpam-1949	241	16	ρ∗	ρ∗	PROPN
ejpam-1949	241	17	//	//	SYM
ejpam-1949	241	18	k̂0(y	k̂0(y	PROPN
ejpam-1949	241	19	)	)	PUNCT
ejpam-1949	241	20	θ	θ	PROPN
ejpam-1949	241	21	//	//	SYM
ejpam-1949	241	22	ǩ0(ρ	ǩ0(ρ	PROPN
ejpam-1949	241	23	)	)	PUNCT
ejpam-1949	241	24	j	j	PROPN
ejpam-1949	241	25	�	�	PROPN
ejpam-1949	241	26	�	�	PROPN
ejpam-1949	241	27	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	241	28	)	)	PUNCT
ejpam-1949	241	29	j	j	PROPN
ejpam-1949	241	30	oo	oo	PROPN
ejpam-1949	241	31	k̂1(y	k̂1(y	PROPN
ejpam-1949	241	32	)	)	PUNCT
ejpam-1949	241	33	θoo	θoo	PROPN
ejpam-1949	241	34	k̂1(x	k̂1(x	PROPN
ejpam-1949	241	35	)	)	PUNCT
ejpam-1949	242	1	ρ∗oo	ρ∗oo	PUNCT
ejpam-1949	243	1	note	note	VERB
ejpam-1949	243	2	that	that	SCONJ
ejpam-1949	243	3	the	the	DET
ejpam-1949	243	4	image	image	NOUN
ejpam-1949	243	5	of	of	ADP
ejpam-1949	243	6	the	the	DET
ejpam-1949	243	7	restriction	restriction	NOUN
ejpam-1949	243	8	of	of	ADP
ejpam-1949	243	9	j	j	PROPN
ejpam-1949	243	10	to	to	ADP
ejpam-1949	243	11	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	243	12	,	,	PUNCT
ejpam-1949	243	13	r	r	NOUN
ejpam-1949	243	14	/	/	SYM
ejpam-1949	243	15	z	z	NOUN
ejpam-1949	243	16	)	)	PUNCT
ejpam-1949	243	17	is	be	AUX
ejpam-1949	243	18	included	include	VERB
ejpam-1949	243	19	in	in	ADP
ejpam-1949	243	20	hom(k∗−1(x	hom(k∗−1(x	NOUN
ejpam-1949	243	21	)	)	PUNCT
ejpam-1949	243	22	,	,	PUNCT
ejpam-1949	244	1	r	r	X
ejpam-1949	244	2	/	/	SYM
ejpam-1949	244	3	z	z	NOUN
ejpam-1949	244	4	)	)	PUNCT
ejpam-1949	244	5	,	,	PUNCT
ejpam-1949	244	6	and	and	CCONJ
ejpam-1949	244	7	the	the	DET
ejpam-1949	244	8	image	image	NOUN
ejpam-1949	244	9	of	of	ADP
ejpam-1949	244	10	the	the	DET
ejpam-1949	244	11	restriction	restriction	NOUN
ejpam-1949	244	12	of	of	ADP
ejpam-1949	244	13	θ	θ	PROPN
ejpam-1949	244	14	to	to	ADP
ejpam-1949	244	15	hom(k∗(y	hom(k∗(y	PROPN
ejpam-1949	244	16	)	)	PUNCT
ejpam-1949	244	17	,	,	PUNCT
ejpam-1949	244	18	r	r	NOUN
ejpam-1949	244	19	/	/	SYM
ejpam-1949	244	20	z	z	NOUN
ejpam-1949	244	21	)	)	PUNCT
ejpam-1949	244	22	is	be	AUX
ejpam-1949	244	23	included	include	VERB
ejpam-1949	244	24	in	in	ADP
ejpam-1949	244	25	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	244	26	,	,	PUNCT
ejpam-1949	244	27	r	r	NOUN
ejpam-1949	244	28	/	/	SYM
ejpam-1949	244	29	z	z	NOUN
ejpam-1949	244	30	)	)	PUNCT
ejpam-1949	244	31	.	.	PUNCT
ejpam-1949	245	1	let	let	VERB
ejpam-1949	245	2	k∗(x	k∗(x	NOUN
ejpam-1949	245	3	,	,	PUNCT
ejpam-1949	245	4	r	r	NOUN
ejpam-1949	245	5	/	/	SYM
ejpam-1949	245	6	z	z	NOUN
ejpam-1949	245	7	)	)	PUNCT
ejpam-1949	245	8	,	,	PUNCT
ejpam-1949	245	9	the	the	DET
ejpam-1949	245	10	k	k	NOUN
ejpam-1949	245	11	-	-	NOUN
ejpam-1949	245	12	theory	theory	NOUN
ejpam-1949	245	13	of	of	ADP
ejpam-1949	245	14	x	x	PUNCT
ejpam-1949	245	15	with	with	ADP
ejpam-1949	245	16	r	r	NOUN
ejpam-1949	245	17	/	/	SYM
ejpam-1949	245	18	z	z	NOUN
ejpam-1949	245	19	coefficients	coefficient	NOUN
ejpam-1949	245	20	.	.	PUNCT
ejpam-1949	246	1	we	we	PRON
ejpam-1949	246	2	have	have	VERB
ejpam-1949	246	3	the	the	DET
ejpam-1949	246	4	six	six	NUM
ejpam-1949	246	5	-	-	PUNCT
ejpam-1949	246	6	term	term	NOUN
ejpam-1949	246	7	exact	exact	ADJ
ejpam-1949	246	8	sequence	sequence	NOUN
ejpam-1949	246	9	k0(x	k0(x	NOUN
ejpam-1949	246	10	,	,	PUNCT
ejpam-1949	246	11	r	r	NOUN
ejpam-1949	246	12	/	/	SYM
ejpam-1949	246	13	z	z	NOUN
ejpam-1949	246	14	)	)	PUNCT
ejpam-1949	246	15	ρ∗	ρ∗	PROPN
ejpam-1949	246	16	//	//	SYM
ejpam-1949	246	17	k0(y	k0(y	X
ejpam-1949	246	18	,	,	PUNCT
ejpam-1949	246	19	r	r	NOUN
ejpam-1949	246	20	/	/	SYM
ejpam-1949	246	21	z	z	NOUN
ejpam-1949	246	22	)	)	PUNCT
ejpam-1949	246	23	θ	θ	PROPN
ejpam-1949	246	24	//	//	SYM
ejpam-1949	246	25	ǩ0(ρ	ǩ0(ρ	PROPN
ejpam-1949	246	26	,	,	PUNCT
ejpam-1949	246	27	r	r	NOUN
ejpam-1949	246	28	/	/	SYM
ejpam-1949	246	29	z	z	NOUN
ejpam-1949	246	30	)	)	PUNCT
ejpam-1949	246	31	j	j	PROPN
ejpam-1949	246	32	�	�	PROPN
ejpam-1949	246	33	�	�	PROPN
ejpam-1949	246	34	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	246	35	,	,	PUNCT
ejpam-1949	246	36	r	r	NOUN
ejpam-1949	246	37	/	/	SYM
ejpam-1949	246	38	z	z	NOUN
ejpam-1949	246	39	)	)	PUNCT
ejpam-1949	246	40	j	j	PROPN
ejpam-1949	246	41	oo	oo	INTJ
ejpam-1949	246	42	k1(y	k1(y	PROPN
ejpam-1949	246	43	,	,	PUNCT
ejpam-1949	246	44	r	r	NOUN
ejpam-1949	246	45	/	/	SYM
ejpam-1949	246	46	z)θoo	z)θoo	PROPN
ejpam-1949	246	47	k1(x	k1(x	PROPN
ejpam-1949	246	48	,	,	PUNCT
ejpam-1949	246	49	r	r	NOUN
ejpam-1949	246	50	/	/	SYM
ejpam-1949	246	51	z	z	NOUN
ejpam-1949	246	52	)	)	PUNCT
ejpam-1949	246	53	ρ∗oo	ρ∗oo	NOUN
ejpam-1949	246	54	obtained	obtain	VERB
ejpam-1949	246	55	from	from	ADP
ejpam-1949	246	56	the	the	DET
ejpam-1949	246	57	above	above	ADJ
ejpam-1949	246	58	exact	exact	ADJ
ejpam-1949	246	59	sequence	sequence	NOUN
ejpam-1949	246	60	and	and	CCONJ
ejpam-1949	246	61	after	after	ADP
ejpam-1949	246	62	identification	identification	NOUN
ejpam-1949	246	63	of	of	ADP
ejpam-1949	246	64	the	the	DET
ejpam-1949	246	65	groups	group	NOUN
ejpam-1949	246	66	k∗(x	k∗(x	ADP
ejpam-1949	246	67	,	,	PUNCT
ejpam-1949	246	68	r	r	NOUN
ejpam-1949	246	69	/	/	SYM
ejpam-1949	246	70	z	z	NOUN
ejpam-1949	246	71	)	)	PUNCT
ejpam-1949	246	72	and	and	CCONJ
ejpam-1949	246	73	hom(k∗(x	hom(k∗(x	ADP
ejpam-1949	246	74	)	)	PUNCT
ejpam-1949	246	75	,	,	PUNCT
ejpam-1949	246	76	r	r	NOUN
ejpam-1949	246	77	/	/	SYM
ejpam-1949	246	78	z	z	NOUN
ejpam-1949	246	79	)	)	PUNCT
ejpam-1949	246	80	following	follow	VERB
ejpam-1949	246	81	[	[	X
ejpam-1949	246	82	2	2	NUM
ejpam-1949	246	83	]	]	PUNCT
ejpam-1949	246	84	.	.	PUNCT
ejpam-1949	247	1	now	now	ADV
ejpam-1949	247	2	,	,	PUNCT
ejpam-1949	247	3	we	we	PRON
ejpam-1949	247	4	show	show	VERB
ejpam-1949	247	5	that	that	SCONJ
ejpam-1949	247	6	the	the	DET
ejpam-1949	247	7	group	group	NOUN
ejpam-1949	247	8	ǩ∗(ρ	ǩ∗(ρ	PROPN
ejpam-1949	247	9	,	,	PUNCT
ejpam-1949	247	10	r	r	NOUN
ejpam-1949	247	11	/	/	SYM
ejpam-1949	247	12	z	z	NOUN
ejpam-1949	247	13	)	)	PUNCT
ejpam-1949	247	14	can	can	AUX
ejpam-1949	247	15	be	be	AUX
ejpam-1949	247	16	identified	identify	VERB
ejpam-1949	247	17	with	with	ADP
ejpam-1949	247	18	the	the	DET
ejpam-1949	247	19	group	group	NOUN
ejpam-1949	247	20	of	of	ADP
ejpam-1949	247	21	homomorphisms	homomorphism	NOUN
ejpam-1949	247	22	from	from	ADP
ejpam-1949	247	23	the	the	DET
ejpam-1949	247	24	relative	relative	ADJ
ejpam-1949	247	25	k	k	ADJ
ejpam-1949	247	26	-	-	PUNCT
ejpam-1949	247	27	homology	homology	NOUN
ejpam-1949	247	28	group	group	NOUN
ejpam-1949	247	29	k∗(ρ	k∗(ρ	PROPN
ejpam-1949	247	30	)	)	PUNCT
ejpam-1949	248	1	[	[	X
ejpam-1949	248	2	8	8	NUM
ejpam-1949	248	3	]	]	PUNCT
ejpam-1949	248	4	to	to	ADP
ejpam-1949	248	5	r	r	PROPN
ejpam-1949	248	6	/	/	SYM
ejpam-1949	248	7	z.	z.	PROPN
ejpam-1949	248	8	let	let	VERB
ejpam-1949	248	9	us	we	PRON
ejpam-1949	248	10	recall	recall	VERB
ejpam-1949	248	11	the	the	DET
ejpam-1949	248	12	construction	construction	NOUN
ejpam-1949	248	13	of	of	ADP
ejpam-1949	248	14	the	the	DET
ejpam-1949	248	15	group	group	NOUN
ejpam-1949	248	16	k∗(ρ	k∗(ρ	NOUN
ejpam-1949	248	17	)	)	PUNCT
ejpam-1949	248	18	following	follow	VERB
ejpam-1949	248	19	[	[	X
ejpam-1949	248	20	8	8	NUM
ejpam-1949	248	21	]	]	PUNCT
ejpam-1949	248	22	.	.	PUNCT
ejpam-1949	249	1	we	we	PRON
ejpam-1949	249	2	set	set	VERB
ejpam-1949	249	3	l∗(ρ	l∗(ρ	NOUN
ejpam-1949	249	4	)	)	PUNCT
ejpam-1949	249	5	:	:	PUNCT
ejpam-1949	250	1	=	=	SYM
ejpam-1949	250	2	l∗(x	l∗(x	ADP
ejpam-1949	250	3	)	)	PUNCT
ejpam-1949	250	4	×	×	NOUN
ejpam-1949	250	5	l∗−1(y	l∗−1(y	ADV
ejpam-1949	250	6	)	)	PUNCT
ejpam-1949	250	7	a.	a.	NOUN
ejpam-1949	250	8	elmrabty	elmrabty	NOUN
ejpam-1949	250	9	,	,	PUNCT
ejpam-1949	250	10	m.	m.	NOUN
ejpam-1949	250	11	maghfoul	maghfoul	PROPN
ejpam-1949	250	12	/	/	SYM
ejpam-1949	250	13	eur	eur	PROPN
ejpam-1949	250	14	.	.	PUNCT
ejpam-1949	251	1	j.	j.	PROPN
ejpam-1949	251	2	pure	pure	PROPN
ejpam-1949	251	3	appl	appl	PROPN
ejpam-1949	251	4	.	.	PROPN
ejpam-1949	251	5	math	math	PROPN
ejpam-1949	251	6	,	,	PUNCT
ejpam-1949	251	7	7	7	NUM
ejpam-1949	251	8	(	(	PUNCT
ejpam-1949	251	9	2014	2014	NUM
ejpam-1949	251	10	)	)	PUNCT
ejpam-1949	251	11	,	,	PUNCT
ejpam-1949	251	12	65	65	NUM
ejpam-1949	251	13	-	-	SYM
ejpam-1949	251	14	76	76	NUM
ejpam-1949	251	15	74	74	NUM
ejpam-1949	251	16	and	and	CCONJ
ejpam-1949	251	17	define	define	VERB
ejpam-1949	251	18	a	a	DET
ejpam-1949	251	19	boundary	boundary	ADJ
ejpam-1949	251	20	map	map	NOUN
ejpam-1949	252	1	∂̂	∂̂	NOUN
ejpam-1949	252	2	:	:	PUNCT
ejpam-1949	252	3	l∗(ρ)→	l∗(ρ)→	PROPN
ejpam-1949	252	4	l∗−1(ρ	l∗−1(ρ	NOUN
ejpam-1949	252	5	)	)	PUNCT
ejpam-1949	252	6	by	by	ADP
ejpam-1949	252	7	the	the	DET
ejpam-1949	252	8	formula	formula	NOUN
ejpam-1949	252	9	:	:	PUNCT
ejpam-1949	252	10	∂̂	∂̂	PROPN
ejpam-1949	252	11	(	(	PUNCT
ejpam-1949	252	12	α	α	X
ejpam-1949	252	13	,	,	PUNCT
ejpam-1949	252	14	β	β	NOUN
ejpam-1949	252	15	)	)	PUNCT
ejpam-1949	252	16	:	:	PUNCT
ejpam-1949	252	17	=	=	SYM
ejpam-1949	252	18	(	(	PUNCT
ejpam-1949	252	19	∂	∂	X
ejpam-1949	252	20	α+ρ∗β	α+ρ∗β	NOUN
ejpam-1949	252	21	,	,	PUNCT
ejpam-1949	252	22	−∂	−∂	PROPN
ejpam-1949	252	23	β	β	X
ejpam-1949	252	24	)	)	PUNCT
ejpam-1949	252	25	.	.	PUNCT
ejpam-1949	253	1	let	let	AUX
ejpam-1949	253	2	c∗(ρ	c∗(ρ	NOUN
ejpam-1949	253	3	)	)	PUNCT
ejpam-1949	253	4	denote	denote	VERB
ejpam-1949	253	5	the	the	DET
ejpam-1949	253	6	kernel	kernel	NOUN
ejpam-1949	253	7	of	of	ADP
ejpam-1949	253	8	∂̂	∂̂	PROPN
ejpam-1949	253	9	.	.	PUNCT
ejpam-1949	254	1	there	there	PRON
ejpam-1949	254	2	is	be	VERB
ejpam-1949	254	3	a	a	DET
ejpam-1949	254	4	well	well	ADV
ejpam-1949	254	5	-	-	PUNCT
ejpam-1949	254	6	defined	define	VERB
ejpam-1949	254	7	operation	operation	NOUN
ejpam-1949	254	8	on	on	ADP
ejpam-1949	254	9	c∗(ρ	c∗(ρ	NOUN
ejpam-1949	254	10	)	)	PUNCT
ejpam-1949	254	11	given	give	VERB
ejpam-1949	254	12	by	by	ADP
ejpam-1949	254	13	disjoint	disjoint	NOUN
ejpam-1949	254	14	union	union	PROPN
ejpam-1949	254	15	of	of	ADP
ejpam-1949	254	16	k	k	PROPN
ejpam-1949	254	17	-	-	PUNCT
ejpam-1949	254	18	chains	chain	NOUN
ejpam-1949	254	19	,	,	PUNCT
ejpam-1949	254	20	(	(	PUNCT
ejpam-1949	254	21	α	α	X
ejpam-1949	254	22	,	,	PUNCT
ejpam-1949	254	23	β	β	NOUN
ejpam-1949	254	24	)	)	PUNCT
ejpam-1949	255	1	+	+	CCONJ
ejpam-1949	255	2	(	(	PUNCT
ejpam-1949	255	3	α′,β	α′,β	NOUN
ejpam-1949	255	4	′	′	NUM
ejpam-1949	255	5	)	)	PUNCT
ejpam-1949	255	6	:	:	PUNCT
ejpam-1949	255	7	=	=	X
ejpam-1949	255	8	(	(	PUNCT
ejpam-1949	255	9	αtα′,β	αtα′,β	X
ejpam-1949	255	10	t	t	NOUN
ejpam-1949	255	11	β	β	X
ejpam-1949	255	12	′	′	NUM
ejpam-1949	255	13	)	)	PUNCT
ejpam-1949	255	14	.	.	PUNCT
ejpam-1949	256	1	bordism	bordism	NOUN
ejpam-1949	256	2	.	.	PUNCT
ejpam-1949	257	1	two	two	NUM
ejpam-1949	257	2	elements	element	NOUN
ejpam-1949	257	3	(	(	PUNCT
ejpam-1949	257	4	α	α	X
ejpam-1949	257	5	,	,	PUNCT
ejpam-1949	257	6	β	β	NOUN
ejpam-1949	257	7	)	)	PUNCT
ejpam-1949	257	8	and	and	CCONJ
ejpam-1949	257	9	(	(	PUNCT
ejpam-1949	257	10	α′,β	α′,β	NOUN
ejpam-1949	257	11	′	′	NOUN
ejpam-1949	257	12	)	)	PUNCT
ejpam-1949	257	13	in	in	ADP
ejpam-1949	257	14	c∗(ρ	c∗(ρ	NOUN
ejpam-1949	257	15	)	)	PUNCT
ejpam-1949	257	16	are	be	AUX
ejpam-1949	257	17	bordant	bordant	ADJ
ejpam-1949	257	18	if	if	SCONJ
ejpam-1949	257	19	there	there	PRON
ejpam-1949	257	20	exists	exist	VERB
ejpam-1949	257	21	(	(	PUNCT
ejpam-1949	257	22	σ	σ	PROPN
ejpam-1949	257	23	,	,	PUNCT
ejpam-1949	257	24	τ	τ	PROPN
ejpam-1949	257	25	)	)	PUNCT
ejpam-1949	257	26	∈	∈	PROPN
ejpam-1949	257	27	l∗+1(ρ	l∗+1(ρ	PROPN
ejpam-1949	257	28	)	)	PUNCT
ejpam-1949	257	29	such	such	ADJ
ejpam-1949	257	30	that	that	SCONJ
ejpam-1949	257	31	(	(	PUNCT
ejpam-1949	257	32	α	α	NOUN
ejpam-1949	257	33	,	,	PUNCT
ejpam-1949	257	34	β	β	NOUN
ejpam-1949	257	35	)	)	PUNCT
ejpam-1949	257	36	+	+	CCONJ
ejpam-1949	257	37	(	(	PUNCT
ejpam-1949	257	38	−α′,−β	−α′,−β	NOUN
ejpam-1949	257	39	′	′	NOUN
ejpam-1949	257	40	)	)	PUNCT
ejpam-1949	257	41	=	=	PUNCT
ejpam-1949	258	1	∂̂	∂̂	PROPN
ejpam-1949	258	2	(	(	PUNCT
ejpam-1949	258	3	σ	σ	PROPN
ejpam-1949	258	4	,	,	PUNCT
ejpam-1949	258	5	τ	τ	PROPN
ejpam-1949	258	6	)	)	PUNCT
ejpam-1949	258	7	.	.	PUNCT
ejpam-1949	259	1	definition	definition	NOUN
ejpam-1949	259	2	7	7	NUM
ejpam-1949	259	3	.	.	PUNCT
ejpam-1949	260	1	we	we	PRON
ejpam-1949	260	2	define	define	VERB
ejpam-1949	260	3	the	the	DET
ejpam-1949	260	4	relative	relative	ADJ
ejpam-1949	260	5	k	k	ADJ
ejpam-1949	260	6	-	-	PUNCT
ejpam-1949	260	7	homology	homology	NOUN
ejpam-1949	260	8	group	group	NOUN
ejpam-1949	260	9	k∗(ρ	k∗(ρ	PROPN
ejpam-1949	260	10	)	)	PUNCT
ejpam-1949	260	11	as	as	SCONJ
ejpam-1949	260	12	the	the	DET
ejpam-1949	260	13	group	group	NOUN
ejpam-1949	260	14	obtained	obtain	VERB
ejpam-1949	260	15	from	from	ADP
ejpam-1949	260	16	quotienting	quotiente	VERB
ejpam-1949	260	17	c∗(ρ	c∗(ρ	NOUN
ejpam-1949	260	18	)	)	PUNCT
ejpam-1949	260	19	by	by	ADP
ejpam-1949	260	20	the	the	DET
ejpam-1949	260	21	equivalence	equivalence	NOUN
ejpam-1949	260	22	relation	relation	NOUN
ejpam-1949	260	23	of	of	ADP
ejpam-1949	260	24	bordism	bordism	NOUN
ejpam-1949	260	25	.	.	PUNCT
ejpam-1949	261	1	we	we	PRON
ejpam-1949	261	2	denote	denote	VERB
ejpam-1949	261	3	by	by	ADP
ejpam-1949	261	4	k̂∗(ρ	k̂∗(ρ	NOUN
ejpam-1949	261	5	,	,	PUNCT
ejpam-1949	261	6	r	r	NOUN
ejpam-1949	261	7	/	/	SYM
ejpam-1949	261	8	z	z	NOUN
ejpam-1949	261	9	)	)	PUNCT
ejpam-1949	261	10	the	the	DET
ejpam-1949	261	11	group	group	NOUN
ejpam-1949	261	12	of	of	ADP
ejpam-1949	261	13	homomorphisms	homomorphism	NOUN
ejpam-1949	261	14	from	from	ADP
ejpam-1949	261	15	k∗(ρ	k∗(ρ	NOUN
ejpam-1949	261	16	)	)	PUNCT
ejpam-1949	261	17	to	to	ADP
ejpam-1949	261	18	r	r	PROPN
ejpam-1949	261	19	/	/	SYM
ejpam-1949	261	20	z.	z.	NOUN
ejpam-1949	261	21	for	for	ADP
ejpam-1949	261	22	every	every	DET
ejpam-1949	261	23	k	k	PROPN
ejpam-1949	261	24	-	-	NOUN
ejpam-1949	261	25	cocycle	cocycle	NOUN
ejpam-1949	261	26	(	(	PUNCT
ejpam-1949	261	27	s	s	PROPN
ejpam-1949	261	28	,	,	PUNCT
ejpam-1949	261	29	t	t	NOUN
ejpam-1949	261	30	)	)	PUNCT
ejpam-1949	261	31	in	in	ADP
ejpam-1949	261	32	ž∗(ρ	ž∗(ρ	NUM
ejpam-1949	261	33	,	,	PUNCT
ejpam-1949	261	34	r	r	NOUN
ejpam-1949	261	35	/	/	SYM
ejpam-1949	261	36	z	z	NOUN
ejpam-1949	261	37	)	)	PUNCT
ejpam-1949	261	38	with	with	ADP
ejpam-1949	261	39	(	(	PUNCT
ejpam-1949	261	40	s	s	PROPN
ejpam-1949	261	41	,	,	PUNCT
ejpam-1949	261	42	t	t	NOUN
ejpam-1949	261	43	)	)	PUNCT
ejpam-1949	261	44	=	=	PUNCT
ejpam-1949	262	1	(	(	PUNCT
ejpam-1949	262	2	(	(	PUNCT
ejpam-1949	262	3	cx	cx	INTJ
ejpam-1949	262	4	,	,	PUNCT
ejpam-1949	262	5	hx	hx	PROPN
ejpam-1949	262	6	,	,	PUNCT
ejpam-1949	262	7	0	0	NUM
ejpam-1949	262	8	)	)	PUNCT
ejpam-1949	262	9	,	,	PUNCT
ejpam-1949	262	10	(	(	PUNCT
ejpam-1949	262	11	cy	cy	PROPN
ejpam-1949	262	12	,	,	PUNCT
ejpam-1949	262	13	hy	hy	PROPN
ejpam-1949	262	14	,	,	PUNCT
ejpam-1949	262	15	0	0	NUM
ejpam-1949	262	16	)	)	PUNCT
ejpam-1949	262	17	)	)	PUNCT
ejpam-1949	262	18	,	,	PUNCT
ejpam-1949	262	19	we	we	PRON
ejpam-1949	262	20	set	set	VERB
ejpam-1949	262	21	µ(s	µ(s	PROPN
ejpam-1949	262	22	,	,	PUNCT
ejpam-1949	262	23	t	t	NOUN
ejpam-1949	262	24	)	)	PUNCT
ejpam-1949	262	25	(	(	PUNCT
ejpam-1949	262	26	α	α	X
ejpam-1949	262	27	,	,	PUNCT
ejpam-1949	262	28	β	β	NOUN
ejpam-1949	262	29	)	)	PUNCT
ejpam-1949	262	30	:	:	PUNCT
ejpam-1949	263	1	=	=	X
ejpam-1949	263	2	fhx(α	fhx(α	NOUN
ejpam-1949	263	3	)	)	PUNCT
ejpam-1949	263	4	+	+	NOUN
ejpam-1949	263	5	fhy(β	fhy(β	NOUN
ejpam-1949	263	6	)	)	PUNCT
ejpam-1949	263	7	for	for	ADP
ejpam-1949	263	8	all	all	DET
ejpam-1949	263	9	(	(	PUNCT
ejpam-1949	263	10	α	α	NOUN
ejpam-1949	263	11	,	,	PUNCT
ejpam-1949	263	12	β	β	NOUN
ejpam-1949	263	13	)	)	PUNCT
ejpam-1949	263	14	∈	∈	PROPN
ejpam-1949	263	15	c∗−1(ρ	c∗−1(ρ	NUM
ejpam-1949	263	16	)	)	PUNCT
ejpam-1949	263	17	.	.	PUNCT
ejpam-1949	264	1	if	if	SCONJ
ejpam-1949	264	2	(	(	PUNCT
ejpam-1949	264	3	s	s	X
ejpam-1949	264	4	,	,	PUNCT
ejpam-1949	264	5	t	t	NOUN
ejpam-1949	264	6	)	)	PUNCT
ejpam-1949	264	7	∈	∈	PROPN
ejpam-1949	264	8	ľ∗(ρ	ľ∗(ρ	PROPN
ejpam-1949	264	9	,	,	PUNCT
ejpam-1949	264	10	r	r	NOUN
ejpam-1949	264	11	/	/	SYM
ejpam-1949	264	12	z	z	NOUN
ejpam-1949	264	13	)	)	PUNCT
ejpam-1949	264	14	with	with	ADP
ejpam-1949	264	15	(	(	PUNCT
ejpam-1949	264	16	s	s	PROPN
ejpam-1949	264	17	,	,	PUNCT
ejpam-1949	264	18	t	t	NOUN
ejpam-1949	264	19	)	)	PUNCT
ejpam-1949	264	20	=	=	PUNCT
ejpam-1949	264	21	(	(	PUNCT
ejpam-1949	264	22	(	(	PUNCT
ejpam-1949	264	23	cx	cx	INTJ
ejpam-1949	264	24	,	,	PUNCT
ejpam-1949	264	25	hx	hx	PROPN
ejpam-1949	264	26	,	,	PUNCT
ejpam-1949	264	27	0	0	NUM
ejpam-1949	264	28	)	)	PUNCT
ejpam-1949	264	29	,	,	PUNCT
ejpam-1949	264	30	(	(	PUNCT
ejpam-1949	264	31	cy	cy	PROPN
ejpam-1949	264	32	,	,	PUNCT
ejpam-1949	264	33	hy	hy	PROPN
ejpam-1949	264	34	,	,	PUNCT
ejpam-1949	264	35	0	0	NUM
ejpam-1949	264	36	)	)	PUNCT
ejpam-1949	264	37	)	)	PUNCT
ejpam-1949	264	38	,	,	PUNCT
ejpam-1949	264	39	then	then	ADV
ejpam-1949	264	40	for	for	ADP
ejpam-1949	264	41	all	all	PRON
ejpam-1949	264	42	(	(	PUNCT
ejpam-1949	264	43	σ	σ	PROPN
ejpam-1949	264	44	,	,	PUNCT
ejpam-1949	264	45	τ	τ	PROPN
ejpam-1949	264	46	)	)	PUNCT
ejpam-1949	264	47	∈	∈	PROPN
ejpam-1949	264	48	l∗(ρ	l∗(ρ	NOUN
ejpam-1949	264	49	)	)	PUNCT
ejpam-1949	264	50	,	,	PUNCT
ejpam-1949	264	51	µ(s	µ(s	X
ejpam-1949	264	52	,	,	PUNCT
ejpam-1949	264	53	t	t	NOUN
ejpam-1949	264	54	)	)	PUNCT
ejpam-1949	264	55	(	(	PUNCT
ejpam-1949	264	56	∂̂	∂̂	PROPN
ejpam-1949	264	57	(	(	PUNCT
ejpam-1949	264	58	σ	σ	PROPN
ejpam-1949	264	59	,	,	PUNCT
ejpam-1949	264	60	τ	τ	PROPN
ejpam-1949	264	61	)	)	PUNCT
ejpam-1949	264	62	)	)	PUNCT
ejpam-1949	265	1	=	=	SYM
ejpam-1949	265	2	µ(s	µ(s	X
ejpam-1949	265	3	,	,	PUNCT
ejpam-1949	265	4	t	t	NOUN
ejpam-1949	265	5	)	)	PUNCT
ejpam-1949	265	6	(	(	PUNCT
ejpam-1949	265	7	∂	∂	NUM
ejpam-1949	265	8	σ+ρ∗τ,−∂	σ+ρ∗τ,−∂	NOUN
ejpam-1949	265	9	τ	τ	NOUN
ejpam-1949	265	10	)	)	PUNCT
ejpam-1949	265	11	=	=	PROPN
ejpam-1949	265	12	fhx(∂	fhx(∂	PROPN
ejpam-1949	265	13	σ	σ	PROPN
ejpam-1949	265	14	)	)	PUNCT
ejpam-1949	265	15	+	+	PROPN
ejpam-1949	265	16	fhx(ρ∗τ)−fhy(∂	fhx(ρ∗τ)−fhy(∂	ADJ
ejpam-1949	265	17	τ	τ	X
ejpam-1949	265	18	)	)	PUNCT
ejpam-1949	265	19	=	=	SYM
ejpam-1949	265	20	þδhx(σ	þδhx(σ	NOUN
ejpam-1949	265	21	)	)	PUNCT
ejpam-1949	266	1	+	+	CCONJ
ejpam-1949	266	2	(	(	PUNCT
ejpam-1949	266	3	àρ∗hx	àρ∗hx	ADP
ejpam-1949	266	4	−þδhy)(τ	−þδhy)(τ	NOUN
ejpam-1949	266	5	)	)	PUNCT
ejpam-1949	266	6	=	=	SYM
ejpam-1949	266	7	µ(δ̂(s	µ(δ̂(s	ADP
ejpam-1949	266	8	,	,	PUNCT
ejpam-1949	266	9	t	t	NOUN
ejpam-1949	266	10	)	)	PUNCT
ejpam-1949	266	11	)	)	PUNCT
ejpam-1949	266	12	(	(	PUNCT
ejpam-1949	266	13	σ	σ	PROPN
ejpam-1949	266	14	,	,	PUNCT
ejpam-1949	266	15	τ	τ	PROPN
ejpam-1949	266	16	)	)	PUNCT
ejpam-1949	266	17	.	.	PUNCT
ejpam-1949	267	1	it	it	PRON
ejpam-1949	267	2	follows	follow	VERB
ejpam-1949	267	3	that	that	SCONJ
ejpam-1949	267	4	µ	µ	PRON
ejpam-1949	267	5	induces	induce	VERB
ejpam-1949	267	6	a	a	DET
ejpam-1949	267	7	well	well	ADV
ejpam-1949	267	8	-	-	PUNCT
ejpam-1949	267	9	defined	define	VERB
ejpam-1949	267	10	homomorphism	homomorphism	PROPN
ejpam-1949	267	11	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	267	12	,	,	PUNCT
ejpam-1949	267	13	r	r	NOUN
ejpam-1949	267	14	/	/	SYM
ejpam-1949	267	15	z)→	z)→	NOUN
ejpam-1949	267	16	k̂∗−1(ρ	k̂∗−1(ρ	PROPN
ejpam-1949	267	17	,	,	PUNCT
ejpam-1949	267	18	r	r	NOUN
ejpam-1949	267	19	/	/	SYM
ejpam-1949	267	20	z	z	NOUN
ejpam-1949	267	21	)	)	PUNCT
ejpam-1949	267	22	,	,	PUNCT
ejpam-1949	267	23	also	also	ADV
ejpam-1949	267	24	denoted	denote	VERB
ejpam-1949	267	25	by	by	ADP
ejpam-1949	267	26	µ.	µ.	NOUN
ejpam-1949	267	27	proposition	proposition	NOUN
ejpam-1949	267	28	1	1	NUM
ejpam-1949	267	29	.	.	PUNCT
ejpam-1949	268	1	the	the	DET
ejpam-1949	268	2	homomorphism	homomorphism	PROPN
ejpam-1949	268	3	µ	µ	X
ejpam-1949	268	4	:	:	PUNCT
ejpam-1949	268	5	ǩ∗(ρ	ǩ∗(ρ	NOUN
ejpam-1949	268	6	,	,	PUNCT
ejpam-1949	268	7	r	r	NOUN
ejpam-1949	268	8	/	/	SYM
ejpam-1949	268	9	z)→	z)→	NOUN
ejpam-1949	268	10	k̂∗−1(ρ	k̂∗−1(ρ	PROPN
ejpam-1949	268	11	,	,	PUNCT
ejpam-1949	268	12	r	r	NOUN
ejpam-1949	268	13	/	/	SYM
ejpam-1949	268	14	z	z	NOUN
ejpam-1949	268	15	)	)	PUNCT
ejpam-1949	268	16	turns	turn	VERB
ejpam-1949	268	17	out	out	ADP
ejpam-1949	268	18	to	to	PART
ejpam-1949	268	19	be	be	AUX
ejpam-1949	268	20	an	an	DET
ejpam-1949	268	21	isomorphism	isomorphism	NOUN
ejpam-1949	268	22	.	.	PUNCT
ejpam-1949	269	1	proof	proof	NOUN
ejpam-1949	269	2	.	.	PUNCT
ejpam-1949	270	1	let	let	VERB
ejpam-1949	270	2	us	we	PRON
ejpam-1949	270	3	recall	recall	VERB
ejpam-1949	270	4	the	the	DET
ejpam-1949	270	5	six	six	NUM
ejpam-1949	270	6	-	-	PUNCT
ejpam-1949	270	7	term	term	NOUN
ejpam-1949	270	8	exact	exact	ADJ
ejpam-1949	270	9	sequence	sequence	NOUN
ejpam-1949	270	10	in	in	ADP
ejpam-1949	270	11	[	[	X
ejpam-1949	270	12	8	8	NUM
ejpam-1949	270	13	,	,	PUNCT
ejpam-1949	270	14	p.	p.	NOUN
ejpam-1949	270	15	8	8	NUM
ejpam-1949	271	1	]	]	SYM
ejpam-1949	271	2	:	:	PUNCT
ejpam-1949	271	3	k̂1(ρ	k̂1(ρ	NOUN
ejpam-1949	271	4	,	,	PUNCT
ejpam-1949	271	5	r	r	NOUN
ejpam-1949	271	6	/	/	SYM
ejpam-1949	271	7	z	z	NOUN
ejpam-1949	271	8	)	)	PUNCT
ejpam-1949	271	9	ζ	ζ	PROPN
ejpam-1949	271	10	//	//	NOUN
ejpam-1949	271	11	k1(x	k1(x	NOUN
ejpam-1949	271	12	,	,	PUNCT
ejpam-1949	271	13	r	r	NOUN
ejpam-1949	271	14	/	/	SYM
ejpam-1949	271	15	z	z	NOUN
ejpam-1949	271	16	)	)	PUNCT
ejpam-1949	271	17	ρ∗	ρ∗	PROPN
ejpam-1949	271	18	//	//	SYM
ejpam-1949	271	19	k1(y	k1(y	PROPN
ejpam-1949	271	20	,	,	PUNCT
ejpam-1949	271	21	r	r	NOUN
ejpam-1949	271	22	/	/	SYM
ejpam-1949	271	23	z	z	NOUN
ejpam-1949	271	24	)	)	PUNCT
ejpam-1949	271	25	∂	∂	NUM
ejpam-1949	271	26	�	�	PROPN
ejpam-1949	271	27	�	�	PROPN
ejpam-1949	271	28	k0(y	k0(y	PROPN
ejpam-1949	271	29	,	,	PUNCT
ejpam-1949	271	30	r	r	NOUN
ejpam-1949	271	31	/	/	SYM
ejpam-1949	271	32	z	z	NOUN
ejpam-1949	271	33	)	)	PUNCT
ejpam-1949	271	34	∂	∂	NOUN
ejpam-1949	271	35	oo	oo	INTJ
ejpam-1949	271	36	k0(x	k0(x	NOUN
ejpam-1949	271	37	,	,	PUNCT
ejpam-1949	271	38	r	r	NOUN
ejpam-1949	271	39	/	/	SYM
ejpam-1949	271	40	z	z	NOUN
ejpam-1949	271	41	)	)	PUNCT
ejpam-1949	271	42	ρ∗oo	ρ∗oo	PROPN
ejpam-1949	271	43	k̂0(ρ	k̂0(ρ	PROPN
ejpam-1949	271	44	,	,	PUNCT
ejpam-1949	271	45	r	r	PROPN
ejpam-1949	271	46	/	/	SYM
ejpam-1949	271	47	z	z	NOUN
ejpam-1949	271	48	)	)	PUNCT
ejpam-1949	271	49	ζoo	ζoo	NOUN
ejpam-1949	271	50	references	reference	NOUN
ejpam-1949	271	51	75	75	NUM
ejpam-1949	271	52	if	if	SCONJ
ejpam-1949	271	53	we	we	PRON
ejpam-1949	271	54	combine	combine	VERB
ejpam-1949	271	55	this	this	DET
ejpam-1949	271	56	six	six	NUM
ejpam-1949	271	57	-	-	PUNCT
ejpam-1949	271	58	term	term	NOUN
ejpam-1949	271	59	exact	exact	ADJ
ejpam-1949	271	60	sequence	sequence	NOUN
ejpam-1949	271	61	with	with	ADP
ejpam-1949	271	62	that	that	PRON
ejpam-1949	271	63	given	give	VERB
ejpam-1949	271	64	by	by	ADP
ejpam-1949	271	65	theorem	theorem	NOUN
ejpam-1949	271	66	1	1	NUM
ejpam-1949	271	67	,	,	PUNCT
ejpam-1949	271	68	then	then	ADV
ejpam-1949	271	69	we	we	PRON
ejpam-1949	271	70	obtain	obtain	VERB
ejpam-1949	271	71	the	the	DET
ejpam-1949	271	72	following	following	ADJ
ejpam-1949	271	73	commutative	commutative	ADJ
ejpam-1949	271	74	diagram	diagram	NOUN
ejpam-1949	271	75	k0(x	k0(x	NOUN
ejpam-1949	271	76	,	,	PUNCT
ejpam-1949	271	77	r	r	NOUN
ejpam-1949	271	78	/	/	SYM
ejpam-1949	271	79	z	z	NOUN
ejpam-1949	271	80	)	)	PUNCT
ejpam-1949	271	81	ρ∗	ρ∗	PROPN
ejpam-1949	271	82	//	//	SYM
ejpam-1949	271	83	k0(y	k0(y	X
ejpam-1949	271	84	,	,	PUNCT
ejpam-1949	271	85	r	r	NOUN
ejpam-1949	271	86	/	/	SYM
ejpam-1949	271	87	z	z	NOUN
ejpam-1949	271	88	)	)	PUNCT
ejpam-1949	271	89	θ	θ	PROPN
ejpam-1949	271	90	//	//	SYM
ejpam-1949	271	91	ǩ0(ρ	ǩ0(ρ	PROPN
ejpam-1949	271	92	,	,	PUNCT
ejpam-1949	271	93	r	r	NOUN
ejpam-1949	271	94	/	/	SYM
ejpam-1949	271	95	z	z	NOUN
ejpam-1949	271	96	)	)	PUNCT
ejpam-1949	271	97	j	j	PROPN
ejpam-1949	271	98	''	''	PUNCT
ejpam-1949	271	99	µ	µ	PROPN
ejpam-1949	271	100	�	�	PROPN
ejpam-1949	271	101	�	�	PROPN
ejpam-1949	271	102	ǩ1(ρ	ǩ1(ρ	PROPN
ejpam-1949	271	103	,	,	PUNCT
ejpam-1949	271	104	r	r	NOUN
ejpam-1949	271	105	/	/	SYM
ejpam-1949	271	106	z	z	NOUN
ejpam-1949	271	107	)	)	PUNCT
ejpam-1949	272	1	j	j	PROPN
ejpam-1949	272	2	gg	gg	PROPN
ejpam-1949	272	3	µ	µ	PROPN
ejpam-1949	272	4	�	�	PROPN
ejpam-1949	272	5	�	�	PROPN
ejpam-1949	272	6	k1(y	k1(y	PROPN
ejpam-1949	272	7	,	,	PUNCT
ejpam-1949	272	8	r	r	NOUN
ejpam-1949	272	9	/	/	SYM
ejpam-1949	272	10	z	z	NOUN
ejpam-1949	272	11	)	)	PUNCT
ejpam-1949	272	12	θ	θ	NOUN
ejpam-1949	273	1	oo	oo	INTJ
ejpam-1949	273	2	k1(x	k1(x	INTJ
ejpam-1949	273	3	,	,	PUNCT
ejpam-1949	273	4	r	r	NOUN
ejpam-1949	273	5	/	/	SYM
ejpam-1949	273	6	z	z	NOUN
ejpam-1949	273	7	)	)	PUNCT
ejpam-1949	273	8	ρ∗	ρ∗	PROPN
ejpam-1949	273	9	oo	oo	INTJ
ejpam-1949	273	10	k0(x	k0(x	PROPN
ejpam-1949	273	11	,	,	PUNCT
ejpam-1949	273	12	r	r	NOUN
ejpam-1949	273	13	/	/	SYM
ejpam-1949	273	14	z	z	NOUN
ejpam-1949	273	15	)	)	PUNCT
ejpam-1949	273	16	ρ∗	ρ∗	PROPN
ejpam-1949	273	17	//	//	SYM
ejpam-1949	274	1	k0(y	k0(y	X
ejpam-1949	274	2	,	,	PUNCT
ejpam-1949	274	3	r	r	NOUN
ejpam-1949	274	4	/	/	SYM
ejpam-1949	274	5	z	z	NOUN
ejpam-1949	274	6	)	)	PUNCT
ejpam-1949	274	7	∂	∂	NUM
ejpam-1949	274	8	//	//	NUM
ejpam-1949	274	9	k̂1(ρ	k̂1(ρ	PROPN
ejpam-1949	274	10	,	,	PUNCT
ejpam-1949	274	11	r	r	NOUN
ejpam-1949	274	12	/	/	SYM
ejpam-1949	274	13	z	z	NOUN
ejpam-1949	274	14	)	)	PUNCT
ejpam-1949	274	15	ζ	ζ	PROPN
ejpam-1949	274	16	''	''	PUNCT
ejpam-1949	274	17	k̂0(ρ	k̂0(ρ	NOUN
ejpam-1949	274	18	,	,	PUNCT
ejpam-1949	274	19	r	r	NOUN
ejpam-1949	274	20	/	/	SYM
ejpam-1949	274	21	z	z	NOUN
ejpam-1949	274	22	)	)	PUNCT
ejpam-1949	274	23	ζ	ζ	PROPN
ejpam-1949	274	24	gg	gg	PROPN
ejpam-1949	274	25	k1(y	k1(y	PROPN
ejpam-1949	274	26	,	,	PUNCT
ejpam-1949	274	27	r	r	NOUN
ejpam-1949	274	28	/	/	SYM
ejpam-1949	274	29	z	z	NOUN
ejpam-1949	274	30	)	)	PUNCT
ejpam-1949	274	31	∂	∂	NOUN
ejpam-1949	274	32	oo	oo	INTJ
ejpam-1949	274	33	k1(x	k1(x	NOUN
ejpam-1949	274	34	,	,	PUNCT
ejpam-1949	274	35	r	r	NOUN
ejpam-1949	274	36	/	/	SYM
ejpam-1949	274	37	z	z	NOUN
ejpam-1949	274	38	)	)	PUNCT
ejpam-1949	274	39	ρ∗	ρ∗	NOUN
ejpam-1949	274	40	oo	oo	INTJ
ejpam-1949	274	41	in	in	ADP
ejpam-1949	274	42	which	which	PRON
ejpam-1949	274	43	the	the	DET
ejpam-1949	274	44	rows	row	NOUN
ejpam-1949	274	45	are	be	AUX
ejpam-1949	274	46	exact	exact	ADJ
ejpam-1949	274	47	sequences	sequence	NOUN
ejpam-1949	274	48	.	.	PUNCT
ejpam-1949	275	1	it	it	PRON
ejpam-1949	275	2	follows	follow	VERB
ejpam-1949	275	3	from	from	ADP
ejpam-1949	275	4	the	the	DET
ejpam-1949	275	5	five	five	NUM
ejpam-1949	275	6	lemma	lemma	PROPN
ejpam-1949	275	7	that	that	SCONJ
ejpam-1949	275	8	the	the	DET
ejpam-1949	275	9	homomorphism	homomorphism	PROPN
ejpam-1949	275	10	µ	µ	X
ejpam-1949	275	11	is	be	AUX
ejpam-1949	275	12	an	an	DET
ejpam-1949	275	13	isomorphism	isomorphism	NOUN
ejpam-1949	275	14	.	.	PUNCT
ejpam-1949	276	1	acknowledgements	acknowledgement	NOUN
ejpam-1949	276	2	we	we	PRON
ejpam-1949	276	3	thank	thank	VERB
ejpam-1949	276	4	the	the	DET
ejpam-1949	276	5	referee	referee	NOUN
ejpam-1949	276	6	for	for	ADP
ejpam-1949	276	7	various	various	ADJ
ejpam-1949	276	8	comments	comment	NOUN
ejpam-1949	276	9	and	and	CCONJ
ejpam-1949	276	10	corrections	correction	NOUN
ejpam-1949	276	11	which	which	PRON
ejpam-1949	276	12	have	have	AUX
ejpam-1949	276	13	helped	help	VERB
ejpam-1949	276	14	to	to	PART
ejpam-1949	276	15	improve	improve	VERB
ejpam-1949	276	16	the	the	DET
ejpam-1949	276	17	material	material	NOUN
ejpam-1949	276	18	presented	present	VERB
ejpam-1949	276	19	herein	herein	NOUN
ejpam-1949	276	20	.	.	PUNCT
ejpam-1949	277	1	references	reference	NOUN
ejpam-1949	277	2	[	[	X
ejpam-1949	277	3	1	1	X
ejpam-1949	277	4	]	]	X
ejpam-1949	277	5	p	p	PROPN
ejpam-1949	277	6	baum	baum	PROPN
ejpam-1949	277	7	and	and	CCONJ
ejpam-1949	277	8	r	r	PROPN
ejpam-1949	277	9	g	g	PROPN
ejpam-1949	277	10	douglas	douglas	PROPN
ejpam-1949	277	11	.	.	PUNCT
ejpam-1949	278	1	k	k	X
ejpam-1949	278	2	-	-	PUNCT
ejpam-1949	278	3	homology	homology	NOUN
ejpam-1949	278	4	and	and	CCONJ
ejpam-1949	278	5	index	index	NOUN
ejpam-1949	278	6	theory	theory	NOUN
ejpam-1949	278	7	.	.	PUNCT
ejpam-1949	279	1	in	in	ADP
ejpam-1949	279	2	operator	operator	NOUN
ejpam-1949	279	3	algebras	algebra	NOUN
ejpam-1949	279	4	and	and	CCONJ
ejpam-1949	279	5	applications	application	NOUN
ejpam-1949	279	6	.	.	PUNCT
ejpam-1949	280	1	proceedings	proceeding	NOUN
ejpam-1949	280	2	of	of	ADP
ejpam-1949	280	3	the	the	DET
ejpam-1949	280	4	symposium	symposium	NOUN
ejpam-1949	280	5	on	on	ADP
ejpam-1949	280	6	pure	pure	ADJ
ejpam-1949	280	7	mathematics	mathematic	NOUN
ejpam-1949	280	8	,	,	PUNCT
ejpam-1949	280	9	volume	volume	NOUN
ejpam-1949	280	10	38	38	NUM
ejpam-1949	280	11	,	,	PUNCT
ejpam-1949	280	12	pages	page	NOUN
ejpam-1949	280	13	117–173	117–173	NUM
ejpam-1949	280	14	,	,	PUNCT
ejpam-1949	280	15	kingston	kingston	PROPN
ejpam-1949	280	16	,	,	PUNCT
ejpam-1949	280	17	ontario	ontario	PROPN
ejpam-1949	280	18	,	,	PUNCT
ejpam-1949	280	19	1982	1982	NUM
ejpam-1949	280	20	.	.	PUNCT
ejpam-1949	281	1	american	american	PROPN
ejpam-1949	281	2	mathematical	mathematical	PROPN
ejpam-1949	281	3	society	society	NOUN
ejpam-1949	281	4	.	.	PUNCT
ejpam-1949	282	1	[	[	X
ejpam-1949	282	2	2	2	NUM
ejpam-1949	282	3	]	]	PUNCT
ejpam-1949	282	4	m	m	VERB
ejpam-1949	282	5	t	t	NOUN
ejpam-1949	282	6	benameur	benameur	NOUN
ejpam-1949	282	7	and	and	CCONJ
ejpam-1949	282	8	m	m	VERB
ejpam-1949	282	9	maghfoul	maghfoul	ADJ
ejpam-1949	282	10	.	.	PUNCT
ejpam-1949	283	1	differential	differential	ADJ
ejpam-1949	283	2	characters	character	NOUN
ejpam-1949	283	3	in	in	ADP
ejpam-1949	283	4	k	k	NOUN
ejpam-1949	283	5	-	-	NOUN
ejpam-1949	283	6	theory	theory	NOUN
ejpam-1949	283	7	.	.	PUNCT
ejpam-1949	284	1	differential	differential	ADJ
ejpam-1949	284	2	geometry	geometry	NOUN
ejpam-1949	284	3	and	and	CCONJ
ejpam-1949	284	4	its	its	PRON
ejpam-1949	284	5	applications	application	NOUN
ejpam-1949	284	6	,	,	PUNCT
ejpam-1949	284	7	24:417–432	24:417–432	NUM
ejpam-1949	284	8	,	,	PUNCT
ejpam-1949	284	9	2006	2006	NUM
ejpam-1949	284	10	.	.	PUNCT
ejpam-1949	285	1	[	[	X
ejpam-1949	285	2	3	3	NUM
ejpam-1949	285	3	]	]	PUNCT
ejpam-1949	285	4	u	u	NOUN
ejpam-1949	285	5	bunke	bunke	NOUN
ejpam-1949	285	6	and	and	CCONJ
ejpam-1949	285	7	t	t	PROPN
ejpam-1949	285	8	schick	schick	PROPN
ejpam-1949	285	9	.	.	PUNCT
ejpam-1949	286	1	smooth	smooth	ADJ
ejpam-1949	286	2	k	k	NOUN
ejpam-1949	286	3	-	-	NOUN
ejpam-1949	286	4	theory	theory	NOUN
ejpam-1949	286	5	.	.	PUNCT
ejpam-1949	287	1	astérisque	astérisque	NOUN
ejpam-1949	287	2	,	,	PUNCT
ejpam-1949	287	3	328:45–135	328:45–135	NUM
ejpam-1949	287	4	,	,	PUNCT
ejpam-1949	287	5	2009	2009	NUM
ejpam-1949	287	6	.	.	PUNCT
ejpam-1949	288	1	[	[	X
ejpam-1949	288	2	4	4	NUM
ejpam-1949	288	3	]	]	SYM
ejpam-1949	288	4	u	u	NOUN
ejpam-1949	288	5	bunke	bunke	NOUN
ejpam-1949	288	6	and	and	CCONJ
ejpam-1949	288	7	t	t	PROPN
ejpam-1949	288	8	schick	schick	PROPN
ejpam-1949	288	9	.	.	PUNCT
ejpam-1949	289	1	differential	differential	VERB
ejpam-1949	290	1	k	k	NOUN
ejpam-1949	290	2	-	-	NOUN
ejpam-1949	290	3	theory	theory	NOUN
ejpam-1949	290	4	.	.	PUNCT
ejpam-1949	291	1	a	a	DET
ejpam-1949	291	2	survey	survey	NOUN
ejpam-1949	291	3	.	.	PUNCT
ejpam-1949	292	1	in	in	ADP
ejpam-1949	292	2	global	global	ADJ
ejpam-1949	292	3	differential	differential	PROPN
ejpam-1949	292	4	geometry	geometry	NOUN
ejpam-1949	292	5	,	,	PUNCT
ejpam-1949	292	6	volume	volume	NOUN
ejpam-1949	292	7	17	17	NUM
ejpam-1949	292	8	,	,	PUNCT
ejpam-1949	292	9	pages	page	VERB
ejpam-1949	292	10	303–358	303–358	PROPN
ejpam-1949	292	11	.	.	PUNCT
ejpam-1949	292	12	springer	springer	NOUN
ejpam-1949	292	13	,	,	PUNCT
ejpam-1949	292	14	heidelberg	heidelberg	PROPN
ejpam-1949	292	15	,	,	PUNCT
ejpam-1949	292	16	2012	2012	NUM
ejpam-1949	292	17	.	.	PUNCT
ejpam-1949	293	1	[	[	X
ejpam-1949	293	2	5	5	NUM
ejpam-1949	293	3	]	]	X
ejpam-1949	293	4	d	d	X
ejpam-1949	293	5	s	s	VERB
ejpam-1949	293	6	freed	free	VERB
ejpam-1949	293	7	and	and	CCONJ
ejpam-1949	293	8	m	m	PROPN
ejpam-1949	293	9	j	j	PROPN
ejpam-1949	293	10	hopkins	hopkins	PROPN
ejpam-1949	293	11	.	.	PUNCT
ejpam-1949	294	1	on	on	ADP
ejpam-1949	294	2	ramond	ramond	ADJ
ejpam-1949	294	3	-	-	PUNCT
ejpam-1949	294	4	ramond	ramond	NOUN
ejpam-1949	294	5	fields	field	NOUN
ejpam-1949	294	6	and	and	CCONJ
ejpam-1949	294	7	k	k	NOUN
ejpam-1949	294	8	-	-	NOUN
ejpam-1949	294	9	theory	theory	NOUN
ejpam-1949	294	10	.	.	PUNCT
ejpam-1949	295	1	journal	journal	NOUN
ejpam-1949	295	2	of	of	ADP
ejpam-1949	295	3	high	high	ADJ
ejpam-1949	295	4	energy	energy	NOUN
ejpam-1949	295	5	physics	physics	NOUN
ejpam-1949	295	6	,	,	PUNCT
ejpam-1949	295	7	5(44	5(44	NUM
ejpam-1949	295	8	)	)	PUNCT
ejpam-1949	295	9	,	,	PUNCT
ejpam-1949	295	10	2000	2000	NUM
ejpam-1949	295	11	.	.	PUNCT
ejpam-1949	296	1	[	[	X
ejpam-1949	296	2	6	6	NUM
ejpam-1949	296	3	]	]	X
ejpam-1949	296	4	d	d	X
ejpam-1949	296	5	s	s	VERB
ejpam-1949	296	6	freed	free	VERB
ejpam-1949	296	7	and	and	CCONJ
ejpam-1949	296	8	j	j	PROPN
ejpam-1949	296	9	lott	lott	PROPN
ejpam-1949	296	10	.	.	PUNCT
ejpam-1949	297	1	an	an	DET
ejpam-1949	297	2	index	index	NOUN
ejpam-1949	297	3	theorem	theorem	VERB
ejpam-1949	297	4	in	in	ADP
ejpam-1949	297	5	differential	differential	ADJ
ejpam-1949	297	6	k	k	NOUN
ejpam-1949	297	7	-	-	NOUN
ejpam-1949	297	8	theory	theory	NOUN
ejpam-1949	297	9	.	.	PUNCT
ejpam-1949	298	1	geometry	geometry	NOUN
ejpam-1949	298	2	and	and	CCONJ
ejpam-1949	298	3	topology	topology	NOUN
ejpam-1949	298	4	,	,	PUNCT
ejpam-1949	298	5	14:903–966	14:903–966	NUM
ejpam-1949	298	6	,	,	PUNCT
ejpam-1949	298	7	2010	2010	NUM
ejpam-1949	298	8	.	.	PUNCT
ejpam-1949	299	1	[	[	X
ejpam-1949	299	2	7	7	X
ejpam-1949	299	3	]	]	X
ejpam-1949	299	4	j	j	PROPN
ejpam-1949	299	5	lott	lott	PROPN
ejpam-1949	299	6	.	.	PUNCT
ejpam-1949	300	1	r	r	X
ejpam-1949	300	2	/	/	SYM
ejpam-1949	300	3	z	z	NOUN
ejpam-1949	300	4	index	index	NOUN
ejpam-1949	300	5	theory	theory	NOUN
ejpam-1949	300	6	.	.	PUNCT
ejpam-1949	301	1	communications	communication	NOUN
ejpam-1949	301	2	in	in	ADP
ejpam-1949	301	3	analysis	analysis	NOUN
ejpam-1949	301	4	and	and	CCONJ
ejpam-1949	301	5	geometry	geometry	NOUN
ejpam-1949	301	6	,	,	PUNCT
ejpam-1949	301	7	2(2):279–311	2(2):279–311	NUM
ejpam-1949	301	8	,	,	PUNCT
ejpam-1949	301	9	1994	1994	NUM
ejpam-1949	301	10	.	.	PUNCT
ejpam-1949	302	1	[	[	X
ejpam-1949	302	2	8	8	NUM
ejpam-1949	302	3	]	]	SYM
ejpam-1949	302	4	m	m	VERB
ejpam-1949	302	5	maghfoul	maghfoul	ADJ
ejpam-1949	302	6	.	.	PUNCT
ejpam-1949	303	1	relative	relative	ADJ
ejpam-1949	303	2	differential	differential	PROPN
ejpam-1949	303	3	k	k	NOUN
ejpam-1949	303	4	-	-	NOUN
ejpam-1949	303	5	characters	character	NOUN
ejpam-1949	303	6	.	.	PUNCT
ejpam-1949	304	1	sigma	sigma	PROPN
ejpam-1949	304	2	,	,	PUNCT
ejpam-1949	304	3	4(35):10	4(35):10	PROPN
ejpam-1949	304	4	,	,	PUNCT
ejpam-1949	304	5	2008	2008	NUM
ejpam-1949	304	6	.	.	PUNCT
ejpam-1949	305	1	references	reference	NOUN
ejpam-1949	305	2	76	76	NUM
ejpam-1949	306	1	[	[	X
ejpam-1949	306	2	9	9	NUM
ejpam-1949	306	3	]	]	SYM
ejpam-1949	306	4	j	j	PROPN
ejpam-1949	306	5	simons	simons	PROPN
ejpam-1949	306	6	and	and	CCONJ
ejpam-1949	306	7	d	d	PROPN
ejpam-1949	306	8	sullivan	sullivan	PROPN
ejpam-1949	306	9	.	.	PUNCT
ejpam-1949	307	1	structured	structured	ADJ
ejpam-1949	307	2	vector	vector	NOUN
ejpam-1949	307	3	bundles	bundle	NOUN
ejpam-1949	307	4	define	define	VERB
ejpam-1949	307	5	differential	differential	ADJ
ejpam-1949	307	6	k	k	NOUN
ejpam-1949	307	7	-	-	NOUN
ejpam-1949	307	8	theory	theory	NOUN
ejpam-1949	307	9	.	.	PUNCT
ejpam-1949	308	1	in	in	ADP
ejpam-1949	308	2	quanta	quanta	PROPN
ejpam-1949	308	3	of	of	ADP
ejpam-1949	308	4	maths	maths	PROPN
ejpam-1949	308	5	,	,	PUNCT
ejpam-1949	308	6	clay	clay	NOUN
ejpam-1949	308	7	math	math	NOUN
ejpam-1949	308	8	.	.	PUNCT
ejpam-1949	309	1	proc	proc	PROPN
ejpam-1949	309	2	.	.	PROPN
ejpam-1949	309	3	,	,	PUNCT
ejpam-1949	309	4	volume	volume	NOUN
ejpam-1949	309	5	11	11	NUM
ejpam-1949	309	6	,	,	PUNCT
ejpam-1949	309	7	pages	page	NOUN
ejpam-1949	309	8	579–599	579–599	NUM
ejpam-1949	309	9	.	.	PUNCT
ejpam-1949	310	1	american	american	PROPN
ejpam-1949	310	2	mathematical	mathematical	PROPN
ejpam-1949	310	3	society	society	NOUN
ejpam-1949	310	4	,	,	PUNCT
ejpam-1949	310	5	2010	2010	NUM
ejpam-1949	310	6	.	.	PUNCT