id	sid	tid	token	lemma	pos
ap-1189	1	1	ap-3-10.dvi	ap-3-10.dvi	PROPN
ap-1189	1	2	acta	acta	PROPN
ap-1189	1	3	polytechnica	polytechnica	PROPN
ap-1189	1	4	vol	vol	NOUN
ap-1189	1	5	.	.	PROPN
ap-1189	2	1	50	50	NUM
ap-1189	2	2	no	no	NOUN
ap-1189	2	3	.	.	PUNCT
ap-1189	3	1	3/2010	3/2010	NUM
ap-1189	3	2	from	from	ADP
ap-1189	3	3	gauge	gauge	NOUN
ap-1189	3	4	anomalies	anomaly	NOUN
ap-1189	3	5	to	to	ADP
ap-1189	3	6	gerbes	gerbe	NOUN
ap-1189	3	7	and	and	CCONJ
ap-1189	3	8	gerbal	gerbal	ADJ
ap-1189	3	9	representations	representation	NOUN
ap-1189	3	10	:	:	PUNCT
ap-1189	3	11	group	group	NOUN
ap-1189	3	12	cocycles	cocycle	NOUN
ap-1189	3	13	in	in	ADP
ap-1189	3	14	quantum	quantum	ADJ
ap-1189	3	15	theory	theory	NOUN
ap-1189	3	16	j.	j.	PROPN
ap-1189	3	17	mickelsson	mickelsson	PROPN
ap-1189	3	18	abstract	abstract	PROPN
ap-1189	3	19	in	in	ADP
ap-1189	3	20	this	this	DET
ap-1189	3	21	paper	paper	NOUN
ap-1189	3	22	i	i	PRON
ap-1189	3	23	shall	shall	AUX
ap-1189	3	24	discuss	discuss	VERB
ap-1189	3	25	the	the	DET
ap-1189	3	26	role	role	NOUN
ap-1189	3	27	of	of	ADP
ap-1189	3	28	group	group	NOUN
ap-1189	3	29	cohomology	cohomology	NOUN
ap-1189	3	30	in	in	ADP
ap-1189	3	31	quantum	quantum	ADJ
ap-1189	3	32	mechanics	mechanic	NOUN
ap-1189	3	33	and	and	CCONJ
ap-1189	3	34	quantum	quantum	NOUN
ap-1189	3	35	field	field	NOUN
ap-1189	3	36	theory	theory	NOUN
ap-1189	3	37	.	.	PUNCT
ap-1189	4	1	first	first	ADV
ap-1189	4	2	,	,	PUNCT
ap-1189	4	3	i	i	PRON
ap-1189	4	4	recall	recall	VERB
ap-1189	4	5	how	how	SCONJ
ap-1189	4	6	cocycles	cocycle	NOUN
ap-1189	4	7	of	of	ADP
ap-1189	4	8	degree	degree	NOUN
ap-1189	4	9	1	1	NUM
ap-1189	4	10	and	and	CCONJ
ap-1189	4	11	2	2	NUM
ap-1189	4	12	appear	appear	VERB
ap-1189	4	13	naturally	naturally	ADV
ap-1189	4	14	in	in	ADP
ap-1189	4	15	the	the	DET
ap-1189	4	16	context	context	NOUN
ap-1189	4	17	of	of	ADP
ap-1189	4	18	gauge	gauge	ADJ
ap-1189	4	19	anomalies	anomaly	NOUN
ap-1189	4	20	.	.	PUNCT
ap-1189	5	1	then	then	ADV
ap-1189	5	2	we	we	PRON
ap-1189	5	3	investigate	investigate	VERB
ap-1189	5	4	how	how	SCONJ
ap-1189	5	5	group	group	NOUN
ap-1189	5	6	cohomology	cohomology	NOUN
ap-1189	5	7	of	of	ADP
ap-1189	5	8	degree	degree	NOUN
ap-1189	5	9	3	3	NUM
ap-1189	5	10	comes	come	VERB
ap-1189	5	11	from	from	ADP
ap-1189	5	12	a	a	DET
ap-1189	5	13	prolongation	prolongation	NOUN
ap-1189	5	14	problem	problem	NOUN
ap-1189	5	15	for	for	ADP
ap-1189	5	16	group	group	NOUN
ap-1189	5	17	extensions	extension	NOUN
ap-1189	5	18	and	and	CCONJ
ap-1189	5	19	we	we	PRON
ap-1189	5	20	discuss	discuss	VERB
ap-1189	5	21	its	its	PRON
ap-1189	5	22	role	role	NOUN
ap-1189	5	23	in	in	ADP
ap-1189	5	24	quantum	quantum	ADJ
ap-1189	5	25	field	field	NOUN
ap-1189	5	26	theory	theory	NOUN
ap-1189	5	27	.	.	PUNCT
ap-1189	6	1	finally	finally	ADV
ap-1189	6	2	,	,	PUNCT
ap-1189	6	3	we	we	PRON
ap-1189	6	4	discuss	discuss	VERB
ap-1189	6	5	a	a	DET
ap-1189	6	6	generalization	generalization	NOUN
ap-1189	6	7	to	to	ADP
ap-1189	6	8	representation	representation	NOUN
ap-1189	6	9	theory	theory	NOUN
ap-1189	6	10	where	where	SCONJ
ap-1189	6	11	a	a	DET
ap-1189	6	12	representation	representation	NOUN
ap-1189	6	13	is	be	AUX
ap-1189	6	14	replaced	replace	VERB
ap-1189	6	15	by	by	ADP
ap-1189	6	16	a	a	DET
ap-1189	6	17	1	1	NUM
ap-1189	6	18	-	-	PUNCT
ap-1189	6	19	cocycle	cocycle	NOUN
ap-1189	6	20	or	or	CCONJ
ap-1189	6	21	its	its	PRON
ap-1189	6	22	prolongation	prolongation	NOUN
ap-1189	6	23	by	by	ADP
ap-1189	6	24	a	a	DET
ap-1189	6	25	circle	circle	NOUN
ap-1189	6	26	,	,	PUNCT
ap-1189	6	27	and	and	CCONJ
ap-1189	6	28	point	point	VERB
ap-1189	6	29	out	out	ADP
ap-1189	6	30	how	how	SCONJ
ap-1189	6	31	this	this	DET
ap-1189	6	32	type	type	NOUN
ap-1189	6	33	of	of	ADP
ap-1189	6	34	situations	situation	NOUN
ap-1189	6	35	come	come	VERB
ap-1189	6	36	up	up	ADP
ap-1189	6	37	in	in	ADP
ap-1189	6	38	the	the	DET
ap-1189	6	39	quantization	quantization	NOUN
ap-1189	6	40	of	of	ADP
ap-1189	6	41	yang	yang	PROPN
ap-1189	6	42	-	-	PUNCT
ap-1189	6	43	mills	mill	NOUN
ap-1189	6	44	theory	theory	NOUN
ap-1189	6	45	.	.	PUNCT
ap-1189	7	1	1	1	NUM
ap-1189	7	2	introduction	introduction	NOUN
ap-1189	7	3	a	a	DET
ap-1189	7	4	projective	projective	ADJ
ap-1189	7	5	bundle	bundle	NOUN
ap-1189	7	6	over	over	ADP
ap-1189	7	7	a	a	DET
ap-1189	7	8	base	base	NOUN
ap-1189	7	9	m	m	VERB
ap-1189	7	10	is	be	AUX
ap-1189	7	11	completely	completely	ADV
ap-1189	7	12	determined	determine	VERB
ap-1189	7	13	,	,	PUNCT
ap-1189	7	14	up	up	ADP
ap-1189	7	15	to	to	ADP
ap-1189	7	16	equivalence	equivalence	NOUN
ap-1189	7	17	,	,	PUNCT
ap-1189	7	18	by	by	ADP
ap-1189	7	19	the	the	DET
ap-1189	7	20	dixmier	dixmier	NOUN
ap-1189	7	21	-	-	PUNCT
ap-1189	7	22	douady	douady	PROPN
ap-1189	7	23	class	class	NOUN
ap-1189	7	24	,	,	PUNCT
ap-1189	7	25	which	which	PRON
ap-1189	7	26	is	be	AUX
ap-1189	7	27	an	an	DET
ap-1189	7	28	element	element	NOUN
ap-1189	7	29	of	of	ADP
ap-1189	7	30	h3(m	h3(m	PROPN
ap-1189	7	31	,	,	PUNCT
ap-1189	7	32	z	z	NOUN
ap-1189	7	33	)	)	PUNCT
ap-1189	7	34	.	.	PUNCT
ap-1189	8	1	this	this	PRON
ap-1189	8	2	is	be	AUX
ap-1189	8	3	the	the	DET
ap-1189	8	4	origin	origin	NOUN
ap-1189	8	5	of	of	ADP
ap-1189	8	6	gerbes	gerbe	NOUN
ap-1189	8	7	in	in	ADP
ap-1189	8	8	quantum	quantum	ADJ
ap-1189	8	9	field	field	NOUN
ap-1189	8	10	theory	theory	NOUN
ap-1189	8	11	:	:	PUNCT
ap-1189	8	12	a	a	DET
ap-1189	8	13	standard	standard	ADJ
ap-1189	8	14	example	example	NOUN
ap-1189	8	15	of	of	ADP
ap-1189	8	16	this	this	DET
ap-1189	8	17	type	type	NOUN
ap-1189	8	18	of	of	ADP
ap-1189	8	19	situation	situation	NOUN
ap-1189	8	20	is	be	AUX
ap-1189	8	21	the	the	DET
ap-1189	8	22	case	case	NOUN
ap-1189	8	23	when	when	SCONJ
ap-1189	8	24	m	m	PROPN
ap-1189	8	25	is	be	AUX
ap-1189	8	26	the	the	DET
ap-1189	8	27	moduli	moduli	ADJ
ap-1189	8	28	space	space	NOUN
ap-1189	8	29	of	of	ADP
ap-1189	8	30	gauge	gauge	ADJ
ap-1189	8	31	connections	connection	NOUN
ap-1189	8	32	in	in	ADP
ap-1189	8	33	a	a	DET
ap-1189	8	34	vector	vector	NOUN
ap-1189	8	35	bundle	bundle	NOUN
ap-1189	8	36	over	over	ADP
ap-1189	8	37	a	a	DET
ap-1189	8	38	compact	compact	ADJ
ap-1189	8	39	spin	spin	NOUN
ap-1189	8	40	manifold	manifold	ADJ
ap-1189	8	41	,	,	PUNCT
ap-1189	8	42	[	[	X
ap-1189	8	43	5	5	NUM
ap-1189	8	44	]	]	PUNCT
ap-1189	8	45	.	.	PUNCT
ap-1189	9	1	topologically	topologically	ADV
ap-1189	9	2	a	a	DET
ap-1189	9	3	gerbe	gerbe	NOUN
ap-1189	9	4	on	on	ADP
ap-1189	9	5	a	a	DET
ap-1189	9	6	spacem	spacem	NOUN
ap-1189	9	7	is	be	AUX
ap-1189	9	8	just	just	ADV
ap-1189	9	9	an	an	DET
ap-1189	9	10	equivalence	equivalence	NOUN
ap-1189	9	11	class	class	NOUN
ap-1189	9	12	of	of	ADP
ap-1189	9	13	pu(h	pu(h	ADJ
ap-1189	9	14	)	)	PUNCT
ap-1189	9	15	=	=	VERB
ap-1189	10	1	u(h)/s1	u(h)/s1	NOUN
ap-1189	10	2	bundles	bundle	VERB
ap-1189	10	3	overm	overm	VERB
ap-1189	10	4	.	.	PUNCT
ap-1189	11	1	here	here	ADV
ap-1189	11	2	u(h	u(h	PROPN
ap-1189	11	3	)	)	PUNCT
ap-1189	11	4	is	be	AUX
ap-1189	11	5	the	the	DET
ap-1189	11	6	(	(	PUNCT
ap-1189	11	7	contractible	contractible	ADJ
ap-1189	11	8	)	)	PUNCT
ap-1189	11	9	unitary	unitary	ADJ
ap-1189	11	10	group	group	NOUN
ap-1189	11	11	in	in	ADP
ap-1189	11	12	a	a	DET
ap-1189	11	13	complex	complex	ADJ
ap-1189	11	14	hilbert	hilbert	NOUN
ap-1189	11	15	space	space	NOUN
ap-1189	11	16	h	h	NOUN
ap-1189	11	17	.	.	PUNCT
ap-1189	12	1	in	in	ADP
ap-1189	12	2	terms	term	NOUN
ap-1189	12	3	of	of	ADP
ap-1189	12	4	čech	čech	NOUN
ap-1189	12	5	cohomology	cohomology	NOUN
ap-1189	12	6	subordinate	subordinate	NOUN
ap-1189	12	7	to	to	ADP
ap-1189	12	8	a	a	DET
ap-1189	12	9	good	good	ADJ
ap-1189	12	10	cover	cover	NOUN
ap-1189	12	11	{	{	PUNCT
ap-1189	12	12	uα	uα	NOUN
ap-1189	12	13	}	}	PUNCT
ap-1189	12	14	of	of	ADP
ap-1189	12	15	x	x	PRON
ap-1189	12	16	,	,	PUNCT
ap-1189	12	17	the	the	DET
ap-1189	12	18	gerbe	gerbe	NOUN
ap-1189	12	19	is	be	AUX
ap-1189	12	20	given	give	VERB
ap-1189	12	21	as	as	ADP
ap-1189	12	22	a	a	DET
ap-1189	12	23	c×-valued	c×-value	VERB
ap-1189	12	24	cocycle	cocycle	NOUN
ap-1189	12	25	{	{	PUNCT
ap-1189	12	26	fαβγ	fαβγ	NOUN
ap-1189	12	27	}	}	PUNCT
ap-1189	12	28	,	,	PUNCT
ap-1189	12	29	fαβγf−1	fαβγf−1	PROPN
ap-1189	12	30	αβδfαγδf	αβδfαγδf	NOUN
ap-1189	12	31	−1	−1	NOUN
ap-1189	12	32	βγδ	βγδ	NOUN
ap-1189	12	33	=	=	SYM
ap-1189	12	34	1	1	NUM
ap-1189	12	35	on	on	ADP
ap-1189	12	36	intersections	intersection	NOUN
ap-1189	12	37	uα∩uβ	uα∩uβ	ADJ
ap-1189	12	38	∩uγ	∩uγ	NOUN
ap-1189	12	39	∩uδ	∩uδ	NOUN
ap-1189	12	40	.	.	PUNCT
ap-1189	13	1	this	this	DET
ap-1189	13	2	cocycle	cocycle	NOUN
ap-1189	13	3	arises	arise	VERB
ap-1189	13	4	from	from	ADP
ap-1189	13	5	the	the	DET
ap-1189	13	6	lifting	lifting	NOUN
ap-1189	13	7	problem	problem	NOUN
ap-1189	13	8	:	:	PUNCT
ap-1189	13	9	a	a	DET
ap-1189	13	10	pu(h	pu(h	NOUN
ap-1189	13	11	)	)	PUNCT
ap-1189	13	12	bundle	bundle	NOUN
ap-1189	13	13	is	be	AUX
ap-1189	13	14	given	give	VERB
ap-1189	13	15	in	in	ADP
ap-1189	13	16	terms	term	NOUN
ap-1189	13	17	of	of	ADP
ap-1189	13	18	transition	transition	NOUN
ap-1189	13	19	functions	function	NOUN
ap-1189	13	20	gαβ	gαβ	PROPN
ap-1189	13	21	with	with	ADP
ap-1189	13	22	values	value	NOUN
ap-1189	13	23	in	in	ADP
ap-1189	13	24	pu(h	pu(h	ADJ
ap-1189	13	25	)	)	PUNCT
ap-1189	13	26	.	.	PUNCT
ap-1189	14	1	after	after	ADP
ap-1189	14	2	lifting	lift	VERB
ap-1189	14	3	these	these	PRON
ap-1189	14	4	to	to	ADP
ap-1189	14	5	u(h	u(h	PROPN
ap-1189	14	6	)	)	PUNCT
ap-1189	14	7	one	one	PRON
ap-1189	14	8	gets	get	VERB
ap-1189	14	9	a	a	DET
ap-1189	14	10	family	family	NOUN
ap-1189	14	11	of	of	ADP
ap-1189	14	12	functions	function	NOUN
ap-1189	14	13	ĝαβ	ĝαβ	ADJ
ap-1189	14	14	which	which	PRON
ap-1189	14	15	satisfy	satisfy	VERB
ap-1189	14	16	the	the	DET
ap-1189	14	17	1	1	NUM
ap-1189	14	18	-	-	PUNCT
ap-1189	14	19	cocycle	cocycle	NOUN
ap-1189	14	20	condition	condition	NOUN
ap-1189	14	21	up	up	ADP
ap-1189	14	22	to	to	ADP
ap-1189	14	23	a	a	DET
ap-1189	14	24	phase	phase	NOUN
ap-1189	14	25	,	,	PUNCT
ap-1189	14	26	ĝαβ	ĝαβ	ADV
ap-1189	14	27	ĝβγ	ĝβγ	VERB
ap-1189	14	28	ĝγα	ĝγα	NOUN
ap-1189	14	29	=	=	SYM
ap-1189	14	30	fαβγ1	fαβγ1	PROPN
ap-1189	14	31	.	.	PUNCT
ap-1189	15	1	the	the	DET
ap-1189	15	2	notion	notion	NOUN
ap-1189	15	3	of	of	ADP
ap-1189	15	4	gerbal	gerbal	PROPN
ap-1189	15	5	representation	representation	NOUN
ap-1189	15	6	was	be	AUX
ap-1189	15	7	introduced	introduce	VERB
ap-1189	15	8	in	in	ADP
ap-1189	15	9	recent	recent	ADJ
ap-1189	15	10	paper	paper	NOUN
ap-1189	15	11	[	[	X
ap-1189	15	12	7	7	NUM
ap-1189	15	13	]	]	PUNCT
ap-1189	15	14	.	.	PUNCT
ap-1189	16	1	this	this	PRON
ap-1189	16	2	is	be	AUX
ap-1189	16	3	to	to	PART
ap-1189	16	4	be	be	AUX
ap-1189	16	5	viewed	view	VERB
ap-1189	16	6	as	as	ADP
ap-1189	16	7	the	the	DET
ap-1189	16	8	next	next	ADJ
ap-1189	16	9	level	level	NOUN
ap-1189	16	10	after	after	ADP
ap-1189	16	11	projective	projective	ADJ
ap-1189	16	12	actions	action	NOUN
ap-1189	16	13	related	relate	VERB
ap-1189	16	14	to	to	ADP
ap-1189	16	15	central	central	ADJ
ap-1189	16	16	extensions	extension	NOUN
ap-1189	16	17	of	of	ADP
ap-1189	16	18	groups	group	NOUN
ap-1189	16	19	and	and	CCONJ
ap-1189	16	20	is	be	AUX
ap-1189	16	21	given	give	VERB
ap-1189	16	22	in	in	ADP
ap-1189	16	23	terms	term	NOUN
ap-1189	16	24	of	of	ADP
ap-1189	16	25	third	third	ADJ
ap-1189	16	26	group	group	NOUN
ap-1189	16	27	cohomology	cohomology	NOUN
ap-1189	16	28	.	.	PUNCT
ap-1189	17	1	one	one	PRON
ap-1189	17	2	can	can	AUX
ap-1189	17	3	view	view	VERB
ap-1189	17	4	this	this	DET
ap-1189	17	5	setting	setting	NOUN
ap-1189	17	6	as	as	ADP
ap-1189	17	7	a	a	DET
ap-1189	17	8	categorification	categorification	NOUN
ap-1189	17	9	of	of	ADP
ap-1189	17	10	the	the	DET
ap-1189	17	11	representation	representation	NOUN
ap-1189	17	12	theory	theory	NOUN
ap-1189	17	13	of	of	ADP
ap-1189	17	14	central	central	ADJ
ap-1189	17	15	extensions	extension	NOUN
ap-1189	17	16	of	of	ADP
ap-1189	17	17	groups	group	NOUN
ap-1189	17	18	.	.	PUNCT
ap-1189	18	1	we	we	PRON
ap-1189	18	2	shall	shall	AUX
ap-1189	18	3	not	not	PART
ap-1189	18	4	discuss	discuss	VERB
ap-1189	18	5	the	the	DET
ap-1189	18	6	problem	problem	NOUN
ap-1189	18	7	in	in	ADP
ap-1189	18	8	this	this	DET
ap-1189	18	9	generality	generality	NOUN
ap-1189	18	10	since	since	SCONJ
ap-1189	18	11	our	our	PRON
ap-1189	18	12	categories	category	NOUN
ap-1189	18	13	are	be	AUX
ap-1189	18	14	of	of	ADP
ap-1189	18	15	special	special	ADJ
ap-1189	18	16	kind	kind	NOUN
ap-1189	18	17	:	:	PUNCT
ap-1189	18	18	a	a	DET
ap-1189	18	19	category	category	NOUN
ap-1189	18	20	of	of	ADP
ap-1189	18	21	groups	group	NOUN
ap-1189	18	22	for	for	ADP
ap-1189	18	23	us	we	PRON
ap-1189	18	24	is	be	AUX
ap-1189	18	25	just	just	ADV
ap-1189	18	26	a	a	DET
ap-1189	18	27	principal	principal	ADJ
ap-1189	18	28	bundle	bundle	NOUN
ap-1189	18	29	over	over	ADP
ap-1189	18	30	a	a	DET
ap-1189	18	31	basem	basem	NOUN
ap-1189	18	32	.	.	PUNCT
ap-1189	19	1	each	each	DET
ap-1189	19	2	fiber	fiber	NOUN
ap-1189	19	3	can	can	AUX
ap-1189	19	4	be	be	AUX
ap-1189	19	5	identified	identify	VERB
ap-1189	19	6	as	as	ADP
ap-1189	19	7	a	a	DET
ap-1189	19	8	group	group	NOUN
ap-1189	19	9	g	g	NOUN
ap-1189	19	10	,	,	PUNCT
ap-1189	19	11	but	but	CCONJ
ap-1189	19	12	only	only	ADV
ap-1189	19	13	after	after	ADP
ap-1189	19	14	fixing	fix	VERB
ap-1189	19	15	a	a	DET
ap-1189	19	16	point	point	NOUN
ap-1189	19	17	in	in	ADP
ap-1189	19	18	the	the	DET
ap-1189	19	19	fiber	fiber	NOUN
ap-1189	19	20	and	and	CCONJ
ap-1189	19	21	calling	call	VERB
ap-1189	19	22	the	the	DET
ap-1189	19	23	chosen	choose	VERB
ap-1189	19	24	point	point	NOUN
ap-1189	19	25	the	the	DET
ap-1189	19	26	unit	unit	NOUN
ap-1189	19	27	element	element	NOUN
ap-1189	19	28	in	in	ADP
ap-1189	19	29	g.	g.	PROPN
ap-1189	19	30	fixing	fix	VERB
ap-1189	19	31	a	a	DET
ap-1189	19	32	representation	representation	NOUN
ap-1189	19	33	of	of	ADP
ap-1189	19	34	g	g	PROPN
ap-1189	19	35	defines	define	VERB
ap-1189	19	36	a	a	DET
ap-1189	19	37	standard	standard	ADJ
ap-1189	19	38	way	way	NOUN
ap-1189	19	39	a	a	DET
ap-1189	19	40	vector	vector	NOUN
ap-1189	19	41	bundle	bundle	NOUN
ap-1189	19	42	over	over	ADP
ap-1189	19	43	m	m	PROPN
ap-1189	19	44	.	.	PUNCT
ap-1189	20	1	however	however	ADV
ap-1189	20	2	,	,	PUNCT
ap-1189	20	3	if	if	SCONJ
ap-1189	20	4	the	the	DET
ap-1189	20	5	representation	representation	NOUN
ap-1189	20	6	is	be	AUX
ap-1189	20	7	only	only	ADV
ap-1189	20	8	a	a	DET
ap-1189	20	9	projective	projective	ADJ
ap-1189	20	10	representation	representation	NOUN
ap-1189	20	11	we	we	PRON
ap-1189	20	12	obtain	obtain	VERB
ap-1189	20	13	in	in	ADP
ap-1189	20	14	general	general	ADJ
ap-1189	20	15	only	only	ADV
ap-1189	20	16	a	a	DET
ap-1189	20	17	projective	projective	ADJ
ap-1189	20	18	vector	vector	NOUN
ap-1189	20	19	bundle	bundle	NOUN
ap-1189	20	20	over	over	ADP
ap-1189	20	21	m	m	PROPN
ap-1189	20	22	.	.	PUNCT
ap-1189	21	1	we	we	PRON
ap-1189	21	2	are	be	AUX
ap-1189	21	3	now	now	ADV
ap-1189	21	4	in	in	ADP
ap-1189	21	5	the	the	DET
ap-1189	21	6	setting	setting	NOUN
ap-1189	21	7	for	for	ADP
ap-1189	21	8	gerbes	gerbe	NOUN
ap-1189	21	9	and	and	CCONJ
ap-1189	21	10	we	we	PRON
ap-1189	21	11	have	have	VERB
ap-1189	21	12	a	a	DET
ap-1189	21	13	characteristic	characteristic	ADJ
ap-1189	21	14	class	class	NOUN
ap-1189	21	15	in	in	ADP
ap-1189	21	16	h3(m	h3(m	PROPN
ap-1189	21	17	,	,	PUNCT
ap-1189	21	18	z	z	NOUN
ap-1189	21	19	)	)	PUNCT
ap-1189	21	20	.	.	PUNCT
ap-1189	22	1	but	but	CCONJ
ap-1189	22	2	there	there	PRON
ap-1189	22	3	is	be	VERB
ap-1189	22	4	a	a	DET
ap-1189	22	5	role	role	NOUN
ap-1189	22	6	also	also	ADV
ap-1189	22	7	for	for	ADP
ap-1189	22	8	third	third	ADJ
ap-1189	22	9	group	group	NOUN
ap-1189	22	10	cohomology	cohomology	NOUN
ap-1189	22	11	.	.	PUNCT
ap-1189	23	1	in	in	ADP
ap-1189	23	2	fact	fact	NOUN
ap-1189	23	3	,	,	PUNCT
ap-1189	23	4	the	the	DET
ap-1189	23	5	appearance	appearance	NOUN
ap-1189	23	6	of	of	ADP
ap-1189	23	7	third	third	ADJ
ap-1189	23	8	group	group	NOUN
ap-1189	23	9	cohomology	cohomology	NOUN
ap-1189	23	10	in	in	ADP
ap-1189	23	11	this	this	DET
ap-1189	23	12	context	context	NOUN
ap-1189	23	13	is	be	AUX
ap-1189	23	14	not	not	PART
ap-1189	23	15	new	new	ADJ
ap-1189	23	16	and	and	CCONJ
ap-1189	23	17	is	be	AUX
ap-1189	23	18	related	relate	VERB
ap-1189	23	19	to	to	ADP
ap-1189	23	20	group	group	NOUN
ap-1189	23	21	extensions	extension	NOUN
ap-1189	23	22	as	as	SCONJ
ap-1189	23	23	explained	explain	VERB
ap-1189	23	24	in	in	ADP
ap-1189	23	25	[	[	PUNCT
ap-1189	23	26	9	9	NUM
ap-1189	23	27	]	]	PUNCT
ap-1189	23	28	.	.	PUNCT
ap-1189	24	1	in	in	ADP
ap-1189	24	2	the	the	DET
ap-1189	24	3	simplest	simple	ADJ
ap-1189	24	4	form	form	NOUN
ap-1189	24	5	,	,	PUNCT
ap-1189	24	6	the	the	DET
ap-1189	24	7	problem	problem	NOUN
ap-1189	24	8	is	be	AUX
ap-1189	24	9	the	the	DET
ap-1189	24	10	following	following	NOUN
ap-1189	24	11	.	.	PUNCT
ap-1189	25	1	let	let	VERB
ap-1189	25	2	f	f	PRON
ap-1189	25	3	be	be	AUX
ap-1189	25	4	an	an	DET
ap-1189	25	5	extension	extension	NOUN
ap-1189	25	6	of	of	ADP
ap-1189	25	7	g	g	NOUN
ap-1189	25	8	by	by	ADP
ap-1189	25	9	the	the	DET
ap-1189	25	10	group	group	NOUN
ap-1189	25	11	n	n	NOUN
ap-1189	25	12	,	,	PUNCT
ap-1189	25	13	1→	1→	NUM
ap-1189	25	14	n	n	NOUN
ap-1189	25	15	→	→	SYM
ap-1189	25	16	f	f	PROPN
ap-1189	25	17	→	→	SYM
ap-1189	25	18	g→	g→	NOUN
ap-1189	25	19	1	1	NUM
ap-1189	25	20	an	an	DET
ap-1189	25	21	exact	exact	ADJ
ap-1189	25	22	sequence	sequence	NOUN
ap-1189	25	23	of	of	ADP
ap-1189	25	24	groups	group	NOUN
ap-1189	25	25	.	.	PUNCT
ap-1189	26	1	suppose	suppose	VERB
ap-1189	26	2	that	that	SCONJ
ap-1189	26	3	1	1	NUM
ap-1189	26	4	→	→	SYM
ap-1189	26	5	a	a	PRON
ap-1189	26	6	→	→	SYM
ap-1189	26	7	n̂	n̂	NUM
ap-1189	26	8	→	→	SYM
ap-1189	26	9	n	n	CCONJ
ap-1189	26	10	→	→	SYM
ap-1189	26	11	1	1	NUM
ap-1189	26	12	is	be	AUX
ap-1189	26	13	a	a	DET
ap-1189	26	14	central	central	ADJ
ap-1189	26	15	extension	extension	NOUN
ap-1189	26	16	by	by	ADP
ap-1189	26	17	the	the	DET
ap-1189	26	18	abelian	abelian	PROPN
ap-1189	26	19	group	group	PROPN
ap-1189	26	20	a.	a.	NOUN
ap-1189	26	21	then	then	ADV
ap-1189	26	22	one	one	PRON
ap-1189	26	23	can	can	AUX
ap-1189	26	24	ask	ask	VERB
ap-1189	26	25	whether	whether	SCONJ
ap-1189	26	26	the	the	DET
ap-1189	26	27	extension	extension	NOUN
ap-1189	26	28	f	f	NOUN
ap-1189	26	29	of	of	ADP
ap-1189	26	30	g	g	PROPN
ap-1189	26	31	by	by	ADP
ap-1189	26	32	n	n	PRON
ap-1189	26	33	can	can	AUX
ap-1189	26	34	be	be	AUX
ap-1189	26	35	prolonged	prolong	VERB
ap-1189	26	36	to	to	ADP
ap-1189	26	37	an	an	DET
ap-1189	26	38	extension	extension	NOUN
ap-1189	26	39	of	of	ADP
ap-1189	26	40	g	g	NOUN
ap-1189	26	41	by	by	ADP
ap-1189	26	42	the	the	DET
ap-1189	26	43	group	group	NOUN
ap-1189	26	44	n̂	n̂	NUM
ap-1189	26	45	.	.	PUNCT
ap-1189	27	1	the	the	DET
ap-1189	27	2	obstruction	obstruction	NOUN
ap-1189	27	3	to	to	ADP
ap-1189	27	4	this	this	PRON
ap-1189	27	5	is	be	AUX
ap-1189	27	6	an	an	DET
ap-1189	27	7	element	element	NOUN
ap-1189	27	8	in	in	ADP
ap-1189	27	9	the	the	DET
ap-1189	27	10	group	group	NOUN
ap-1189	27	11	cohomology	cohomology	NOUN
ap-1189	27	12	h3(g	h3(g	PROPN
ap-1189	27	13	,	,	PUNCT
ap-1189	27	14	a	a	PRON
ap-1189	27	15	)	)	PUNCT
ap-1189	27	16	with	with	ADP
ap-1189	27	17	coefficients	coefficient	NOUN
ap-1189	27	18	in	in	ADP
ap-1189	27	19	a.	a.	NOUN
ap-1189	27	20	in	in	ADP
ap-1189	27	21	the	the	DET
ap-1189	27	22	case	case	NOUN
ap-1189	27	23	of	of	ADP
ap-1189	27	24	lie	lie	NOUN
ap-1189	27	25	groups	group	NOUN
ap-1189	27	26	,	,	PUNCT
ap-1189	27	27	there	there	PRON
ap-1189	27	28	is	be	VERB
ap-1189	27	29	a	a	DET
ap-1189	27	30	corresponding	correspond	VERB
ap-1189	27	31	lie	lie	NOUN
ap-1189	27	32	algebra	algebra	NOUN
ap-1189	27	33	cocycle	cocycle	NOUN
ap-1189	27	34	representing	represent	VERB
ap-1189	27	35	a	a	DET
ap-1189	27	36	class	class	NOUN
ap-1189	27	37	in	in	ADP
ap-1189	27	38	h3(g	h3(g	PROPN
ap-1189	27	39	,	,	PUNCT
ap-1189	27	40	a	a	PRON
ap-1189	27	41	)	)	PUNCT
ap-1189	27	42	,	,	PUNCT
ap-1189	27	43	where	where	SCONJ
ap-1189	27	44	a	a	PRON
ap-1189	27	45	is	be	AUX
ap-1189	27	46	the	the	DET
ap-1189	27	47	lie	lie	NOUN
ap-1189	27	48	algebra	algebra	NOUN
ap-1189	27	49	of	of	ADP
ap-1189	27	50	a.	a.	NOUN
ap-1189	27	51	we	we	PRON
ap-1189	27	52	shall	shall	AUX
ap-1189	27	53	demonstrate	demonstrate	VERB
ap-1189	27	54	this	this	PRON
ap-1189	27	55	in	in	ADP
ap-1189	27	56	detail	detail	NOUN
ap-1189	27	57	for	for	ADP
ap-1189	27	58	an	an	DET
ap-1189	27	59	example	example	NOUN
ap-1189	27	60	arising	arise	VERB
ap-1189	27	61	from	from	ADP
ap-1189	27	62	the	the	DET
ap-1189	27	63	quantization	quantization	NOUN
ap-1189	27	64	of	of	ADP
ap-1189	27	65	gauge	gauge	NOUN
ap-1189	27	66	theory	theory	NOUN
ap-1189	27	67	.	.	PUNCT
ap-1189	28	1	it	it	PRON
ap-1189	28	2	is	be	AUX
ap-1189	28	3	closely	closely	ADV
ap-1189	28	4	related	relate	VERB
ap-1189	28	5	to	to	ADP
ap-1189	28	6	the	the	DET
ap-1189	28	7	idea	idea	NOUN
ap-1189	28	8	in	in	ADP
ap-1189	28	9	[	[	X
ap-1189	28	10	2	2	NUM
ap-1189	28	11	]	]	PUNCT
ap-1189	28	12	,	,	PUNCT
ap-1189	28	13	further	far	ADV
ap-1189	28	14	elaborated	elaborate	VERB
ap-1189	28	15	in	in	ADP
ap-1189	28	16	[	[	X
ap-1189	28	17	3	3	NUM
ap-1189	28	18	]	]	PUNCT
ap-1189	28	19	,	,	PUNCT
ap-1189	28	20	which	which	PRON
ap-1189	28	21	in	in	ADP
ap-1189	28	22	turn	turn	NOUN
ap-1189	28	23	was	be	AUX
ap-1189	28	24	a	a	DET
ap-1189	28	25	response	response	NOUN
ap-1189	28	26	to	to	ADP
ap-1189	28	27	a	a	DET
ap-1189	28	28	discussion	discussion	NOUN
ap-1189	28	29	in	in	ADP
ap-1189	28	30	1985	1985	NUM
ap-1189	28	31	on	on	ADP
ap-1189	28	32	breaking	break	VERB
ap-1189	28	33	of	of	ADP
ap-1189	28	34	the	the	DET
ap-1189	28	35	jacobi	jacobi	PROPN
ap-1189	28	36	identity	identity	NOUN
ap-1189	28	37	for	for	ADP
ap-1189	28	38	the	the	DET
ap-1189	28	39	field	field	NOUN
ap-1189	28	40	algebra	algebra	NOUN
ap-1189	28	41	in	in	ADP
ap-1189	28	42	yang	yang	PROPN
ap-1189	28	43	-	-	PUNCT
ap-1189	28	44	mills	mill	NOUN
ap-1189	28	45	theory	theory	NOUN
ap-1189	28	46	[	[	X
ap-1189	28	47	6	6	NUM
ap-1189	28	48	]	]	PUNCT
ap-1189	28	49	.	.	PUNCT
ap-1189	29	1	the	the	DET
ap-1189	29	2	paper	paper	NOUN
ap-1189	29	3	is	be	AUX
ap-1189	29	4	organized	organize	VERB
ap-1189	29	5	as	as	SCONJ
ap-1189	29	6	follows	follow	VERB
ap-1189	29	7	.	.	PUNCT
ap-1189	30	1	in	in	ADP
ap-1189	30	2	section	section	NOUN
ap-1189	30	3	2	2	NUM
ap-1189	30	4	we	we	PRON
ap-1189	30	5	recall	recall	VERB
ap-1189	30	6	the	the	DET
ap-1189	30	7	basics	basic	NOUN
ap-1189	30	8	about	about	ADP
ap-1189	30	9	the	the	DET
ap-1189	30	10	role	role	NOUN
ap-1189	30	11	of	of	ADP
ap-1189	30	12	group	group	NOUN
ap-1189	30	13	cohomology	cohomology	NOUN
ap-1189	30	14	of	of	ADP
ap-1189	30	15	degree	degree	NOUN
ap-1189	30	16	1	1	NUM
ap-1189	30	17	and	and	CCONJ
ap-1189	30	18	2	2	NUM
ap-1189	30	19	in	in	ADP
ap-1189	30	20	quantum	quantum	ADJ
ap-1189	30	21	theory	theory	NOUN
ap-1189	30	22	.	.	PUNCT
ap-1189	31	1	in	in	ADP
ap-1189	31	2	section	section	NOUN
ap-1189	31	3	3	3	NUM
ap-1189	31	4	we	we	PRON
ap-1189	31	5	then	then	ADV
ap-1189	31	6	explain	explain	VERB
ap-1189	31	7	how	how	SCONJ
ap-1189	31	8	3	3	NUM
ap-1189	31	9	-	-	PUNCT
ap-1189	31	10	cocycles	cocycle	NOUN
ap-1189	31	11	come	come	VERB
ap-1189	31	12	from	from	ADP
ap-1189	31	13	a	a	DET
ap-1189	31	14	prolongation	prolongation	NOUN
ap-1189	31	15	problem	problem	NOUN
ap-1189	31	16	for	for	ADP
ap-1189	31	17	group	group	NOUN
ap-1189	31	18	extensions	extension	NOUN
ap-1189	31	19	.	.	PUNCT
ap-1189	32	1	in	in	ADP
ap-1189	32	2	section	section	NOUN
ap-1189	32	3	4	4	NUM
ap-1189	32	4	we	we	PRON
ap-1189	32	5	take	take	VERB
ap-1189	32	6	as	as	ADP
ap-1189	32	7	an	an	DET
ap-1189	32	8	example	example	NOUN
ap-1189	32	9	the	the	DET
ap-1189	32	10	gauge	gauge	NOUN
ap-1189	32	11	group	group	NOUN
ap-1189	32	12	extensions	extension	NOUN
ap-1189	32	13	arising	arise	VERB
ap-1189	32	14	from	from	ADP
ap-1189	32	15	the	the	DET
ap-1189	32	16	gauge	gauge	ADJ
ap-1189	32	17	action	action	NOUN
ap-1189	32	18	on	on	ADP
ap-1189	32	19	bundles	bundle	NOUN
ap-1189	32	20	of	of	ADP
ap-1189	32	21	fermionic	fermionic	NOUN
ap-1189	32	22	fock	fock	ADJ
ap-1189	32	23	spaces	space	NOUN
ap-1189	32	24	over	over	ADP
ap-1189	32	25	background	background	NOUN
ap-1189	32	26	gauge	gauge	NOUN
ap-1189	32	27	fields	field	NOUN
ap-1189	32	28	and	and	CCONJ
ap-1189	32	29	the	the	DET
ap-1189	32	30	corresponding	correspond	VERB
ap-1189	32	31	lie	lie	NOUN
ap-1189	32	32	algebra	algebra	NOUN
ap-1189	32	33	cocycles	cocycle	NOUN
ap-1189	32	34	.	.	PUNCT
ap-1189	33	1	in	in	ADP
ap-1189	33	2	sections	section	NOUN
ap-1189	33	3	5	5	NUM
ap-1189	33	4	and	and	CCONJ
ap-1189	33	5	6	6	NUM
ap-1189	33	6	we	we	PRON
ap-1189	33	7	explain	explain	VERB
ap-1189	33	8	the	the	DET
ap-1189	33	9	use	use	NOUN
ap-1189	33	10	of	of	ADP
ap-1189	33	11	1	1	NUM
ap-1189	33	12	-	-	PUNCT
ap-1189	33	13	cocycles	cocycle	NOUN
ap-1189	33	14	as	as	ADP
ap-1189	33	15	generalized	generalized	ADJ
ap-1189	33	16	representations	representation	NOUN
ap-1189	33	17	,	,	PUNCT
ap-1189	33	18	with	with	ADP
ap-1189	33	19	an	an	DET
ap-1189	33	20	example	example	NOUN
ap-1189	33	21	from	from	ADP
ap-1189	33	22	quantum	quantum	ADJ
ap-1189	33	23	field	field	NOUN
ap-1189	33	24	theory	theory	NOUN
ap-1189	33	25	.	.	PUNCT
ap-1189	34	1	2	2	NUM
ap-1189	34	2	cocycles	cocycle	NOUN
ap-1189	34	3	of	of	ADP
ap-1189	34	4	degree	degree	NOUN
ap-1189	34	5	1	1	NUM
ap-1189	34	6	and	and	CCONJ
ap-1189	34	7	2	2	NUM
ap-1189	34	8	in	in	ADP
ap-1189	34	9	quantum	quantum	ADJ
ap-1189	34	10	theory	theory	NOUN
ap-1189	34	11	in	in	ADP
ap-1189	34	12	quantum	quantum	ADJ
ap-1189	34	13	mechanics	mechanic	NOUN
ap-1189	34	14	a	a	DET
ap-1189	34	15	symmetry	symmetry	NOUN
ap-1189	34	16	group	group	NOUN
ap-1189	34	17	g	g	PROPN
ap-1189	34	18	(	(	PUNCT
ap-1189	34	19	e.g.	e.g.	ADV
ap-1189	34	20	,	,	PUNCT
ap-1189	34	21	the	the	DET
ap-1189	34	22	group	group	NOUN
ap-1189	34	23	of	of	ADP
ap-1189	34	24	galilean	galilean	PROPN
ap-1189	34	25	symmetries	symmetries	PROPN
ap-1189	34	26	)	)	PUNCT
ap-1189	34	27	acts	act	VERB
ap-1189	34	28	on	on	ADP
ap-1189	34	29	schrödinger	schrödinger	NOUN
ap-1189	34	30	wave	wave	NOUN
ap-1189	34	31	functions	function	NOUN
ap-1189	34	32	as	as	ADP
ap-1189	34	33	42	42	NUM
ap-1189	34	34	acta	acta	PROPN
ap-1189	34	35	polytechnica	polytechnica	PROPN
ap-1189	34	36	vol	vol	NOUN
ap-1189	34	37	.	.	PROPN
ap-1189	35	1	50	50	NUM
ap-1189	35	2	no	no	NOUN
ap-1189	35	3	.	.	PUNCT
ap-1189	36	1	3/2010	3/2010	NUM
ap-1189	36	2	(	(	PUNCT
ap-1189	36	3	t	t	PROPN
ap-1189	36	4	(	(	PUNCT
ap-1189	36	5	g)ψ)(x	g)ψ)(x	PROPN
ap-1189	36	6	)	)	PUNCT
ap-1189	36	7	=	=	SYM
ap-1189	36	8	ω(g;x)ψ(g−1x	ω(g;x)ψ(g−1x	NOUN
ap-1189	36	9	)	)	PUNCT
ap-1189	36	10	where	where	SCONJ
ap-1189	36	11	ω(g;x	ω(g;x	PROPN
ap-1189	36	12	)	)	PUNCT
ap-1189	36	13	,	,	PUNCT
ap-1189	36	14	for	for	ADP
ap-1189	36	15	g	g	PROPN
ap-1189	36	16	∈	∈	PROPN
ap-1189	36	17	g	g	NOUN
ap-1189	36	18	,	,	PUNCT
ap-1189	36	19	is	be	AUX
ap-1189	36	20	a	a	DET
ap-1189	36	21	(	(	PUNCT
ap-1189	36	22	matrix	matrix	NOUN
ap-1189	36	23	valued	value	VERB
ap-1189	36	24	)	)	PUNCT
ap-1189	36	25	phase	phase	NOUN
ap-1189	36	26	factor	factor	NOUN
ap-1189	36	27	.	.	PUNCT
ap-1189	37	1	in	in	ADP
ap-1189	37	2	order	order	NOUN
ap-1189	37	3	that	that	SCONJ
ap-1189	37	4	the	the	DET
ap-1189	37	5	group	group	NOUN
ap-1189	37	6	multiplication	multiplication	NOUN
ap-1189	37	7	rule	rule	NOUN
ap-1189	37	8	is	be	AUX
ap-1189	37	9	preserved	preserve	VERB
ap-1189	37	10	it	it	PRON
ap-1189	37	11	has	have	VERB
ap-1189	37	12	to	to	PART
ap-1189	37	13	satisfy	satisfy	VERB
ap-1189	37	14	as	as	ADP
ap-1189	37	15	consistency	consistency	NOUN
ap-1189	37	16	the	the	DET
ap-1189	37	17	1	1	NUM
ap-1189	37	18	-	-	PUNCT
ap-1189	37	19	cocycle	cocycle	NOUN
ap-1189	37	20	condition	condition	NOUN
ap-1189	37	21	ω(g1;x)ω(g2	ω(g1;x)ω(g2	NOUN
ap-1189	37	22	;	;	PUNCT
ap-1189	37	23	g	g	PROPN
ap-1189	37	24	−1	−1	NOUN
ap-1189	37	25	1	1	NUM
ap-1189	37	26	x)ω(g1g2;x)−1	x)ω(g1g2;x)−1	NOUN
ap-1189	37	27	=	=	SYM
ap-1189	37	28	1	1	X
ap-1189	37	29	.	.	PUNCT
ap-1189	38	1	it	it	PRON
ap-1189	38	2	may	may	AUX
ap-1189	38	3	happen	happen	VERB
ap-1189	38	4	that	that	SCONJ
ap-1189	38	5	the	the	DET
ap-1189	38	6	cocycle	cocycle	NOUN
ap-1189	38	7	condition	condition	NOUN
ap-1189	38	8	does	do	AUX
ap-1189	38	9	not	not	PART
ap-1189	38	10	hold	hold	VERB
ap-1189	38	11	,	,	PUNCT
ap-1189	38	12	for	for	ADP
ap-1189	38	13	example	example	NOUN
ap-1189	38	14	in	in	ADP
ap-1189	38	15	the	the	DET
ap-1189	38	16	case	case	NOUN
ap-1189	38	17	of	of	ADP
ap-1189	38	18	the	the	DET
ap-1189	38	19	galilean	galilean	PROPN
ap-1189	38	20	transformations	transformation	NOUN
ap-1189	38	21	on	on	ADP
ap-1189	38	22	wave	wave	NOUN
ap-1189	38	23	functions	function	NOUN
ap-1189	38	24	of	of	ADP
ap-1189	38	25	massive	massive	ADJ
ap-1189	38	26	particles	particle	NOUN
ap-1189	38	27	;	;	PUNCT
ap-1189	38	28	in	in	ADP
ap-1189	38	29	this	this	DET
ap-1189	38	30	case	case	NOUN
ap-1189	38	31	the	the	DET
ap-1189	38	32	left	left	ADJ
ap-1189	38	33	-	-	PUNCT
ap-1189	38	34	hand	hand	NOUN
ap-1189	38	35	-	-	PUNCT
ap-1189	38	36	side	side	NOUN
ap-1189	38	37	defines	define	NOUN
ap-1189	38	38	a	a	DET
ap-1189	38	39	s1	s1	NOUN
ap-1189	38	40	valued	value	VERB
ap-1189	38	41	(	(	PUNCT
ap-1189	38	42	it	it	PRON
ap-1189	38	43	does	do	AUX
ap-1189	38	44	not	not	PART
ap-1189	38	45	depend	depend	VERB
ap-1189	38	46	on	on	ADP
ap-1189	38	47	the	the	DET
ap-1189	38	48	coordinate	coordinate	NOUN
ap-1189	38	49	x	x	NOUN
ap-1189	38	50	)	)	PUNCT
ap-1189	38	51	2	2	NUM
ap-1189	38	52	-	-	PUNCT
ap-1189	38	53	cocycle	cocycle	NOUN
ap-1189	38	54	.	.	PUNCT
ap-1189	39	1	the	the	DET
ap-1189	39	2	representation	representation	NOUN
ap-1189	39	3	of	of	ADP
ap-1189	39	4	the	the	DET
ap-1189	39	5	galilei	galilei	NOUN
ap-1189	39	6	group	group	NOUN
ap-1189	39	7	is	be	AUX
ap-1189	39	8	now	now	ADV
ap-1189	39	9	projective	projective	ADJ
ap-1189	39	10	but	but	CCONJ
ap-1189	39	11	it	it	PRON
ap-1189	39	12	can	can	AUX
ap-1189	39	13	still	still	ADV
ap-1189	39	14	be	be	AUX
ap-1189	39	15	viewed	view	VERB
ap-1189	39	16	as	as	ADP
ap-1189	39	17	a	a	DET
ap-1189	39	18	true	true	ADJ
ap-1189	39	19	representation	representation	NOUN
ap-1189	39	20	for	for	ADP
ap-1189	39	21	a	a	DET
ap-1189	39	22	central	central	ADJ
ap-1189	39	23	extension	extension	NOUN
ap-1189	39	24	ĝ	ĝ	NOUN
ap-1189	39	25	of	of	ADP
ap-1189	39	26	g	g	PROPN
ap-1189	39	27	,	,	PUNCT
ap-1189	39	28	[	[	X
ap-1189	39	29	1	1	NUM
ap-1189	39	30	]	]	PUNCT
ap-1189	39	31	.	.	PUNCT
ap-1189	40	1	1	1	NUM
ap-1189	40	2	-	-	PUNCT
ap-1189	40	3	cocycles	cocycle	NOUN
ap-1189	40	4	appear	appear	VERB
ap-1189	40	5	also	also	ADV
ap-1189	40	6	in	in	ADP
ap-1189	40	7	the	the	DET
ap-1189	40	8	context	context	NOUN
ap-1189	40	9	of	of	ADP
ap-1189	40	10	symmetry	symmetry	NOUN
ap-1189	40	11	breaking	break	VERB
ap-1189	40	12	in	in	ADP
ap-1189	40	13	qft	qft	PROPN
ap-1189	40	14	.	.	PUNCT
ap-1189	41	1	classically	classically	ADV
ap-1189	41	2	,	,	PUNCT
ap-1189	41	3	one	one	PRON
ap-1189	41	4	might	might	AUX
ap-1189	41	5	expect	expect	VERB
ap-1189	41	6	that	that	SCONJ
ap-1189	41	7	the	the	DET
ap-1189	41	8	(	(	PUNCT
ap-1189	41	9	exponentiated	exponentiated	ADJ
ap-1189	41	10	)	)	PUNCT
ap-1189	41	11	quantum	quantum	NOUN
ap-1189	41	12	action	action	NOUN
ap-1189	41	13	is	be	AUX
ap-1189	41	14	invariant	invariant	ADJ
ap-1189	41	15	under	under	ADP
ap-1189	41	16	a	a	DET
ap-1189	41	17	group	group	NOUN
ap-1189	41	18	g	g	PROPN
ap-1189	41	19	(	(	PUNCT
ap-1189	41	20	group	group	NOUN
ap-1189	41	21	of	of	ADP
ap-1189	41	22	gauge	gauge	ADJ
ap-1189	41	23	symmetries	symmetry	NOUN
ap-1189	41	24	or	or	CCONJ
ap-1189	41	25	group	group	NOUN
ap-1189	41	26	of	of	ADP
ap-1189	41	27	diffeomorphisms	diffeomorphism	NOUN
ap-1189	41	28	of	of	ADP
ap-1189	41	29	space	space	NOUN
ap-1189	41	30	-	-	PUNCT
ap-1189	41	31	time	time	NOUN
ap-1189	41	32	)	)	PUNCT
ap-1189	41	33	,	,	PUNCT
ap-1189	41	34	z(a	z(a	NUM
ap-1189	41	35	)	)	PUNCT
ap-1189	41	36	=	=	SYM
ap-1189	41	37	z(ag	z(ag	NOUN
ap-1189	41	38	)	)	PUNCT
ap-1189	41	39	where	where	SCONJ
ap-1189	41	40	a	a	DET
ap-1189	41	41	denotes	denote	NOUN
ap-1189	41	42	a	a	DET
ap-1189	41	43	set	set	NOUN
ap-1189	41	44	of	of	ADP
ap-1189	41	45	fields	field	NOUN
ap-1189	41	46	;	;	PUNCT
ap-1189	41	47	in	in	ADP
ap-1189	41	48	the	the	DET
ap-1189	41	49	case	case	NOUN
ap-1189	41	50	of	of	ADP
ap-1189	41	51	a	a	DET
ap-1189	41	52	gauge	gauge	ADJ
ap-1189	41	53	action	action	NOUN
ap-1189	41	54	the	the	DET
ap-1189	41	55	right	right	ADJ
ap-1189	41	56	action	action	NOUN
ap-1189	41	57	is	be	AUX
ap-1189	41	58	ag	ag	PROPN
ap-1189	41	59	=	=	PROPN
ap-1189	41	60	g−1ag	g−1ag	PROPN
ap-1189	41	61	+	+	CCONJ
ap-1189	41	62	g−1dg	g−1dg	NOUN
ap-1189	41	63	.	.	PUNCT
ap-1189	42	1	but	but	CCONJ
ap-1189	42	2	in	in	ADP
ap-1189	42	3	case	case	NOUN
ap-1189	42	4	of	of	ADP
ap-1189	42	5	chiral	chiral	ADJ
ap-1189	42	6	anomaly	anomaly	NOUN
ap-1189	42	7	,	,	PUNCT
ap-1189	42	8	for	for	ADP
ap-1189	42	9	example	example	NOUN
ap-1189	42	10	,	,	PUNCT
ap-1189	42	11	z(ag	z(ag	NOUN
ap-1189	42	12	)	)	PUNCT
ap-1189	42	13	=	=	SYM
ap-1189	42	14	ω(g;a)z(a	ω(g;a)z(a	NOUN
ap-1189	42	15	)	)	PUNCT
ap-1189	42	16	where	where	SCONJ
ap-1189	42	17	ω	ω	PROPN
ap-1189	42	18	is	be	AUX
ap-1189	42	19	a	a	DET
ap-1189	42	20	phase	phase	NOUN
ap-1189	42	21	factor	factor	NOUN
ap-1189	42	22	.	.	PUNCT
ap-1189	43	1	consistency	consistency	NOUN
ap-1189	43	2	requires	require	VERB
ap-1189	43	3	again	again	ADV
ap-1189	43	4	that	that	SCONJ
ap-1189	43	5	ω	ω	PROPN
ap-1189	43	6	is	be	AUX
ap-1189	43	7	a	a	DET
ap-1189	43	8	1	1	NUM
ap-1189	43	9	-	-	PUNCT
ap-1189	43	10	cocycle	cocycle	NOUN
ap-1189	43	11	.	.	PUNCT
ap-1189	44	1	however	however	ADV
ap-1189	44	2	,	,	PUNCT
ap-1189	44	3	unlike	unlike	ADP
ap-1189	44	4	in	in	ADP
ap-1189	44	5	the	the	DET
ap-1189	44	6	case	case	NOUN
ap-1189	44	7	of	of	ADP
ap-1189	44	8	the	the	DET
ap-1189	44	9	galilei	galilei	NOUN
ap-1189	44	10	group	group	NOUN
ap-1189	44	11	,	,	PUNCT
ap-1189	44	12	the	the	DET
ap-1189	44	13	nontrivial	nontrivial	ADJ
ap-1189	44	14	1	1	NUM
ap-1189	44	15	-	-	PUNCT
ap-1189	44	16	cocycle	cocycle	NOUN
ap-1189	44	17	has	have	VERB
ap-1189	44	18	serious	serious	ADJ
ap-1189	44	19	physical	physical	ADJ
ap-1189	44	20	consequences	consequence	NOUN
ap-1189	44	21	:	:	PUNCT
ap-1189	44	22	it	it	PRON
ap-1189	44	23	signals	signal	VERB
ap-1189	44	24	the	the	DET
ap-1189	44	25	breaking	breaking	NOUN
ap-1189	44	26	of	of	ADP
ap-1189	44	27	gauge	gauge	NOUN
ap-1189	44	28	symmetry	symmetry	NOUN
ap-1189	44	29	.	.	PUNCT
ap-1189	45	1	nontriviality	nontriviality	PROPN
ap-1189	45	2	means	mean	VERB
ap-1189	45	3	that	that	SCONJ
ap-1189	45	4	there	there	PRON
ap-1189	45	5	is	be	VERB
ap-1189	45	6	no	no	DET
ap-1189	45	7	way	way	NOUN
ap-1189	45	8	to	to	PART
ap-1189	45	9	modify	modify	VERB
ap-1189	45	10	the	the	DET
ap-1189	45	11	quantum	quantum	ADJ
ap-1189	45	12	effective	effective	ADJ
ap-1189	45	13	action	action	NOUN
ap-1189	45	14	by	by	ADP
ap-1189	45	15	a	a	DET
ap-1189	45	16	multiplicative	multiplicative	ADJ
ap-1189	45	17	phase	phase	NOUN
ap-1189	45	18	,	,	PUNCT
ap-1189	45	19	z(a	z(a	NUM
ap-1189	45	20	)	)	PUNCT
ap-1189	45	21	�	�	PROPN
ap-1189	45	22	→	→	SYM
ap-1189	45	23	z	z	NOUN
ap-1189	45	24	′(a	′(a	ADV
ap-1189	45	25	)	)	PUNCT
ap-1189	45	26	=	=	SYM
ap-1189	45	27	η(a)z(a	η(a)z(a	NOUN
ap-1189	45	28	)	)	PUNCT
ap-1189	45	29	,	,	PUNCT
ap-1189	45	30	such	such	ADJ
ap-1189	45	31	that	that	SCONJ
ap-1189	45	32	the	the	DET
ap-1189	45	33	modified	modified	ADJ
ap-1189	45	34	action	action	NOUN
ap-1189	45	35	z	z	NOUN
ap-1189	45	36	′	′	NOUN
ap-1189	45	37	would	would	AUX
ap-1189	45	38	be	be	AUX
ap-1189	45	39	gauge	gauge	NOUN
ap-1189	45	40	invariant	invariant	ADJ
ap-1189	45	41	.	.	PUNCT
ap-1189	46	1	this	this	PRON
ap-1189	46	2	means	mean	VERB
ap-1189	46	3	that	that	SCONJ
ap-1189	46	4	ω(g;a	ω(g;a	NOUN
ap-1189	46	5	)	)	PUNCT
ap-1189	46	6	�	�	PROPN
ap-1189	46	7	=	=	SYM
ap-1189	46	8	η(ag)η(a)−1	η(ag)η(a)−1	NOUN
ap-1189	46	9	for	for	ADP
ap-1189	46	10	any	any	DET
ap-1189	46	11	phase	phase	NOUN
ap-1189	46	12	function	function	NOUN
ap-1189	46	13	η	η	PROPN
ap-1189	46	14	.	.	PROPN
ap-1189	46	15	in	in	ADP
ap-1189	46	16	case	case	NOUN
ap-1189	46	17	of	of	ADP
ap-1189	46	18	an	an	DET
ap-1189	46	19	equality	equality	NOUN
ap-1189	46	20	,	,	PUNCT
ap-1189	46	21	we	we	PRON
ap-1189	46	22	say	say	VERB
ap-1189	46	23	that	that	SCONJ
ap-1189	46	24	the	the	DET
ap-1189	46	25	1	1	NUM
ap-1189	46	26	-	-	PUNCT
ap-1189	46	27	cocycle	cocycle	NOUN
ap-1189	46	28	ω	ω	PROPN
ap-1189	46	29	is	be	AUX
ap-1189	46	30	a	a	DET
ap-1189	46	31	coboundary	coboundary	NOUN
ap-1189	46	32	of	of	ADP
ap-1189	46	33	the	the	DET
ap-1189	46	34	0	0	NUM
ap-1189	46	35	-	-	PUNCT
ap-1189	46	36	cochain	cochain	NOUN
ap-1189	46	37	η	η	PROPN
ap-1189	46	38	.	.	PROPN
ap-1189	46	39	denote	denote	VERB
ap-1189	46	40	by	by	ADP
ap-1189	46	41	a	a	DET
ap-1189	46	42	the	the	DET
ap-1189	46	43	space	space	NOUN
ap-1189	46	44	of	of	ADP
ap-1189	46	45	all	all	DET
ap-1189	46	46	(	(	PUNCT
ap-1189	46	47	smooth	smooth	ADJ
ap-1189	46	48	)	)	PUNCT
ap-1189	46	49	fields	field	NOUN
ap-1189	46	50	a.	a.	NOUN
ap-1189	46	51	if	if	SCONJ
ap-1189	46	52	g	g	PROPN
ap-1189	46	53	acts	act	VERB
ap-1189	46	54	smoothly	smoothly	ADV
ap-1189	46	55	and	and	CCONJ
ap-1189	46	56	freely	freely	ADV
ap-1189	46	57	on	on	ADP
ap-1189	46	58	a	a	DET
ap-1189	46	59	then	then	NOUN
ap-1189	46	60	x	x	SCONJ
ap-1189	46	61	=	=	PUNCT
ap-1189	46	62	a	a	X
ap-1189	46	63	/	/	SYM
ap-1189	46	64	g	g	NOUN
ap-1189	46	65	is	be	AUX
ap-1189	46	66	a	a	DET
ap-1189	46	67	manifold	manifold	ADJ
ap-1189	46	68	and	and	CCONJ
ap-1189	46	69	the	the	DET
ap-1189	46	70	cocycle	cocycle	PROPN
ap-1189	46	71	ω	ω	PROPN
ap-1189	46	72	defines	define	VERB
ap-1189	46	73	a	a	DET
ap-1189	46	74	complex	complex	ADJ
ap-1189	46	75	line	line	NOUN
ap-1189	46	76	bundle	bundle	NOUN
ap-1189	46	77	l.	l.	PROPN
ap-1189	46	78	sections	section	NOUN
ap-1189	46	79	of	of	ADP
ap-1189	46	80	l	l	NOUN
ap-1189	46	81	are	be	AUX
ap-1189	46	82	complex	complex	ADJ
ap-1189	46	83	functions	function	NOUN
ap-1189	46	84	on	on	ADP
ap-1189	46	85	a	a	DET
ap-1189	46	86	satisfying	satisfying	ADJ
ap-1189	46	87	ψ(ag	ψ(ag	NOUN
ap-1189	46	88	)	)	PUNCT
ap-1189	46	89	=	=	SYM
ap-1189	46	90	ω(g;a)ψ(a	ω(g;a)ψ(a	NOUN
ap-1189	46	91	)	)	PUNCT
ap-1189	46	92	.	.	PUNCT
ap-1189	47	1	the	the	DET
ap-1189	47	2	complex	complex	ADJ
ap-1189	47	3	line	line	NOUN
ap-1189	47	4	bundle	bundle	NOUN
ap-1189	47	5	has	have	VERB
ap-1189	47	6	chern	chern	PROPN
ap-1189	47	7	class	class	PROPN
ap-1189	47	8	c	c	PROPN
ap-1189	47	9	∈	∈	PROPN
ap-1189	47	10	h2(x	h2(x	PROPN
ap-1189	47	11	,	,	PUNCT
ap-1189	47	12	z	z	NOUN
ap-1189	47	13	)	)	PUNCT
ap-1189	47	14	which	which	PRON
ap-1189	47	15	is	be	AUX
ap-1189	47	16	obtained	obtain	VERB
ap-1189	47	17	by	by	ADP
ap-1189	47	18	transgression	transgression	NOUN
ap-1189	47	19	from	from	ADP
ap-1189	47	20	ω	ω	PROPN
ap-1189	47	21	.	.	PUNCT
ap-1189	48	1	in	in	ADP
ap-1189	48	2	the	the	DET
ap-1189	48	3	case	case	NOUN
ap-1189	48	4	of	of	ADP
ap-1189	48	5	the	the	DET
ap-1189	48	6	chiral	chiral	ADJ
ap-1189	48	7	anomaly	anomaly	NOUN
ap-1189	48	8	,	,	PUNCT
ap-1189	48	9	the	the	DET
ap-1189	48	10	action	action	NOUN
ap-1189	48	11	z	z	NOUN
ap-1189	48	12	is	be	AUX
ap-1189	48	13	thus	thus	ADV
ap-1189	48	14	a	a	DET
ap-1189	48	15	section	section	NOUN
ap-1189	48	16	of	of	ADP
ap-1189	48	17	the	the	DET
ap-1189	48	18	complex	complex	ADJ
ap-1189	48	19	line	line	NOUN
ap-1189	48	20	bundle	bundle	NOUN
ap-1189	48	21	l	l	NOUN
ap-1189	48	22	,	,	PUNCT
ap-1189	48	23	which	which	PRON
ap-1189	48	24	is	be	AUX
ap-1189	48	25	called	call	VERB
ap-1189	48	26	the	the	DET
ap-1189	48	27	dirac	dirac	NOUN
ap-1189	48	28	determinant	determinant	ADJ
ap-1189	48	29	bundle	bundle	NOUN
ap-1189	48	30	.	.	PUNCT
ap-1189	49	1	indeed	indeed	ADV
ap-1189	49	2	,	,	PUNCT
ap-1189	49	3	the	the	DET
ap-1189	49	4	function	function	NOUN
ap-1189	49	5	z(a	z(a	NOUN
ap-1189	49	6	)	)	PUNCT
ap-1189	49	7	can	can	AUX
ap-1189	49	8	be	be	AUX
ap-1189	49	9	viewed	view	VERB
ap-1189	49	10	as	as	ADP
ap-1189	49	11	a	a	DET
ap-1189	49	12	regularized	regularize	VERB
ap-1189	49	13	determinant	determinant	ADJ
ap-1189	49	14	of	of	ADP
ap-1189	49	15	the	the	DET
ap-1189	49	16	massless	massless	ADJ
ap-1189	49	17	weyl	weyl	VERB
ap-1189	49	18	-	-	PUNCT
ap-1189	49	19	dirac	dirac	NOUN
ap-1189	49	20	operator	operator	NOUN
ap-1189	49	21	d+a	d+a	NUM
ap-1189	49	22	which	which	PRON
ap-1189	49	23	is	be	AUX
ap-1189	49	24	a	a	DET
ap-1189	49	25	linear	linear	ADJ
ap-1189	49	26	map	map	NOUN
ap-1189	49	27	from	from	ADP
ap-1189	49	28	the	the	DET
ap-1189	49	29	left	left	ADJ
ap-1189	49	30	-	-	PUNCT
ap-1189	49	31	handed	hand	VERB
ap-1189	49	32	spinor	spinor	NOUN
ap-1189	49	33	fields	field	NOUN
ap-1189	49	34	to	to	ADP
ap-1189	49	35	the	the	DET
ap-1189	49	36	right	right	ADV
ap-1189	49	37	-	-	PUNCT
ap-1189	49	38	handed	handed	ADJ
ap-1189	49	39	sector	sector	NOUN
ap-1189	49	40	.	.	PUNCT
ap-1189	50	1	to	to	PART
ap-1189	50	2	define	define	VERB
ap-1189	50	3	the	the	DET
ap-1189	50	4	determinant	determinant	ADJ
ap-1189	50	5	,	,	PUNCT
ap-1189	50	6	one	one	NUM
ap-1189	50	7	fixes	fix	VERB
ap-1189	50	8	a	a	DET
ap-1189	50	9	map	map	NOUN
ap-1189	50	10	d−	d−	PROPN
ap-1189	50	11	a0	a0	PROPN
ap-1189	50	12	from	from	ADP
ap-1189	50	13	right	right	ADV
ap-1189	50	14	-	-	PUNCT
ap-1189	50	15	handed	handed	ADJ
ap-1189	50	16	sector	sector	NOUN
ap-1189	50	17	to	to	ADP
ap-1189	50	18	the	the	DET
ap-1189	50	19	left	left	ADJ
ap-1189	50	20	-	-	PUNCT
ap-1189	50	21	handed	hand	VERB
ap-1189	50	22	sector	sector	NOUN
ap-1189	50	23	,	,	PUNCT
ap-1189	50	24	by	by	ADP
ap-1189	50	25	fixing	fix	VERB
ap-1189	50	26	a	a	DET
ap-1189	50	27	background	background	NOUN
ap-1189	50	28	potential	potential	ADJ
ap-1189	50	29	a0	a0	NOUN
ap-1189	50	30	,	,	PUNCT
ap-1189	50	31	and	and	CCONJ
ap-1189	50	32	then	then	ADV
ap-1189	50	33	one	one	NUM
ap-1189	50	34	applies	apply	VERB
ap-1189	50	35	the	the	DET
ap-1189	50	36	zeta	zeta	NOUN
ap-1189	50	37	function	function	NOUN
ap-1189	50	38	regularization	regularization	NOUN
ap-1189	50	39	to	to	ADP
ap-1189	50	40	the	the	DET
ap-1189	50	41	determinant	determinant	NOUN
ap-1189	50	42	of	of	ADP
ap-1189	50	43	the	the	DET
ap-1189	50	44	operator	operator	NOUN
ap-1189	50	45	d−	d−	PROPN
ap-1189	50	46	a0	a0	PROPN
ap-1189	50	47	d+a	d+a	NUM
ap-1189	50	48	.	.	PUNCT
ap-1189	51	1	in	in	ADP
ap-1189	51	2	hamiltonian	hamiltonian	ADJ
ap-1189	51	3	quantization	quantization	NOUN
ap-1189	51	4	the	the	DET
ap-1189	51	5	breaking	breaking	NOUN
ap-1189	51	6	of	of	ADP
ap-1189	51	7	(	(	PUNCT
ap-1189	51	8	gauge	gauge	ADJ
ap-1189	51	9	,	,	PUNCT
ap-1189	51	10	diffeomorphism	diffeomorphism	NOUN
ap-1189	51	11	)	)	PUNCT
ap-1189	51	12	symmetry	symmetry	NOUN
ap-1189	51	13	is	be	AUX
ap-1189	51	14	best	well	ADV
ap-1189	51	15	seen	see	VERB
ap-1189	51	16	in	in	ADP
ap-1189	51	17	the	the	DET
ap-1189	51	18	modified	modify	VERB
ap-1189	51	19	commutation	commutation	NOUN
ap-1189	51	20	relations	relation	NOUN
ap-1189	51	21	in	in	ADP
ap-1189	51	22	the	the	DET
ap-1189	51	23	lie	lie	NOUN
ap-1189	51	24	algebra	algebra	VERB
ap-1189	51	25	g	g	NOUN
ap-1189	51	26	of	of	ADP
ap-1189	51	27	g	g	PROPN
ap-1189	51	28	,	,	PUNCT
ap-1189	51	29	[	[	X
ap-1189	51	30	x	x	X
ap-1189	51	31	,	,	PUNCT
ap-1189	51	32	y	y	PROPN
ap-1189	51	33	]	]	PUNCT
ap-1189	51	34	�	�	PROPN
ap-1189	51	35	→	→	SYM
ap-1189	51	36	[	[	X
ap-1189	51	37	x	x	X
ap-1189	51	38	,	,	PUNCT
ap-1189	51	39	y	y	PROPN
ap-1189	51	40	]	]	PUNCT
ap-1189	52	1	+	+	CCONJ
ap-1189	52	2	c(x	c(x	NOUN
ap-1189	52	3	,	,	PUNCT
ap-1189	52	4	y	y	PROPN
ap-1189	52	5	)	)	PUNCT
ap-1189	52	6	where	where	SCONJ
ap-1189	52	7	c	c	NOUN
ap-1189	52	8	takes	take	VERB
ap-1189	52	9	values	value	NOUN
ap-1189	52	10	in	in	ADP
ap-1189	52	11	an	an	DET
ap-1189	52	12	abelian	abelian	ADJ
ap-1189	52	13	ideal	ideal	NOUN
ap-1189	52	14	a	a	X
ap-1189	52	15	;	;	PUNCT
ap-1189	52	16	in	in	ADP
ap-1189	52	17	the	the	DET
ap-1189	52	18	simplest	simple	ADJ
ap-1189	52	19	case	case	NOUN
ap-1189	52	20	a	a	DET
ap-1189	52	21	=	=	SYM
ap-1189	52	22	c	c	NOUN
ap-1189	52	23	and	and	CCONJ
ap-1189	52	24	c	c	NOUN
ap-1189	52	25	satisfies	satisfy	VERB
ap-1189	52	26	the	the	DET
ap-1189	52	27	lie	lie	NOUN
ap-1189	52	28	algebra	algebra	VERB
ap-1189	52	29	2	2	NUM
ap-1189	52	30	-	-	PUNCT
ap-1189	52	31	cocycle	cocycle	NOUN
ap-1189	52	32	condition	condition	NOUN
ap-1189	52	33	c(x	c(x	NOUN
ap-1189	52	34	,	,	PUNCT
ap-1189	52	35	[	[	X
ap-1189	52	36	y	y	X
ap-1189	52	37	,	,	PUNCT
ap-1189	52	38	z	z	NOUN
ap-1189	52	39	]	]	X
ap-1189	52	40	)	)	PUNCT
ap-1189	53	1	+	+	CCONJ
ap-1189	53	2	c(y	c(y	PROPN
ap-1189	53	3	,	,	PUNCT
ap-1189	53	4	[	[	X
ap-1189	53	5	z	z	X
ap-1189	53	6	,	,	PUNCT
ap-1189	53	7	x	x	X
ap-1189	53	8	]	]	PUNCT
ap-1189	53	9	)	)	PUNCT
ap-1189	54	1	+	+	CCONJ
ap-1189	54	2	c(z	c(z	NUM
ap-1189	54	3	,	,	PUNCT
ap-1189	54	4	[	[	X
ap-1189	54	5	x	x	X
ap-1189	54	6	,	,	PUNCT
ap-1189	54	7	y	y	PROPN
ap-1189	54	8	]	]	PUNCT
ap-1189	54	9	)	)	PUNCT
ap-1189	54	10	=	=	SYM
ap-1189	54	11	0	0	PUNCT
ap-1189	55	1	a	a	DET
ap-1189	55	2	famous	famous	ADJ
ap-1189	55	3	example	example	NOUN
ap-1189	55	4	is	be	AUX
ap-1189	55	5	given	give	VERB
ap-1189	55	6	by	by	ADP
ap-1189	55	7	the	the	DET
ap-1189	55	8	central	central	ADJ
ap-1189	55	9	extension	extension	NOUN
ap-1189	55	10	of	of	ADP
ap-1189	55	11	the	the	DET
ap-1189	55	12	loop	loop	NOUN
ap-1189	55	13	algebra	algebra	NOUN
ap-1189	55	14	lg	lg	NOUN
ap-1189	55	15	of	of	ADP
ap-1189	55	16	smooth	smooth	ADJ
ap-1189	55	17	functions	function	NOUN
ap-1189	55	18	on	on	ADP
ap-1189	55	19	the	the	DET
ap-1189	55	20	unit	unit	NOUN
ap-1189	55	21	circle	circle	NOUN
ap-1189	55	22	with	with	ADP
ap-1189	55	23	values	value	NOUN
ap-1189	55	24	in	in	ADP
ap-1189	55	25	a	a	DET
ap-1189	55	26	semisimple	semisimple	NOUN
ap-1189	55	27	lie	lie	NOUN
ap-1189	55	28	algebra	algebra	NOUN
ap-1189	55	29	g	g	NOUN
ap-1189	55	30	,	,	PUNCT
ap-1189	55	31	c(x	c(x	NOUN
ap-1189	55	32	,	,	PUNCT
ap-1189	55	33	y	y	PROPN
ap-1189	55	34	)	)	PUNCT
ap-1189	56	1	=	=	PUNCT
ap-1189	57	1	k	k	PROPN
ap-1189	57	2	2πi	2πi	PROPN
ap-1189	57	3	∫	∫	PROPN
ap-1189	57	4	s1	s1	PROPN
ap-1189	57	5	〈	〈	PROPN
ap-1189	57	6	x(φ	x(φ	PROPN
ap-1189	57	7	)	)	PUNCT
ap-1189	57	8	,	,	PUNCT
ap-1189	57	9	y	y	PROPN
ap-1189	57	10	′(φ)〉dφ	′(φ)〉dφ	PUNCT
ap-1189	57	11	where	where	SCONJ
ap-1189	57	12	k	k	PROPN
ap-1189	57	13	is	be	AUX
ap-1189	57	14	a	a	DET
ap-1189	57	15	constant	constant	ADJ
ap-1189	57	16	(	(	PUNCT
ap-1189	57	17	“	"	PUNCT
ap-1189	57	18	level	level	NOUN
ap-1189	57	19	”	"	PUNCT
ap-1189	57	20	of	of	ADP
ap-1189	57	21	a	a	DET
ap-1189	57	22	representation	representation	NOUN
ap-1189	57	23	)	)	PUNCT
ap-1189	57	24	,	,	PUNCT
ap-1189	57	25	which	which	PRON
ap-1189	57	26	is	be	AUX
ap-1189	57	27	equal	equal	ADJ
ap-1189	57	28	to	to	ADP
ap-1189	57	29	a	a	DET
ap-1189	57	30	nonnegative	nonnegative	ADJ
ap-1189	57	31	integer	integer	NOUN
ap-1189	57	32	in	in	ADP
ap-1189	57	33	a	a	DET
ap-1189	57	34	positive	positive	ADJ
ap-1189	57	35	energy	energy	NOUN
ap-1189	57	36	representation	representation	NOUN
ap-1189	57	37	when	when	SCONJ
ap-1189	57	38	the	the	DET
ap-1189	57	39	invariant	invariant	ADJ
ap-1189	57	40	bilinear	bilinear	NOUN
ap-1189	57	41	form	form	NOUN
ap-1189	57	42	〈	〈	PROPN
ap-1189	57	43	·	·	SYM
ap-1189	57	44	,	,	PUNCT
ap-1189	57	45	·	·	PUNCT
ap-1189	57	46	〉	〉	NOUN
ap-1189	57	47	on	on	ADP
ap-1189	57	48	g	g	PROPN
ap-1189	57	49	is	be	AUX
ap-1189	57	50	properly	properly	ADV
ap-1189	57	51	normalized	normalize	VERB
ap-1189	57	52	.	.	PUNCT
ap-1189	58	1	given	give	VERB
ap-1189	58	2	a	a	DET
ap-1189	58	3	(	(	PUNCT
ap-1189	58	4	central	central	ADJ
ap-1189	58	5	)	)	PUNCT
ap-1189	58	6	extension	extension	NOUN
ap-1189	58	7	of	of	ADP
ap-1189	58	8	a	a	DET
ap-1189	58	9	lie	lie	NOUN
ap-1189	58	10	algebra	algebra	NOUN
ap-1189	58	11	one	one	NUM
ap-1189	58	12	expects	expect	VERB
ap-1189	58	13	that	that	SCONJ
ap-1189	58	14	there	there	PRON
ap-1189	58	15	is	be	VERB
ap-1189	58	16	a	a	DET
ap-1189	58	17	central	central	ADJ
ap-1189	58	18	extension	extension	NOUN
ap-1189	58	19	of	of	ADP
ap-1189	58	20	the	the	DET
ap-1189	58	21	corresponding	corresponding	ADJ
ap-1189	58	22	group	group	NOUN
ap-1189	58	23	.	.	PUNCT
ap-1189	59	1	in	in	ADP
ap-1189	59	2	case	case	NOUN
ap-1189	59	3	of	of	ADP
ap-1189	59	4	lg	lg	NOUN
ap-1189	59	5	the	the	DET
ap-1189	59	6	group	group	NOUN
ap-1189	59	7	is	be	AUX
ap-1189	59	8	the	the	DET
ap-1189	59	9	loop	loop	NOUN
ap-1189	59	10	group	group	NOUN
ap-1189	59	11	lg	lg	NOUN
ap-1189	59	12	of	of	ADP
ap-1189	59	13	maps	map	NOUN
ap-1189	59	14	from	from	ADP
ap-1189	59	15	s1	s1	PROPN
ap-1189	59	16	to	to	ADP
ap-1189	59	17	a	a	DET
ap-1189	59	18	(	(	PUNCT
ap-1189	59	19	compact	compact	ADJ
ap-1189	59	20	)	)	PUNCT
ap-1189	59	21	group	group	NOUN
ap-1189	59	22	g.	g.	PROPN
ap-1189	59	23	a	a	DET
ap-1189	59	24	central	central	ADJ
ap-1189	59	25	extension	extension	NOUN
ap-1189	59	26	of	of	ADP
ap-1189	59	27	lg	lg	NOUN
ap-1189	59	28	would	would	AUX
ap-1189	59	29	then	then	ADV
ap-1189	59	30	be	be	AUX
ap-1189	59	31	given	give	VERB
ap-1189	59	32	by	by	ADP
ap-1189	59	33	a	a	DET
ap-1189	59	34	circle	circle	NOUN
ap-1189	59	35	valued	value	VERB
ap-1189	60	1	function	function	NOUN
ap-1189	60	2	ω	ω	NOUN
ap-1189	60	3	:	:	PUNCT
ap-1189	60	4	lg	lg	PROPN
ap-1189	60	5	×	×	PROPN
ap-1189	60	6	lg	lg	PROPN
ap-1189	60	7	→	→	SYM
ap-1189	60	8	s1	s1	NOUN
ap-1189	60	9	with	with	ADP
ap-1189	60	10	group	group	NOUN
ap-1189	60	11	2	2	NUM
ap-1189	60	12	-	-	PUNCT
ap-1189	60	13	cocycle	cocycle	NOUN
ap-1189	60	14	property	property	NOUN
ap-1189	60	15	ω(g1	ω(g1	NOUN
ap-1189	60	16	,	,	PUNCT
ap-1189	60	17	g2)ω(g1g2	g2)ω(g1g2	NOUN
ap-1189	60	18	,	,	PUNCT
ap-1189	60	19	g3	g3	PROPN
ap-1189	60	20	)	)	PUNCT
ap-1189	60	21	=	=	SYM
ap-1189	60	22	ω(g1	ω(g1	NOUN
ap-1189	60	23	,	,	PUNCT
ap-1189	60	24	g2g3)ω(g2	g2g3)ω(g2	PROPN
ap-1189	60	25	,	,	PUNCT
ap-1189	60	26	g3	g3	PROPN
ap-1189	60	27	)	)	PUNCT
ap-1189	60	28	.	.	PUNCT
ap-1189	61	1	however	however	ADV
ap-1189	61	2	,	,	PUNCT
ap-1189	61	3	in	in	ADP
ap-1189	61	4	case	case	NOUN
ap-1189	61	5	of	of	ADP
ap-1189	61	6	lg	lg	NOUN
ap-1189	61	7	there	there	PRON
ap-1189	61	8	is	be	VERB
ap-1189	61	9	a	a	DET
ap-1189	61	10	topological	topological	ADJ
ap-1189	61	11	obstruction	obstruction	NOUN
ap-1189	61	12	,	,	PUNCT
ap-1189	61	13	ω	ω	PROPN
ap-1189	61	14	is	be	AUX
ap-1189	61	15	defined	define	VERB
ap-1189	61	16	only	only	ADV
ap-1189	61	17	in	in	ADP
ap-1189	61	18	an	an	DET
ap-1189	61	19	open	open	ADJ
ap-1189	61	20	neighborhood	neighborhood	NOUN
ap-1189	61	21	of	of	ADP
ap-1189	61	22	the	the	DET
ap-1189	61	23	unit	unit	NOUN
ap-1189	61	24	element	element	NOUN
ap-1189	61	25	.	.	PUNCT
ap-1189	62	1	the	the	DET
ap-1189	62	2	obstruction	obstruction	NOUN
ap-1189	62	3	is	be	AUX
ap-1189	62	4	given	give	VERB
ap-1189	62	5	by	by	ADP
ap-1189	62	6	an	an	DET
ap-1189	62	7	element	element	NOUN
ap-1189	62	8	in	in	ADP
ap-1189	62	9	h2(lg	h2(lg	PROPN
ap-1189	62	10	,	,	PUNCT
ap-1189	62	11	z	z	NOUN
ap-1189	62	12	)	)	PUNCT
ap-1189	62	13	whose	whose	DET
ap-1189	62	14	de	de	ADP
ap-1189	62	15	rham	rham	PROPN
ap-1189	62	16	representative	representative	NOUN
ap-1189	62	17	is	be	AUX
ap-1189	62	18	a	a	DET
ap-1189	62	19	left	left	ADJ
ap-1189	62	20	invariant	invariant	ADJ
ap-1189	62	21	2	2	NUM
ap-1189	62	22	-	-	PUNCT
ap-1189	62	23	form	form	NOUN
ap-1189	62	24	fixed	fix	VERB
ap-1189	62	25	by	by	ADP
ap-1189	62	26	the	the	DET
ap-1189	62	27	lie	lie	NOUN
ap-1189	62	28	algebra	algebra	VERB
ap-1189	62	29	2	2	NUM
ap-1189	62	30	-	-	PUNCT
ap-1189	62	31	cocycle	cocycle	NOUN
ap-1189	62	32	c.	c.	NOUN
ap-1189	62	33	in	in	ADP
ap-1189	62	34	case	case	NOUN
ap-1189	62	35	of	of	ADP
ap-1189	62	36	a	a	DET
ap-1189	62	37	compact	compact	ADJ
ap-1189	62	38	simple	simple	NOUN
ap-1189	62	39	simply	simply	ADV
ap-1189	62	40	connected	connect	VERB
ap-1189	62	41	lie	lie	NOUN
ap-1189	62	42	group	group	NOUN
ap-1189	62	43	the	the	DET
ap-1189	62	44	cohomologyh2(lg	cohomologyh2(lg	PROPN
ap-1189	62	45	,	,	PUNCT
ap-1189	62	46	z	z	NOUN
ap-1189	62	47	)	)	PUNCT
ap-1189	62	48	is	be	AUX
ap-1189	62	49	equal	equal	ADJ
ap-1189	62	50	toh3(g	toh3(g	NOUN
ap-1189	62	51	,	,	PUNCT
ap-1189	62	52	z	z	NOUN
ap-1189	62	53	)	)	PUNCT
ap-1189	62	54	is	be	AUX
ap-1189	62	55	equal	equal	ADJ
ap-1189	62	56	to	to	ADP
ap-1189	62	57	z.	z.	PROPN
ap-1189	62	58	the	the	DET
ap-1189	62	59	lie	lie	NOUN
ap-1189	62	60	algebra	algebra	PROPN
ap-1189	62	61	cocycle	cocycle	NOUN
ap-1189	62	62	for	for	ADP
ap-1189	62	63	lg	lg	NOUN
ap-1189	62	64	can	can	AUX
ap-1189	62	65	be	be	AUX
ap-1189	62	66	viewed	view	VERB
ap-1189	62	67	as	as	ADP
ap-1189	62	68	a	a	DET
ap-1189	62	69	left	left	ADJ
ap-1189	62	70	invariant	invariant	ADJ
ap-1189	62	71	2	2	NUM
ap-1189	62	72	-	-	PUNCT
ap-1189	62	73	form	form	NOUN
ap-1189	62	74	on	on	ADP
ap-1189	62	75	the	the	DET
ap-1189	62	76	group	group	NOUN
ap-1189	62	77	lg	lg	PROPN
ap-1189	62	78	.	.	PROPN
ap-1189	62	79	for	for	ADP
ap-1189	62	80	a	a	DET
ap-1189	62	81	correct	correct	ADJ
ap-1189	62	82	choice	choice	NOUN
ap-1189	62	83	of	of	ADP
ap-1189	62	84	normalization	normalization	NOUN
ap-1189	62	85	of	of	ADP
ap-1189	62	86	the	the	DET
ap-1189	62	87	bilinear	bilinear	NOUN
ap-1189	62	88	form	form	NOUN
ap-1189	62	89	〈	〈	PROPN
ap-1189	62	90	,	,	PUNCT
ap-1189	62	91	·	·	PUNCT
ap-1189	62	92	,	,	PUNCT
ap-1189	62	93	·	·	PUNCT
ap-1189	62	94	〉	〉	NOUN
ap-1189	62	95	on	on	ADP
ap-1189	62	96	g	g	PROPN
ap-1189	62	97	the	the	DET
ap-1189	62	98	generator	generator	NOUN
ap-1189	62	99	in	in	ADP
ap-1189	62	100	h2(lg	h2(lg	PROPN
ap-1189	62	101	,	,	PUNCT
ap-1189	62	102	z	z	NOUN
ap-1189	62	103	)	)	PUNCT
ap-1189	62	104	corresponds	correspond	VERB
ap-1189	62	105	to	to	ADP
ap-1189	62	106	the	the	DET
ap-1189	62	107	basic	basic	ADJ
ap-1189	62	108	extension	extension	NOUN
ap-1189	62	109	with	with	ADP
ap-1189	62	110	level	level	NOUN
ap-1189	62	111	k	k	NOUN
ap-1189	63	1	=	=	SYM
ap-1189	64	1	1	1	NUM
ap-1189	64	2	.	.	NOUN
ap-1189	64	3	3	3	NUM
ap-1189	64	4	3	3	NUM
ap-1189	64	5	-	-	PUNCT
ap-1189	64	6	cocycles	cocycle	NOUN
ap-1189	64	7	group	group	NOUN
ap-1189	64	8	and	and	CCONJ
ap-1189	64	9	lie	lie	VERB
ap-1189	64	10	algebra	algebra	NOUN
ap-1189	64	11	cohomology	cohomology	NOUN
ap-1189	64	12	with	with	ADP
ap-1189	64	13	coefficients	coefficient	NOUN
ap-1189	64	14	in	in	ADP
ap-1189	64	15	an	an	DET
ap-1189	64	16	abelian	abelian	ADJ
ap-1189	64	17	group	group	NOUN
ap-1189	64	18	(	(	PUNCT
ap-1189	64	19	lie	lie	NOUN
ap-1189	64	20	algebra	algebra	NOUN
ap-1189	64	21	)	)	PUNCT
ap-1189	64	22	is	be	AUX
ap-1189	64	23	defined	define	VERB
ap-1189	64	24	in	in	ADP
ap-1189	64	25	any	any	DET
ap-1189	64	26	degree	degree	NOUN
ap-1189	64	27	.	.	PUNCT
ap-1189	65	1	so	so	ADV
ap-1189	65	2	what	what	PRON
ap-1189	65	3	about	about	ADP
ap-1189	65	4	degree	degree	NOUN
ap-1189	65	5	3	3	NUM
ap-1189	65	6	?	?	PUNCT
ap-1189	66	1	and	and	CCONJ
ap-1189	66	2	the	the	DET
ap-1189	66	3	relation	relation	NOUN
ap-1189	66	4	to	to	PART
ap-1189	66	5	de	de	X
ap-1189	66	6	rham	rham	PROPN
ap-1189	66	7	cohomology	cohomology	NOUN
ap-1189	66	8	in	in	ADP
ap-1189	66	9	dimension	dimension	NOUN
ap-1189	66	10	3	3	NUM
ap-1189	66	11	?	?	PUNCT
ap-1189	66	12	first	first	ADV
ap-1189	66	13	,	,	PUNCT
ap-1189	66	14	let	let	VERB
ap-1189	66	15	us	we	PRON
ap-1189	66	16	recall	recall	VERB
ap-1189	66	17	the	the	DET
ap-1189	66	18	basic	basic	ADJ
ap-1189	66	19	definitions	definition	NOUN
ap-1189	66	20	.	.	PUNCT
ap-1189	67	1	assume	assume	VERB
ap-1189	67	2	that	that	SCONJ
ap-1189	67	3	a	a	DET
ap-1189	67	4	group	group	NOUN
ap-1189	67	5	g	g	NOUN
ap-1189	67	6	acts	act	VERB
ap-1189	67	7	as	as	ADP
ap-1189	67	8	automorphisms	automorphism	NOUN
ap-1189	67	9	of	of	ADP
ap-1189	67	10	an	an	DET
ap-1189	67	11	abelian	abelian	ADJ
ap-1189	67	12	group	group	NOUN
ap-1189	67	13	a.	a.	NOUN
ap-1189	67	14	a	a	DET
ap-1189	67	15	map	map	NOUN
ap-1189	68	1	f	f	PROPN
ap-1189	68	2	:	:	PUNCT
ap-1189	68	3	g×g×	g×g×	PROPN
ap-1189	68	4	.	.	PUNCT
ap-1189	68	5	.	.	PUNCT
ap-1189	69	1	.g:→	.g:→	PROPN
ap-1189	69	2	a	a	DET
ap-1189	69	3	(	(	PUNCT
ap-1189	69	4	n	n	PRON
ap-1189	69	5	arguments	argument	NOUN
ap-1189	69	6	)	)	PUNCT
ap-1189	69	7	43	43	NUM
ap-1189	69	8	acta	acta	PROPN
ap-1189	69	9	polytechnica	polytechnica	PROPN
ap-1189	69	10	vol	vol	NOUN
ap-1189	69	11	.	.	PROPN
ap-1189	70	1	50	50	NUM
ap-1189	70	2	no	no	NOUN
ap-1189	70	3	.	.	PUNCT
ap-1189	71	1	3/2010	3/2010	NUM
ap-1189	71	2	is	be	AUX
ap-1189	71	3	a	a	DET
ap-1189	71	4	n	n	CCONJ
ap-1189	71	5	-	-	PUNCT
ap-1189	71	6	cocycle	cocycle	NOUN
ap-1189	71	7	if	if	SCONJ
ap-1189	71	8	δf	δf	PROPN
ap-1189	71	9	=	=	SYM
ap-1189	71	10	0	0	NUM
ap-1189	71	11	where	where	SCONJ
ap-1189	71	12	the	the	DET
ap-1189	71	13	coboundary	coboundary	ADJ
ap-1189	71	14	operator	operator	NOUN
ap-1189	71	15	δ	δ	PROPN
ap-1189	71	16	is	be	AUX
ap-1189	71	17	defined	define	VERB
ap-1189	71	18	by	by	ADP
ap-1189	71	19	(	(	PUNCT
ap-1189	71	20	δf)(g1	δf)(g1	PROPN
ap-1189	71	21	,	,	PUNCT
ap-1189	71	22	g2	g2	PROPN
ap-1189	71	23	,	,	PUNCT
ap-1189	71	24	.	.	PUNCT
ap-1189	71	25	.	.	PUNCT
ap-1189	72	1	.	.	PUNCT
ap-1189	73	1	,	,	PUNCT
ap-1189	73	2	gn+1	gn+1	PROPN
ap-1189	73	3	)	)	PUNCT
ap-1189	73	4	=	=	PUNCT
ap-1189	74	1	i	i	PROPN
ap-1189	74	2	=	=	PROPN
ap-1189	74	3	n∑	n∑	PROPN
ap-1189	74	4	i=1	i=1	PROPN
ap-1189	74	5	(	(	PUNCT
ap-1189	74	6	−1)if(g1	−1)if(g1	NOUN
ap-1189	74	7	,	,	PUNCT
ap-1189	74	8	.	.	PUNCT
ap-1189	74	9	.	.	PUNCT
ap-1189	74	10	.	.	PUNCT
ap-1189	75	1	gigi+1	gigi+1	PROPN
ap-1189	75	2	,	,	PUNCT
ap-1189	75	3	.	.	PUNCT
ap-1189	75	4	.	.	PUNCT
ap-1189	76	1	.	.	PUNCT
ap-1189	77	1	,	,	PUNCT
ap-1189	77	2	gn+1	gn+1	PROPN
ap-1189	77	3	)	)	PUNCT
ap-1189	78	1	+	+	CCONJ
ap-1189	78	2	(	(	PUNCT
ap-1189	78	3	−1)n+1f(g1	−1)n+1f(g1	ADJ
ap-1189	78	4	,	,	PUNCT
ap-1189	78	5	.	.	PUNCT
ap-1189	78	6	.	.	PUNCT
ap-1189	79	1	.	.	PUNCT
ap-1189	80	1	,	,	PUNCT
ap-1189	80	2	gn	gn	PROPN
ap-1189	80	3	)	)	PUNCT
ap-1189	80	4	+	+	CCONJ
ap-1189	80	5	g1	g1	PROPN
ap-1189	80	6	·	·	PUNCT
ap-1189	80	7	f(g2	f(g2	ADJ
ap-1189	80	8	,	,	PUNCT
ap-1189	80	9	.	.	PUNCT
ap-1189	80	10	.	.	PUNCT
ap-1189	80	11	.	.	PUNCT
ap-1189	81	1	,	,	PUNCT
ap-1189	81	2	gn+1	gn+1	PROPN
ap-1189	81	3	)	)	PUNCT
ap-1189	81	4	.	.	PUNCT
ap-1189	82	1	cocycles	cocycle	NOUN
ap-1189	82	2	of	of	ADP
ap-1189	82	3	type	type	NOUN
ap-1189	82	4	δf	δf	NOUN
ap-1189	82	5	are	be	AUX
ap-1189	82	6	exact	exact	ADJ
ap-1189	82	7	cocycles	cocycle	NOUN
ap-1189	82	8	.	.	PUNCT
ap-1189	83	1	the	the	DET
ap-1189	83	2	group	group	NOUN
ap-1189	83	3	cohomology	cohomology	NOUN
ap-1189	83	4	in	in	ADP
ap-1189	83	5	degree	degree	NOUN
ap-1189	83	6	n	n	NOUN
ap-1189	83	7	is	be	AUX
ap-1189	83	8	then	then	ADV
ap-1189	83	9	defined	define	VERB
ap-1189	83	10	as	as	ADP
ap-1189	83	11	the	the	DET
ap-1189	83	12	abelian	abelian	ADJ
ap-1189	83	13	group	group	NOUN
ap-1189	83	14	hn(g;a	hn(g;a	NOUN
ap-1189	83	15	)	)	PUNCT
ap-1189	83	16	of	of	ADP
ap-1189	83	17	n	n	CCONJ
ap-1189	83	18	-	-	PUNCT
ap-1189	83	19	cocycles	cocycle	NOUN
ap-1189	83	20	modulo	modulo	PART
ap-1189	83	21	exact	exact	ADJ
ap-1189	83	22	cocycles	cocycle	NOUN
ap-1189	83	23	.	.	PUNCT
ap-1189	84	1	in	in	ADP
ap-1189	84	2	case	case	NOUN
ap-1189	84	3	of	of	ADP
ap-1189	84	4	a	a	DET
ap-1189	84	5	lie	lie	NOUN
ap-1189	84	6	algebra	algebra	NOUN
ap-1189	84	7	g	g	PROPN
ap-1189	84	8	the	the	DET
ap-1189	84	9	cochains	cochain	NOUN
ap-1189	84	10	are	be	AUX
ap-1189	84	11	alternating	alternate	VERB
ap-1189	84	12	multilinear	multilinear	NOUN
ap-1189	84	13	maps	map	NOUN
ap-1189	84	14	f	f	X
ap-1189	84	15	:	:	PUNCT
ap-1189	85	1	g×	g×	X
ap-1189	85	2	.	.	PUNCT
ap-1189	85	3	.	.	PUNCT
ap-1189	86	1	.×	.×	PROPN
ap-1189	86	2	g	g	PROPN
ap-1189	86	3	→	→	PUNCT
ap-1189	86	4	a.	a.	NOUN
ap-1189	86	5	the	the	DET
ap-1189	86	6	cocycles	cocycle	NOUN
ap-1189	86	7	are	be	AUX
ap-1189	86	8	elements	element	NOUN
ap-1189	86	9	in	in	ADP
ap-1189	86	10	the	the	DET
ap-1189	86	11	kernel	kernel	NOUN
ap-1189	86	12	of	of	ADP
ap-1189	86	13	the	the	DET
ap-1189	86	14	lie	lie	NOUN
ap-1189	86	15	algebra	algebra	NOUN
ap-1189	86	16	coboundary	coboundary	ADJ
ap-1189	86	17	operator	operator	NOUN
ap-1189	86	18	,	,	PUNCT
ap-1189	86	19	which	which	PRON
ap-1189	86	20	is	be	AUX
ap-1189	86	21	now	now	ADV
ap-1189	86	22	defined	define	VERB
ap-1189	86	23	as	as	ADP
ap-1189	86	24	(	(	PUNCT
ap-1189	86	25	δf)(x1	δf)(x1	X
ap-1189	86	26	,	,	PUNCT
ap-1189	86	27	.	.	PUNCT
ap-1189	86	28	.	.	PUNCT
ap-1189	87	1	.	.	PUNCT
ap-1189	88	1	,	,	PUNCT
ap-1189	88	2	xn+1	xn+1	X
ap-1189	88	3	)	)	PUNCT
ap-1189	89	1	=	=	X
ap-1189	89	2	∑	∑	PUNCT
ap-1189	89	3	i	i	PROPN
ap-1189	89	4	<	<	X
ap-1189	89	5	j	j	PROPN
ap-1189	89	6	(	(	PUNCT
ap-1189	89	7	−1)i+j+1f([xi	−1)i+j+1f([xi	PROPN
ap-1189	89	8	,	,	PUNCT
ap-1189	89	9	xj	xj	PROPN
ap-1189	89	10	]	]	X
ap-1189	89	11	,	,	PUNCT
ap-1189	89	12	x1	x1	PROPN
ap-1189	89	13	,	,	PUNCT
ap-1189	89	14	.	.	PUNCT
ap-1189	89	15	.	.	PUNCT
ap-1189	89	16	.	.	PUNCT
ap-1189	90	1	x̂i	x̂i	PROPN
ap-1189	90	2	.	.	PUNCT
ap-1189	90	3	.	.	PUNCT
ap-1189	90	4	.	.	PUNCT
ap-1189	91	1	x̂j	x̂j	PROPN
ap-1189	91	2	.	.	PUNCT
ap-1189	91	3	.	.	PUNCT
ap-1189	91	4	.	.	PUNCT
ap-1189	92	1	xn+1	xn+1	X
ap-1189	92	2	)	)	PUNCT
ap-1189	93	1	+	+	CCONJ
ap-1189	93	2	i	i	PRON
ap-1189	93	3	=	=	PROPN
ap-1189	93	4	n+1∑	n+1∑	ADJ
ap-1189	93	5	i=1	i=1	PROPN
ap-1189	93	6	(	(	PUNCT
ap-1189	93	7	−1)ixi	−1)ixi	X
ap-1189	93	8	·	·	PUNCT
ap-1189	93	9	f(x1	f(x1	NOUN
ap-1189	93	10	,	,	PUNCT
ap-1189	93	11	.	.	PUNCT
ap-1189	93	12	.	.	PUNCT
ap-1189	93	13	.	.	PUNCT
ap-1189	94	1	x̂i	x̂i	PROPN
ap-1189	94	2	.	.	PUNCT
ap-1189	94	3	.	.	PUNCT
ap-1189	94	4	.	.	PUNCT
ap-1189	95	1	xn+1	xn+1	X
ap-1189	95	2	)	)	PUNCT
ap-1189	95	3	,	,	PUNCT
ap-1189	95	4	where	where	SCONJ
ap-1189	95	5	the	the	DET
ap-1189	95	6	argument	argument	NOUN
ap-1189	95	7	under	under	ADP
ap-1189	95	8	the	the	DET
ap-1189	95	9	hat	hat	NOUN
ap-1189	95	10	is	be	AUX
ap-1189	95	11	deleted	delete	VERB
ap-1189	95	12	.	.	PUNCT
ap-1189	96	1	here	here	ADV
ap-1189	96	2	the	the	DET
ap-1189	96	3	lie	lie	NOUN
ap-1189	96	4	algebra	algebra	NOUN
ap-1189	96	5	g	g	NOUN
ap-1189	96	6	acts	act	VERB
ap-1189	96	7	as	as	ADP
ap-1189	96	8	endomorphisms	endomorphism	NOUN
ap-1189	96	9	of	of	ADP
ap-1189	96	10	the	the	DET
ap-1189	96	11	abelian	abelian	ADJ
ap-1189	96	12	lie	lie	NOUN
ap-1189	96	13	algebra	algebra	NOUN
ap-1189	96	14	a.	a.	NOUN
ap-1189	96	15	the	the	DET
ap-1189	96	16	lie	lie	NOUN
ap-1189	96	17	algebra	algebra	VERB
ap-1189	96	18	cohomology	cohomology	NOUN
ap-1189	96	19	hn(g	hn(g	PUNCT
ap-1189	96	20	;	;	PUNCT
ap-1189	96	21	a	a	X
ap-1189	96	22	)	)	PUNCT
ap-1189	96	23	is	be	AUX
ap-1189	96	24	now	now	ADV
ap-1189	96	25	the	the	DET
ap-1189	96	26	abelian	abelian	ADJ
ap-1189	96	27	group	group	NOUN
ap-1189	96	28	of	of	ADP
ap-1189	96	29	n	n	CCONJ
ap-1189	96	30	-	-	PUNCT
ap-1189	96	31	cocycles	cocycle	NOUN
ap-1189	96	32	modulo	modulo	VERB
ap-1189	96	33	exact	exact	ADJ
ap-1189	96	34	n	n	CCONJ
ap-1189	96	35	-	-	PUNCT
ap-1189	96	36	cocycles	cocycle	NOUN
ap-1189	96	37	.	.	PUNCT
ap-1189	97	1	let	let	VERB
ap-1189	97	2	b	b	X
ap-1189	97	3	be	be	AUX
ap-1189	97	4	an	an	DET
ap-1189	97	5	associative	associative	ADJ
ap-1189	97	6	algebra	algebra	NOUN
ap-1189	97	7	and	and	CCONJ
ap-1189	97	8	g	g	ADP
ap-1189	97	9	a	a	DET
ap-1189	97	10	group	group	NOUN
ap-1189	97	11	.	.	PUNCT
ap-1189	98	1	assume	assume	VERB
ap-1189	98	2	that	that	SCONJ
ap-1189	98	3	we	we	PRON
ap-1189	98	4	have	have	VERB
ap-1189	98	5	a	a	DET
ap-1189	98	6	group	group	NOUN
ap-1189	98	7	homomorphism	homomorphism	NOUN
ap-1189	98	8	s	s	X
ap-1189	98	9	:	:	PUNCT
ap-1189	98	10	g	g	NOUN
ap-1189	98	11	→	→	SYM
ap-1189	98	12	out(b	out(b	NOUN
ap-1189	98	13	)	)	PUNCT
ap-1189	98	14	where	where	SCONJ
ap-1189	98	15	out(b	out(b	NOUN
ap-1189	98	16	)	)	PUNCT
ap-1189	98	17	is	be	AUX
ap-1189	98	18	the	the	DET
ap-1189	98	19	group	group	NOUN
ap-1189	98	20	of	of	ADP
ap-1189	98	21	outer	outer	ADJ
ap-1189	98	22	automorphisms	automorphism	NOUN
ap-1189	98	23	of	of	ADP
ap-1189	98	24	b	b	PROPN
ap-1189	98	25	,	,	PUNCT
ap-1189	98	26	that	that	ADV
ap-1189	98	27	is	is	ADV
ap-1189	98	28	,	,	PUNCT
ap-1189	98	29	out(b	out(b	X
ap-1189	98	30	)	)	PUNCT
ap-1189	98	31	=	=	SYM
ap-1189	98	32	aut(b)/in(b	aut(b)/in(b	PROPN
ap-1189	98	33	)	)	PUNCT
ap-1189	98	34	,	,	PUNCT
ap-1189	98	35	all	all	DET
ap-1189	98	36	automorphisms	automorphisms	PROPN
ap-1189	98	37	modulo	modulo	VERB
ap-1189	98	38	the	the	DET
ap-1189	98	39	normal	normal	ADJ
ap-1189	98	40	subgroup	subgroup	NOUN
ap-1189	98	41	of	of	ADP
ap-1189	98	42	inner	inner	ADJ
ap-1189	98	43	automorphisms	automorphism	NOUN
ap-1189	98	44	.	.	PUNCT
ap-1189	99	1	if	if	SCONJ
ap-1189	99	2	one	one	PRON
ap-1189	99	3	chooses	choose	VERB
ap-1189	99	4	any	any	DET
ap-1189	99	5	lift	lift	NOUN
ap-1189	99	6	s̃:g	s̃:g	NOUN
ap-1189	99	7	→	→	SYM
ap-1189	99	8	aut(b	aut(b	NOUN
ap-1189	99	9	)	)	PUNCT
ap-1189	99	10	then	then	ADV
ap-1189	99	11	we	we	PRON
ap-1189	99	12	can	can	AUX
ap-1189	99	13	write	write	VERB
ap-1189	99	14	s̃(g)s̃(g′	s̃(g)s̃(g′	NOUN
ap-1189	99	15	)	)	PUNCT
ap-1189	99	16	=	=	SYM
ap-1189	99	17	σ(g	σ(g	NOUN
ap-1189	99	18	,	,	PUNCT
ap-1189	99	19	g′	g′	NOUN
ap-1189	99	20	)	)	PUNCT
ap-1189	99	21	·	·	PUNCT
ap-1189	99	22	s̃(gg′	s̃(gg′	NOUN
ap-1189	99	23	)	)	PUNCT
ap-1189	99	24	for	for	ADP
ap-1189	99	25	some	some	DET
ap-1189	99	26	σ(g	σ(g	NOUN
ap-1189	99	27	,	,	PUNCT
ap-1189	99	28	g′	g′	NOUN
ap-1189	99	29	)	)	PUNCT
ap-1189	99	30	∈	∈	PROPN
ap-1189	99	31	in(b	in(b	NUM
ap-1189	99	32	)	)	PUNCT
ap-1189	99	33	.	.	PUNCT
ap-1189	100	1	from	from	ADP
ap-1189	100	2	the	the	DET
ap-1189	100	3	definition	definition	NOUN
ap-1189	100	4	follows	follow	VERB
ap-1189	100	5	immediately	immediately	ADV
ap-1189	100	6	the	the	DET
ap-1189	100	7	cocycle	cocycle	NOUN
ap-1189	100	8	property	property	NOUN
ap-1189	100	9	σ(g	σ(g	NOUN
ap-1189	100	10	,	,	PUNCT
ap-1189	100	11	g′)σ(gg′	g′)σ(gg′	NOUN
ap-1189	100	12	,	,	PUNCT
ap-1189	100	13	g′′	g′′	NOUN
ap-1189	100	14	)	)	PUNCT
ap-1189	100	15	=	=	PUNCT
ap-1189	101	1	[	[	X
ap-1189	101	2	s̃(g)σ(g′	s̃(g)σ(g′	X
ap-1189	101	3	,	,	PUNCT
ap-1189	101	4	g′′)s̃(g)−1]σ(g	g′′)s̃(g)−1]σ(g	PROPN
ap-1189	101	5	,	,	PUNCT
ap-1189	101	6	g′g′′	g′g′′	NOUN
ap-1189	101	7	)	)	PUNCT
ap-1189	101	8	let	let	VERB
ap-1189	101	9	next	next	ADJ
ap-1189	101	10	h	h	NOUN
ap-1189	101	11	be	be	AUX
ap-1189	101	12	any	any	DET
ap-1189	101	13	central	central	ADJ
ap-1189	101	14	extension	extension	NOUN
ap-1189	101	15	of	of	ADP
ap-1189	101	16	in(b	in(b	NOUN
ap-1189	101	17	)	)	PUNCT
ap-1189	101	18	by	by	ADP
ap-1189	101	19	an	an	DET
ap-1189	101	20	abelian	abelian	PROPN
ap-1189	101	21	group	group	NOUN
ap-1189	101	22	a.	a.	NOUN
ap-1189	101	23	that	that	PRON
ap-1189	101	24	is	be	AUX
ap-1189	101	25	,	,	PUNCT
ap-1189	101	26	we	we	PRON
ap-1189	101	27	have	have	VERB
ap-1189	101	28	an	an	DET
ap-1189	101	29	exact	exact	ADJ
ap-1189	101	30	sequence	sequence	NOUN
ap-1189	101	31	of	of	ADP
ap-1189	101	32	groups	group	NOUN
ap-1189	101	33	,	,	PUNCT
ap-1189	101	34	1→	1→	NUM
ap-1189	101	35	a	a	PRON
ap-1189	101	36	→	→	SYM
ap-1189	101	37	h	h	NOUN
ap-1189	101	38	→	→	SYM
ap-1189	101	39	in(b)→	in(b)→	VERB
ap-1189	101	40	1	1	NUM
ap-1189	101	41	.	.	PUNCT
ap-1189	102	1	let	let	VERB
ap-1189	102	2	σ̂	σ̂	X
ap-1189	102	3	be	be	AUX
ap-1189	102	4	a	a	DET
ap-1189	102	5	lift	lift	NOUN
ap-1189	102	6	of	of	ADP
ap-1189	102	7	the	the	DET
ap-1189	102	8	map	map	NOUN
ap-1189	102	9	σ	σ	NOUN
ap-1189	102	10	:	:	PUNCT
ap-1189	102	11	g×g→	g×g→	NOUN
ap-1189	102	12	in(b	in(b	NOUN
ap-1189	102	13	)	)	PUNCT
ap-1189	102	14	to	to	ADP
ap-1189	102	15	a	a	DET
ap-1189	102	16	map	map	NOUN
ap-1189	102	17	σ̂:g	σ̂:g	NOUN
ap-1189	102	18	×g	×g	NOUN
ap-1189	102	19	→	→	SYM
ap-1189	102	20	h	h	NOUN
ap-1189	102	21	(	(	PUNCT
ap-1189	102	22	by	by	ADP
ap-1189	102	23	a	a	DET
ap-1189	102	24	choice	choice	NOUN
ap-1189	102	25	of	of	ADP
ap-1189	102	26	a	a	DET
ap-1189	102	27	section	section	NOUN
ap-1189	102	28	in(b	in(b	NUM
ap-1189	102	29	)	)	PUNCT
ap-1189	102	30	→	→	SYM
ap-1189	102	31	h	h	X
ap-1189	102	32	)	)	PUNCT
ap-1189	102	33	.	.	PUNCT
ap-1189	103	1	we	we	PRON
ap-1189	103	2	have	have	VERB
ap-1189	103	3	then	then	ADV
ap-1189	103	4	σ̂(g	σ̂(g	NOUN
ap-1189	103	5	,	,	PUNCT
ap-1189	103	6	g′)σ̂(gg′	g′)σ̂(gg′	PRON
ap-1189	103	7	,	,	PUNCT
ap-1189	103	8	g′′	g′′	NOUN
ap-1189	103	9	)	)	PUNCT
ap-1189	103	10	=	=	PUNCT
ap-1189	104	1	[	[	X
ap-1189	104	2	s̃(g)σ̂(g′	s̃(g)σ̂(g′	PROPN
ap-1189	104	3	,	,	PUNCT
ap-1189	104	4	g′′)s̃(g)−1	g′′)s̃(g)−1	NOUN
ap-1189	104	5	]	]	PUNCT
ap-1189	104	6	×σ̂(g	×σ̂(g	X
ap-1189	104	7	,	,	PUNCT
ap-1189	104	8	g′g′′	g′g′′	NOUN
ap-1189	104	9	)	)	PUNCT
ap-1189	104	10	·	·	PUNCT
ap-1189	105	1	α(g	α(g	NUM
ap-1189	105	2	,	,	PUNCT
ap-1189	105	3	g′	g′	NOUN
ap-1189	105	4	,	,	PUNCT
ap-1189	105	5	g′′	g′′	PROPN
ap-1189	105	6	)	)	PUNCT
ap-1189	105	7	for	for	ADP
ap-1189	105	8	all	all	DET
ap-1189	105	9	g	g	NOUN
ap-1189	105	10	,	,	PUNCT
ap-1189	105	11	g′	g′	NOUN
ap-1189	105	12	,	,	PUNCT
ap-1189	105	13	g′′	g′′	PROPN
ap-1189	105	14	∈	∈	PROPN
ap-1189	105	15	g	g	PROPN
ap-1189	105	16	where	where	SCONJ
ap-1189	105	17	α	α	X
ap-1189	105	18	:	:	PUNCT
ap-1189	105	19	g×g×g	g×g×g	PROPN
ap-1189	105	20	→	→	SYM
ap-1189	105	21	a.	a.	NOUN
ap-1189	105	22	here	here	ADV
ap-1189	105	23	the	the	DET
ap-1189	105	24	action	action	NOUN
ap-1189	105	25	of	of	ADP
ap-1189	105	26	the	the	DET
ap-1189	105	27	outer	outer	ADJ
ap-1189	105	28	automorphism	automorphism	NOUN
ap-1189	105	29	s(g	s(g	PROPN
ap-1189	105	30	)	)	PUNCT
ap-1189	105	31	on	on	ADP
ap-1189	105	32	σ̂(∗	σ̂(∗	PROPN
ap-1189	105	33	)	)	PUNCT
ap-1189	105	34	is	be	AUX
ap-1189	105	35	defined	define	VERB
ap-1189	105	36	by	by	ADP
ap-1189	105	37	s̃(g)σ̂(∗)s̃(g)−1	s̃(g)σ̂(∗)s̃(g)−1	NOUN
ap-1189	105	38	=	=	PUNCT
ap-1189	105	39	the	the	DET
ap-1189	105	40	lift	lift	NOUN
ap-1189	105	41	of	of	ADP
ap-1189	105	42	s̃(g)σ(∗)s̃(g)−1	s̃(g)σ(∗)s̃(g)−1	NOUN
ap-1189	105	43	∈	∈	PROPN
ap-1189	105	44	in(b	in(b	NOUN
ap-1189	105	45	)	)	PUNCT
ap-1189	105	46	to	to	ADP
ap-1189	105	47	an	an	DET
ap-1189	105	48	element	element	NOUN
ap-1189	105	49	in	in	ADP
ap-1189	105	50	h	h	NOUN
ap-1189	105	51	.	.	PUNCT
ap-1189	106	1	one	one	PRON
ap-1189	106	2	can	can	AUX
ap-1189	106	3	show	show	VERB
ap-1189	106	4	that	that	SCONJ
ap-1189	106	5	α	α	PRON
ap-1189	106	6	is	be	AUX
ap-1189	106	7	a	a	DET
ap-1189	106	8	3	3	NUM
ap-1189	106	9	-	-	PUNCT
ap-1189	106	10	cocycle	cocycle	NOUN
ap-1189	106	11	,	,	PUNCT
ap-1189	107	1	[	[	X
ap-1189	107	2	9	9	NUM
ap-1189	107	3	]	]	PUNCT
ap-1189	107	4	,	,	PUNCT
ap-1189	107	5	α(g2	α(g2	PROPN
ap-1189	107	6	,	,	PUNCT
ap-1189	107	7	g3	g3	PROPN
ap-1189	107	8	,	,	PUNCT
ap-1189	107	9	g4)α(g1g2	g4)α(g1g2	PROPN
ap-1189	107	10	,	,	PUNCT
ap-1189	107	11	g3	g3	NOUN
ap-1189	107	12	,	,	PUNCT
ap-1189	107	13	g4)−1α(g1	g4)−1α(g1	PROPN
ap-1189	107	14	,	,	PUNCT
ap-1189	107	15	g2g3	g2g3	NOUN
ap-1189	107	16	,	,	PUNCT
ap-1189	107	17	g4	g4	NOUN
ap-1189	107	18	)	)	PUNCT
ap-1189	107	19	×α(g1	×α(g1	PROPN
ap-1189	107	20	,	,	PUNCT
ap-1189	107	21	g2	g2	PROPN
ap-1189	107	22	,	,	PUNCT
ap-1189	107	23	g3g4)−1α(g1	g3g4)−1α(g1	NOUN
ap-1189	107	24	,	,	PUNCT
ap-1189	107	25	g2	g2	PROPN
ap-1189	107	26	,	,	PUNCT
ap-1189	107	27	g3	g3	PROPN
ap-1189	107	28	)	)	PUNCT
ap-1189	107	29	=	=	SYM
ap-1189	107	30	1	1	NUM
ap-1189	107	31	,	,	PUNCT
ap-1189	107	32	where	where	SCONJ
ap-1189	107	33	we	we	PRON
ap-1189	107	34	have	have	AUX
ap-1189	107	35	used	use	VERB
ap-1189	107	36	the	the	DET
ap-1189	107	37	multiplicative	multiplicative	ADJ
ap-1189	107	38	notation	notation	NOUN
ap-1189	107	39	for	for	ADP
ap-1189	107	40	the	the	DET
ap-1189	107	41	group	group	NOUN
ap-1189	107	42	product	product	NOUN
ap-1189	107	43	in	in	ADP
ap-1189	107	44	a	a	PRON
ap-1189	107	45	(	(	PUNCT
ap-1189	107	46	instead	instead	ADV
ap-1189	107	47	of	of	ADP
ap-1189	107	48	the	the	DET
ap-1189	107	49	additive	additive	ADJ
ap-1189	107	50	notation	notation	NOUN
ap-1189	107	51	in	in	ADP
ap-1189	107	52	the	the	DET
ap-1189	107	53	definition	definition	NOUN
ap-1189	107	54	of	of	ADP
ap-1189	107	55	the	the	DET
ap-1189	107	56	coboundary	coboundary	ADJ
ap-1189	107	57	operator	operator	NOUN
ap-1189	107	58	)	)	PUNCT
ap-1189	107	59	.	.	PUNCT
ap-1189	108	1	the	the	DET
ap-1189	108	2	group	group	NOUN
ap-1189	108	3	g	g	PROPN
ap-1189	108	4	acts	act	VERB
ap-1189	108	5	trivially	trivially	ADV
ap-1189	108	6	on	on	ADP
ap-1189	108	7	a.	a.	NOUN
ap-1189	108	8	remark	remark	NOUN
ap-1189	108	9	if	if	SCONJ
ap-1189	108	10	we	we	PRON
ap-1189	108	11	work	work	VERB
ap-1189	108	12	in	in	ADP
ap-1189	108	13	the	the	DET
ap-1189	108	14	category	category	NOUN
ap-1189	108	15	of	of	ADP
ap-1189	108	16	topological	topological	ADJ
ap-1189	108	17	groups	group	NOUN
ap-1189	108	18	(	(	PUNCT
ap-1189	108	19	or	or	CCONJ
ap-1189	108	20	lie	lie	VERB
ap-1189	108	21	groups	group	NOUN
ap-1189	108	22	)	)	PUNCT
ap-1189	108	23	the	the	DET
ap-1189	108	24	lifts	lift	NOUN
ap-1189	108	25	above	above	ADV
ap-1189	108	26	are	be	AUX
ap-1189	108	27	in	in	ADP
ap-1189	108	28	general	general	ADJ
ap-1189	108	29	discontinuous	discontinuous	NOUN
ap-1189	108	30	;	;	PUNCT
ap-1189	108	31	normally	normally	ADV
ap-1189	108	32	,	,	PUNCT
ap-1189	108	33	we	we	PRON
ap-1189	108	34	can	can	AUX
ap-1189	108	35	require	require	VERB
ap-1189	108	36	continuity	continuity	NOUN
ap-1189	108	37	(	(	PUNCT
ap-1189	108	38	or	or	CCONJ
ap-1189	108	39	smoothness	smoothness	ADJ
ap-1189	108	40	)	)	PUNCT
ap-1189	108	41	only	only	ADV
ap-1189	108	42	in	in	ADP
ap-1189	108	43	an	an	DET
ap-1189	108	44	open	open	ADJ
ap-1189	108	45	neighborhood	neighborhood	NOUN
ap-1189	108	46	of	of	ADP
ap-1189	108	47	the	the	DET
ap-1189	108	48	unit	unit	NOUN
ap-1189	108	49	element	element	NOUN
ap-1189	108	50	.	.	PUNCT
ap-1189	109	1	4	4	NUM
ap-1189	109	2	a	a	DET
ap-1189	109	3	qft	qft	PROPN
ap-1189	109	4	example	example	NOUN
ap-1189	109	5	next	next	ADV
ap-1189	109	6	we	we	PRON
ap-1189	109	7	construct	construct	VERB
ap-1189	109	8	an	an	DET
ap-1189	109	9	example	example	NOUN
ap-1189	109	10	from	from	ADP
ap-1189	109	11	quantum	quantum	ADJ
ap-1189	109	12	field	field	NOUN
ap-1189	109	13	theory	theory	NOUN
ap-1189	109	14	.	.	PUNCT
ap-1189	110	1	let	let	VERB
ap-1189	110	2	g	g	PRON
ap-1189	110	3	be	be	AUX
ap-1189	110	4	a	a	DET
ap-1189	110	5	compact	compact	ADJ
ap-1189	110	6	simply	simply	ADV
ap-1189	110	7	connected	connect	VERB
ap-1189	110	8	lie	lie	NOUN
ap-1189	110	9	group	group	NOUN
ap-1189	110	10	and	and	CCONJ
ap-1189	110	11	p	p	X
ap-1189	110	12	the	the	DET
ap-1189	110	13	space	space	NOUN
ap-1189	110	14	of	of	ADP
ap-1189	110	15	smooth	smooth	ADJ
ap-1189	110	16	paths	path	NOUN
ap-1189	111	1	f	f	NOUN
ap-1189	111	2	:	:	PUNCT
ap-1189	112	1	[	[	X
ap-1189	112	2	0	0	NUM
ap-1189	112	3	,	,	PUNCT
ap-1189	112	4	1]→	1]→	ADJ
ap-1189	112	5	g	g	NOUN
ap-1189	112	6	with	with	ADP
ap-1189	112	7	initial	initial	ADJ
ap-1189	112	8	point	point	NOUN
ap-1189	112	9	f(0	f(0	NOUN
ap-1189	112	10	)	)	PUNCT
ap-1189	112	11	=	=	SYM
ap-1189	113	1	e	e	NOUN
ap-1189	113	2	,	,	PUNCT
ap-1189	113	3	the	the	DET
ap-1189	113	4	neutral	neutral	ADJ
ap-1189	113	5	element	element	NOUN
ap-1189	113	6	,	,	PUNCT
ap-1189	113	7	and	and	CCONJ
ap-1189	113	8	quasiperiodicity	quasiperiodicity	NOUN
ap-1189	113	9	condition	condition	NOUN
ap-1189	113	10	f−1df	f−1df	VERB
ap-1189	113	11	a	a	DET
ap-1189	113	12	smooth	smooth	ADJ
ap-1189	113	13	function	function	NOUN
ap-1189	113	14	.	.	PUNCT
ap-1189	114	1	p	p	NOUN
ap-1189	114	2	is	be	AUX
ap-1189	114	3	a	a	DET
ap-1189	114	4	group	group	NOUN
ap-1189	114	5	under	under	ADP
ap-1189	114	6	point	point	NOUN
ap-1189	114	7	-	-	PUNCT
ap-1189	114	8	wise	wise	ADJ
ap-1189	114	9	multiplication	multiplication	NOUN
ap-1189	114	10	but	but	CCONJ
ap-1189	114	11	it	it	PRON
ap-1189	114	12	is	be	AUX
ap-1189	114	13	also	also	ADV
ap-1189	114	14	a	a	DET
ap-1189	114	15	principal	principal	NOUN
ap-1189	114	16	ωg	ωg	PART
ap-1189	114	17	bundle	bundle	NOUN
ap-1189	114	18	over	over	ADP
ap-1189	114	19	g.	g.	PROPN
ap-1189	114	20	here	here	ADV
ap-1189	114	21	ωg	ωg	PROPN
ap-1189	114	22	⊂	⊂	PROPN
ap-1189	114	23	p	p	X
ap-1189	114	24	is	be	AUX
ap-1189	114	25	the	the	DET
ap-1189	114	26	based	base	VERB
ap-1189	114	27	loop	loop	NOUN
ap-1189	114	28	group	group	NOUN
ap-1189	114	29	with	with	ADP
ap-1189	114	30	f(0	f(0	NOUN
ap-1189	114	31	)	)	PUNCT
ap-1189	114	32	=	=	PUNCT
ap-1189	115	1	f(1	f(1	PROPN
ap-1189	115	2	)	)	PUNCT
ap-1189	115	3	=	=	SYM
ap-1189	115	4	e	e	PROPN
ap-1189	115	5	and	and	CCONJ
ap-1189	115	6	π	π	PROPN
ap-1189	115	7	:p	:p	PROPN
ap-1189	115	8	→	→	SYM
ap-1189	115	9	g	g	PROPN
ap-1189	115	10	is	be	AUX
ap-1189	115	11	the	the	DET
ap-1189	115	12	projection	projection	NOUN
ap-1189	115	13	to	to	ADP
ap-1189	115	14	the	the	DET
ap-1189	115	15	end	end	NOUN
ap-1189	115	16	point	point	NOUN
ap-1189	115	17	f(1	f(1	PROPN
ap-1189	115	18	)	)	PUNCT
ap-1189	115	19	.	.	PUNCT
ap-1189	116	1	fix	fix	VERB
ap-1189	116	2	an	an	DET
ap-1189	116	3	unitary	unitary	ADJ
ap-1189	116	4	representation	representation	NOUN
ap-1189	116	5	ρ	ρ	NOUN
ap-1189	116	6	of	of	ADP
ap-1189	116	7	g	g	PROPN
ap-1189	116	8	in	in	ADP
ap-1189	116	9	cn	cn	PROPN
ap-1189	116	10	and	and	CCONJ
ap-1189	116	11	denote	denote	VERB
ap-1189	116	12	h	h	NOUN
ap-1189	116	13	=	=	PUNCT
ap-1189	116	14	l2(s1,cn	l2(s1,cn	ADV
ap-1189	116	15	)	)	PUNCT
ap-1189	116	16	.	.	PUNCT
ap-1189	117	1	for	for	ADP
ap-1189	117	2	each	each	DET
ap-1189	117	3	polarization	polarization	NOUN
ap-1189	117	4	h	h	NOUN
ap-1189	117	5	=	=	SYM
ap-1189	117	6	h−	h−	PROPN
ap-1189	117	7	⊕	⊕	PROPN
ap-1189	117	8	h+	h+	VERB
ap-1189	117	9	we	we	PRON
ap-1189	117	10	have	have	VERB
ap-1189	117	11	a	a	DET
ap-1189	117	12	vacuum	vacuum	NOUN
ap-1189	117	13	representation	representation	NOUN
ap-1189	117	14	of	of	ADP
ap-1189	117	15	the	the	DET
ap-1189	117	16	canonical	canonical	ADJ
ap-1189	117	17	anticommutation	anticommutation	NOUN
ap-1189	117	18	relations	relation	NOUN
ap-1189	117	19	algebra	algebra	NOUN
ap-1189	117	20	(	(	PUNCT
ap-1189	117	21	car	car	NOUN
ap-1189	117	22	)	)	PUNCT
ap-1189	117	23	b(h	b(h	PROPN
ap-1189	117	24	)	)	PUNCT
ap-1189	117	25	in	in	ADP
ap-1189	117	26	a	a	DET
ap-1189	117	27	hilbert	hilbert	NOUN
ap-1189	117	28	space	space	NOUN
ap-1189	117	29	f(h+	f(h+	NOUN
ap-1189	117	30	)	)	PUNCT
ap-1189	117	31	.	.	PUNCT
ap-1189	118	1	denote	denote	VERB
ap-1189	118	2	by	by	ADP
ap-1189	118	3	c	c	PROPN
ap-1189	118	4	the	the	DET
ap-1189	118	5	category	category	NOUN
ap-1189	118	6	of	of	ADP
ap-1189	118	7	these	these	DET
ap-1189	118	8	representations	representation	NOUN
ap-1189	118	9	.	.	PUNCT
ap-1189	119	1	denote	denote	VERB
ap-1189	119	2	by	by	ADP
ap-1189	119	3	a(v	a(v	NOUN
ap-1189	119	4	)	)	PUNCT
ap-1189	119	5	,	,	PUNCT
ap-1189	119	6	a∗(v	a∗(v	PROPN
ap-1189	119	7	)	)	PUNCT
ap-1189	119	8	the	the	DET
ap-1189	119	9	generators	generator	NOUN
ap-1189	119	10	of	of	ADP
ap-1189	119	11	b(h	b(h	PROPN
ap-1189	119	12	)	)	PUNCT
ap-1189	119	13	corresponding	correspond	VERB
ap-1189	119	14	to	to	ADP
ap-1189	119	15	a	a	DET
ap-1189	119	16	vector	vector	NOUN
ap-1189	119	17	v	v	ADP
ap-1189	119	18	∈	∈	PROPN
ap-1189	119	19	h	h	NOUN
ap-1189	119	20	,	,	PUNCT
ap-1189	119	21	a∗(u)a(v	a∗(u)a(v	PROPN
ap-1189	119	22	)	)	PUNCT
ap-1189	120	1	+	+	NUM
ap-1189	120	2	a(v)a∗(u	a(v)a∗(u	NOUN
ap-1189	120	3	)	)	PUNCT
ap-1189	120	4	=	=	SYM
ap-1189	120	5	2〈v	2〈v	NOUN
ap-1189	120	6	,	,	PUNCT
ap-1189	120	7	u	u	NOUN
ap-1189	120	8	〉	〉	NOUN
ap-1189	120	9	·	·	SYM
ap-1189	120	10	1	1	NUM
ap-1189	120	11	and	and	CCONJ
ap-1189	120	12	all	all	DET
ap-1189	120	13	the	the	DET
ap-1189	120	14	other	other	ADJ
ap-1189	120	15	anticommutators	anticommutator	NOUN
ap-1189	120	16	equal	equal	ADJ
ap-1189	120	17	to	to	ADP
ap-1189	120	18	zero	zero	NUM
ap-1189	120	19	.	.	PUNCT
ap-1189	121	1	any	any	DET
ap-1189	121	2	element	element	NOUN
ap-1189	121	3	f	f	PROPN
ap-1189	121	4	∈	∈	PROPN
ap-1189	121	5	p	p	NOUN
ap-1189	121	6	defines	define	VERB
ap-1189	121	7	a	a	DET
ap-1189	121	8	unique	unique	ADJ
ap-1189	121	9	automorphism	automorphism	NOUN
ap-1189	121	10	of	of	ADP
ap-1189	121	11	b(h	b(h	PROPN
ap-1189	121	12	)	)	PUNCT
ap-1189	121	13	with	with	ADP
ap-1189	121	14	φf	φf	DET
ap-1189	121	15	(	(	PUNCT
ap-1189	121	16	a∗(v	a∗(v	PROPN
ap-1189	121	17	)	)	PUNCT
ap-1189	121	18	)	)	PUNCT
ap-1189	122	1	=	=	SYM
ap-1189	122	2	a∗(f	a∗(f	PROPN
ap-1189	122	3	·	·	PUNCT
ap-1189	122	4	v	v	X
ap-1189	122	5	)	)	PUNCT
ap-1189	122	6	,	,	PUNCT
ap-1189	122	7	where	where	SCONJ
ap-1189	122	8	f	f	PROPN
ap-1189	122	9	·	·	PUNCT
ap-1189	122	10	v	v	NOUN
ap-1189	122	11	is	be	AUX
ap-1189	122	12	the	the	DET
ap-1189	122	13	function	function	NOUN
ap-1189	122	14	on	on	ADP
ap-1189	122	15	the	the	DET
ap-1189	122	16	circle	circle	NOUN
ap-1189	122	17	defined	define	VERB
ap-1189	122	18	by	by	ADP
ap-1189	122	19	ρ(f(x))v(x	ρ(f(x))v(x	NUM
ap-1189	122	20	)	)	PUNCT
ap-1189	122	21	.	.	PUNCT
ap-1189	123	1	these	these	DET
ap-1189	123	2	automorphisms	automorphism	NOUN
ap-1189	123	3	are	be	AUX
ap-1189	123	4	in	in	ADP
ap-1189	123	5	general	general	ADJ
ap-1189	123	6	not	not	PART
ap-1189	123	7	inner	inner	ADJ
ap-1189	123	8	except	except	SCONJ
ap-1189	123	9	when	when	SCONJ
ap-1189	123	10	f	f	PROPN
ap-1189	123	11	is	be	AUX
ap-1189	123	12	periodic	periodic	ADJ
ap-1189	123	13	.	.	PUNCT
ap-1189	124	1	we	we	PRON
ap-1189	124	2	have	have	VERB
ap-1189	124	3	now	now	ADV
ap-1189	124	4	a	a	DET
ap-1189	124	5	map	map	NOUN
ap-1189	124	6	s	s	NOUN
ap-1189	124	7	:	:	PUNCT
ap-1189	124	8	g→	g→	NOUN
ap-1189	124	9	aut(b)/in(b	aut(b)/in(b	PROPN
ap-1189	124	10	)	)	PUNCT
ap-1189	124	11	given	give	VERB
ap-1189	124	12	by	by	ADP
ap-1189	124	13	g	g	PROPN
ap-1189	124	14	�	�	PROPN
ap-1189	124	15	→	→	SYM
ap-1189	124	16	f	f	X
ap-1189	124	17	(	(	PUNCT
ap-1189	124	18	g	g	NOUN
ap-1189	124	19	)	)	PUNCT
ap-1189	124	20	where	where	SCONJ
ap-1189	124	21	f	f	PROPN
ap-1189	124	22	(	(	PUNCT
ap-1189	124	23	g	g	NOUN
ap-1189	124	24	)	)	PUNCT
ap-1189	124	25	is	be	AUX
ap-1189	124	26	an	an	DET
ap-1189	124	27	arbitrary	arbitrary	ADJ
ap-1189	124	28	smooth	smooth	ADJ
ap-1189	124	29	quasiperiodic	quasiperiodic	ADJ
ap-1189	124	30	function	function	NOUN
ap-1189	124	31	on	on	ADP
ap-1189	124	32	[	[	X
ap-1189	124	33	0	0	NUM
ap-1189	124	34	,	,	PUNCT
ap-1189	124	35	1	1	NUM
ap-1189	124	36	]	]	PUNCT
ap-1189	124	37	such	such	ADJ
ap-1189	124	38	that	that	SCONJ
ap-1189	124	39	f	f	PROPN
ap-1189	124	40	(	(	PUNCT
ap-1189	124	41	g)(1	g)(1	X
ap-1189	124	42	)	)	PUNCT
ap-1189	125	1	=	=	VERB
ap-1189	125	2	g.	g.	NOUN
ap-1189	125	3	any	any	DET
ap-1189	125	4	two	two	NUM
ap-1189	125	5	such	such	ADJ
ap-1189	125	6	functions	function	NOUN
ap-1189	125	7	f	f	X
ap-1189	125	8	(	(	PUNCT
ap-1189	125	9	g	g	NOUN
ap-1189	125	10	)	)	PUNCT
ap-1189	125	11	,	,	PUNCT
ap-1189	125	12	f	f	PROPN
ap-1189	125	13	′(g	′(g	NOUN
ap-1189	125	14	)	)	PUNCT
ap-1189	125	15	differ	differ	VERB
ap-1189	125	16	by	by	ADP
ap-1189	125	17	an	an	DET
ap-1189	125	18	element	element	NOUN
ap-1189	125	19	σ	σ	NOUN
ap-1189	125	20	of	of	ADP
ap-1189	125	21	ωg	ωg	PROPN
ap-1189	125	22	,	,	PUNCT
ap-1189	125	23	f	f	PROPN
ap-1189	125	24	(	(	PUNCT
ap-1189	125	25	g)(x	g)(x	PROPN
ap-1189	125	26	)	)	PUNCT
ap-1189	125	27	=	=	SYM
ap-1189	125	28	f	f	PROPN
ap-1189	125	29	′(g)(x)σ(x	′(g)(x)σ(x	PROPN
ap-1189	125	30	)	)	PUNCT
ap-1189	125	31	.	.	PUNCT
ap-1189	126	1	now	now	ADV
ap-1189	126	2	σ	σ	PROPN
ap-1189	126	3	is	be	AUX
ap-1189	126	4	an	an	DET
ap-1189	126	5	inner	inner	ADJ
ap-1189	126	6	automorphism	automorphism	NOUN
ap-1189	126	7	through	through	ADP
ap-1189	126	8	a	a	DET
ap-1189	126	9	projective	projective	ADJ
ap-1189	126	10	representation	representation	NOUN
ap-1189	126	11	of	of	ADP
ap-1189	126	12	the	the	DET
ap-1189	126	13	loop	loop	NOUN
ap-1189	126	14	group	group	PROPN
ap-1189	126	15	ωg	ωg	PROPN
ap-1189	126	16	in	in	ADP
ap-1189	126	17	f(h+	f(h+	NOUN
ap-1189	126	18	)	)	PUNCT
ap-1189	126	19	.	.	PUNCT
ap-1189	127	1	in	in	ADP
ap-1189	127	2	an	an	DET
ap-1189	127	3	open	open	ADJ
ap-1189	127	4	neighborhood	neighborhood	NOUN
ap-1189	127	5	u	u	NOUN
ap-1189	127	6	of	of	ADP
ap-1189	127	7	the	the	DET
ap-1189	127	8	neutral	neutral	ADJ
ap-1189	127	9	element	element	NOUN
ap-1189	127	10	e	e	NOUN
ap-1189	127	11	in	in	ADP
ap-1189	127	12	g	g	PROPN
ap-1189	127	13	we	we	PRON
ap-1189	127	14	can	can	AUX
ap-1189	127	15	fix	fix	VERB
ap-1189	127	16	in	in	ADP
ap-1189	127	17	a	a	DET
ap-1189	127	18	smooth	smooth	ADJ
ap-1189	127	19	way	way	NOUN
ap-1189	127	20	for	for	ADP
ap-1189	127	21	any	any	DET
ap-1189	127	22	g	g	PROPN
ap-1189	127	23	∈	∈	PROPN
ap-1189	127	24	u	u	NOUN
ap-1189	127	25	a	a	DET
ap-1189	127	26	path	path	NOUN
ap-1189	127	27	f	f	X
ap-1189	127	28	(	(	PUNCT
ap-1189	127	29	g	g	NOUN
ap-1189	127	30	)	)	PUNCT
ap-1189	127	31	with	with	ADP
ap-1189	127	32	f	f	PROPN
ap-1189	127	33	(	(	PUNCT
ap-1189	127	34	g)(0	g)(0	X
ap-1189	127	35	)	)	PUNCT
ap-1189	127	36	=	=	SYM
ap-1189	127	37	e	e	NOUN
ap-1189	127	38	and	and	CCONJ
ap-1189	127	39	f	f	PROPN
ap-1189	127	40	(	(	PUNCT
ap-1189	127	41	g)(1	g)(1	X
ap-1189	127	42	)	)	PUNCT
ap-1189	128	1	=	=	SYM
ap-1189	129	1	g.	g.	PROPN
ap-1189	129	2	of	of	ADP
ap-1189	129	3	course	course	ADV
ap-1189	129	4	,	,	PUNCT
ap-1189	129	5	for	for	ADP
ap-1189	129	6	a	a	DET
ap-1189	129	7	connected	connected	ADJ
ap-1189	129	8	group	group	NOUN
ap-1189	129	9	g	g	NOUN
ap-1189	129	10	we	we	PRON
ap-1189	129	11	can	can	AUX
ap-1189	129	12	make	make	VERB
ap-1189	129	13	this	this	DET
ap-1189	129	14	choice	choice	NOUN
ap-1189	129	15	globally	globally	ADV
ap-1189	129	16	on	on	ADP
ap-1189	129	17	g	g	PROPN
ap-1189	130	1	but	but	CCONJ
ap-1189	130	2	then	then	ADV
ap-1189	130	3	the	the	DET
ap-1189	130	4	dependence	dependence	NOUN
ap-1189	130	5	of	of	ADP
ap-1189	130	6	the	the	DET
ap-1189	130	7	path	path	NOUN
ap-1189	130	8	f	f	X
ap-1189	130	9	(	(	PUNCT
ap-1189	130	10	g	g	NOUN
ap-1189	130	11	)	)	PUNCT
ap-1189	130	12	would	would	AUX
ap-1189	130	13	not	not	PART
ap-1189	130	14	be	be	AUX
ap-1189	130	15	a	a	DET
ap-1189	130	16	continuous	continuous	ADJ
ap-1189	130	17	function	function	NOUN
ap-1189	130	18	of	of	ADP
ap-1189	130	19	the	the	DET
ap-1189	130	20	end	end	NOUN
ap-1189	130	21	point	point	NOUN
ap-1189	130	22	.	.	PUNCT
ap-1189	131	1	for	for	ADP
ap-1189	131	2	a	a	DET
ap-1189	131	3	pair	pair	NOUN
ap-1189	131	4	g1	g1	NOUN
ap-1189	131	5	,	,	PUNCT
ap-1189	131	6	g2	g2	PROPN
ap-1189	131	7	∈	∈	PROPN
ap-1189	132	1	g	g	NOUN
ap-1189	132	2	we	we	PRON
ap-1189	132	3	have	have	VERB
ap-1189	132	4	44	44	NUM
ap-1189	132	5	acta	acta	PROPN
ap-1189	132	6	polytechnica	polytechnica	PROPN
ap-1189	132	7	vol	vol	NOUN
ap-1189	132	8	.	.	PROPN
ap-1189	133	1	50	50	NUM
ap-1189	133	2	no	no	NOUN
ap-1189	133	3	.	.	PUNCT
ap-1189	134	1	3/2010	3/2010	NUM
ap-1189	134	2	σ(g1	σ(g1	NOUN
ap-1189	134	3	,	,	PUNCT
ap-1189	134	4	g2)f	g2)f	NOUN
ap-1189	134	5	(	(	PUNCT
ap-1189	134	6	g1g2	g1g2	NOUN
ap-1189	134	7	)	)	PUNCT
ap-1189	134	8	=	=	SYM
ap-1189	134	9	f	f	PROPN
ap-1189	134	10	(	(	PUNCT
ap-1189	134	11	g1)f	g1)f	PROPN
ap-1189	134	12	(	(	PUNCT
ap-1189	134	13	g2	g2	PROPN
ap-1189	134	14	)	)	PUNCT
ap-1189	134	15	with	with	ADP
ap-1189	134	16	σ(g1	σ(g1	NOUN
ap-1189	134	17	,	,	PUNCT
ap-1189	134	18	g1	g1	NOUN
ap-1189	134	19	)	)	PUNCT
ap-1189	134	20	∈	∈	PROPN
ap-1189	134	21	ωg	ωg	NOUN
ap-1189	134	22	.	.	PROPN
ap-1189	134	23	for	for	ADP
ap-1189	134	24	a	a	DET
ap-1189	134	25	triple	triple	NOUN
ap-1189	134	26	of	of	ADP
ap-1189	134	27	elements	element	NOUN
ap-1189	134	28	g1	g1	NOUN
ap-1189	134	29	,	,	PUNCT
ap-1189	134	30	g2	g2	PROPN
ap-1189	134	31	,	,	PUNCT
ap-1189	134	32	g3	g3	NOUN
ap-1189	134	33	we	we	PRON
ap-1189	134	34	have	have	VERB
ap-1189	134	35	now	now	ADV
ap-1189	134	36	f	f	X
ap-1189	134	37	(	(	PUNCT
ap-1189	134	38	g1)f	g1)f	PROPN
ap-1189	134	39	(	(	PUNCT
ap-1189	134	40	g2)f	g2)f	NOUN
ap-1189	134	41	(	(	PUNCT
ap-1189	134	42	g3	g3	NOUN
ap-1189	134	43	)	)	PUNCT
ap-1189	134	44	=	=	PUNCT
ap-1189	134	45	σ(g1	σ(g1	NOUN
ap-1189	134	46	,	,	PUNCT
ap-1189	134	47	g2)f	g2)f	NOUN
ap-1189	134	48	(	(	PUNCT
ap-1189	134	49	g1g2)f	g1g2)f	PROPN
ap-1189	134	50	(	(	PUNCT
ap-1189	134	51	g3	g3	NOUN
ap-1189	134	52	)	)	PUNCT
ap-1189	134	53	=	=	PUNCT
ap-1189	134	54	σ(g1	σ(g1	NOUN
ap-1189	134	55	,	,	PUNCT
ap-1189	134	56	g2)σ(g1g2	g2)σ(g1g2	NOUN
ap-1189	134	57	,	,	PUNCT
ap-1189	134	58	g3)f	g3)f	PROPN
ap-1189	134	59	(	(	PUNCT
ap-1189	134	60	g1g2g3	g1g2g3	PROPN
ap-1189	134	61	)	)	PUNCT
ap-1189	134	62	.	.	PUNCT
ap-1189	135	1	in	in	ADP
ap-1189	135	2	the	the	DET
ap-1189	135	3	same	same	ADJ
ap-1189	135	4	way	way	NOUN
ap-1189	135	5	,	,	PUNCT
ap-1189	135	6	f	f	PROPN
ap-1189	135	7	(	(	PUNCT
ap-1189	135	8	g1)f	g1)f	PROPN
ap-1189	135	9	(	(	PUNCT
ap-1189	135	10	g2)f	g2)f	NOUN
ap-1189	135	11	(	(	PUNCT
ap-1189	135	12	g3	g3	PROPN
ap-1189	135	13	)	)	PUNCT
ap-1189	135	14	=	=	SYM
ap-1189	135	15	f	f	PROPN
ap-1189	135	16	(	(	PUNCT
ap-1189	135	17	g1)σ(g2	g1)σ(g2	PROPN
ap-1189	135	18	,	,	PUNCT
ap-1189	135	19	g3)f	g3)f	PROPN
ap-1189	135	20	(	(	PUNCT
ap-1189	135	21	g2g3	g2g3	X
ap-1189	135	22	)	)	PUNCT
ap-1189	135	23	=	=	PUNCT
ap-1189	136	1	[	[	X
ap-1189	136	2	g1σ(g2	g1σ(g2	X
ap-1189	136	3	,	,	PUNCT
ap-1189	136	4	g3)g	g3)g	ADJ
ap-1189	136	5	−1	−1	NOUN
ap-1189	136	6	1	1	NUM
ap-1189	136	7	]	]	SYM
ap-1189	136	8	f	f	X
ap-1189	136	9	(	(	PUNCT
ap-1189	136	10	g1)f	g1)f	PROPN
ap-1189	136	11	(	(	PUNCT
ap-1189	136	12	g2g3	g2g3	X
ap-1189	136	13	)	)	PUNCT
ap-1189	136	14	=	=	PUNCT
ap-1189	137	1	[	[	X
ap-1189	137	2	g1σ(g2	g1σ(g2	X
ap-1189	137	3	,	,	PUNCT
ap-1189	137	4	g3)g	g3)g	ADJ
ap-1189	137	5	−1	−1	NOUN
ap-1189	137	6	1	1	NUM
ap-1189	137	7	]	]	PUNCT
ap-1189	137	8	σ(g1	σ(g1	NOUN
ap-1189	137	9	,	,	PUNCT
ap-1189	137	10	g2g3)f	g2g3)f	PROPN
ap-1189	137	11	(	(	PUNCT
ap-1189	137	12	g1g2g3	g1g2g3	PROPN
ap-1189	137	13	)	)	PUNCT
ap-1189	137	14	which	which	PRON
ap-1189	137	15	proves	prove	VERB
ap-1189	137	16	the	the	DET
ap-1189	137	17	2	2	NUM
ap-1189	137	18	-	-	PUNCT
ap-1189	137	19	cocycle	cocycle	NOUN
ap-1189	137	20	relation	relation	NOUN
ap-1189	137	21	for	for	ADP
ap-1189	137	22	σ	σ	PROPN
ap-1189	137	23	.	.	PUNCT
ap-1189	137	24	lifting	lift	VERB
ap-1189	137	25	the	the	DET
ap-1189	137	26	loop	loop	NOUN
ap-1189	137	27	group	group	NOUN
ap-1189	137	28	elements	element	NOUN
ap-1189	137	29	σ	σ	NOUN
ap-1189	137	30	to	to	ADP
ap-1189	137	31	inner	inner	ADJ
ap-1189	137	32	automorphisms	automorphism	NOUN
ap-1189	137	33	σ̂	σ̂	X
ap-1189	137	34	through	through	ADP
ap-1189	137	35	a	a	DET
ap-1189	137	36	projective	projective	ADJ
ap-1189	137	37	representation	representation	NOUN
ap-1189	137	38	of	of	ADP
ap-1189	137	39	ωg	ωg	PROPN
ap-1189	137	40	we	we	PRON
ap-1189	137	41	can	can	AUX
ap-1189	137	42	write	write	VERB
ap-1189	137	43	σ̂(g1	σ̂(g1	PRON
ap-1189	137	44	,	,	PUNCT
ap-1189	137	45	g2)σ̂(g1g2	g2)σ̂(g1g2	NOUN
ap-1189	137	46	,	,	PUNCT
ap-1189	137	47	g3	g3	NOUN
ap-1189	137	48	)	)	PUNCT
ap-1189	137	49	=	=	SYM
ap-1189	138	1	aut(g1)[σ̂(g2	aut(g1)[σ̂(g2	PROPN
ap-1189	138	2	,	,	PUNCT
ap-1189	138	3	g3)]σ̂(g1	g3)]σ̂(g1	PROPN
ap-1189	138	4	,	,	PUNCT
ap-1189	138	5	g2g3)α(g1	g2g3)α(g1	PROPN
ap-1189	138	6	,	,	PUNCT
ap-1189	138	7	g2	g2	PROPN
ap-1189	138	8	,	,	PUNCT
ap-1189	138	9	g3	g3	PROPN
ap-1189	138	10	)	)	PUNCT
ap-1189	138	11	,	,	PUNCT
ap-1189	138	12	where	where	SCONJ
ap-1189	138	13	α	α	X
ap-1189	138	14	:	:	PUNCT
ap-1189	138	15	g×g×g→	g×g×g→	ADJ
ap-1189	138	16	s1	s1	NOUN
ap-1189	138	17	is	be	AUX
ap-1189	138	18	some	some	DET
ap-1189	138	19	phase	phase	NOUN
ap-1189	138	20	function	function	NOUN
ap-1189	138	21	arising	arise	VERB
ap-1189	138	22	from	from	ADP
ap-1189	138	23	the	the	DET
ap-1189	138	24	fact	fact	NOUN
ap-1189	138	25	that	that	SCONJ
ap-1189	138	26	the	the	DET
ap-1189	138	27	projective	projective	ADJ
ap-1189	138	28	lift	lift	NOUN
ap-1189	138	29	is	be	AUX
ap-1189	138	30	not	not	PART
ap-1189	138	31	necessarily	necessarily	ADV
ap-1189	138	32	a	a	DET
ap-1189	138	33	group	group	NOUN
ap-1189	138	34	homomorphism	homomorphism	NOUN
ap-1189	138	35	.	.	PUNCT
ap-1189	139	1	since	since	SCONJ
ap-1189	139	2	(	(	PUNCT
ap-1189	139	3	in	in	ADP
ap-1189	139	4	the	the	DET
ap-1189	139	5	case	case	NOUN
ap-1189	139	6	of	of	ADP
ap-1189	139	7	a	a	DET
ap-1189	139	8	lie	lie	NOUN
ap-1189	139	9	group	group	NOUN
ap-1189	139	10	)	)	PUNCT
ap-1189	139	11	the	the	DET
ap-1189	139	12	function	function	NOUN
ap-1189	139	13	f	f	PROPN
ap-1189	139	14	(	(	PUNCT
ap-1189	139	15	·	·	PUNCT
ap-1189	139	16	)	)	PUNCT
ap-1189	139	17	is	be	AUX
ap-1189	139	18	smooth	smooth	ADJ
ap-1189	139	19	only	only	ADV
ap-1189	139	20	in	in	ADP
ap-1189	139	21	a	a	DET
ap-1189	139	22	neighborhood	neighborhood	NOUN
ap-1189	139	23	of	of	ADP
ap-1189	139	24	the	the	DET
ap-1189	139	25	neutral	neutral	ADJ
ap-1189	139	26	element	element	NOUN
ap-1189	139	27	,	,	PUNCT
ap-1189	139	28	the	the	DET
ap-1189	139	29	same	same	ADJ
ap-1189	139	30	is	be	AUX
ap-1189	139	31	true	true	ADJ
ap-1189	139	32	also	also	ADV
ap-1189	139	33	for	for	ADP
ap-1189	139	34	σ	σ	PROPN
ap-1189	139	35	and	and	CCONJ
ap-1189	139	36	finally	finally	ADV
ap-1189	139	37	for	for	ADP
ap-1189	139	38	the	the	DET
ap-1189	139	39	3	3	NUM
ap-1189	139	40	-	-	PUNCT
ap-1189	139	41	cocycle	cocycle	NOUN
ap-1189	139	42	α	α	NOUN
ap-1189	139	43	.	.	PUNCT
ap-1189	140	1	an	an	DET
ap-1189	140	2	equivalent	equivalent	ADJ
ap-1189	140	3	point	point	NOUN
ap-1189	140	4	of	of	ADP
ap-1189	140	5	view	view	NOUN
ap-1189	140	6	to	to	ADP
ap-1189	140	7	the	the	DET
ap-1189	140	8	construction	construction	NOUN
ap-1189	140	9	of	of	ADP
ap-1189	140	10	the	the	DET
ap-1189	140	11	3	3	NUM
ap-1189	140	12	-	-	PUNCT
ap-1189	140	13	cocycle	cocycle	NOUN
ap-1189	140	14	α	α	PROPN
ap-1189	140	15	is	be	AUX
ap-1189	140	16	this	this	PRON
ap-1189	140	17	:	:	PUNCT
ap-1189	140	18	we	we	PRON
ap-1189	140	19	are	be	AUX
ap-1189	140	20	trying	try	VERB
ap-1189	140	21	to	to	PART
ap-1189	140	22	construct	construct	VERB
ap-1189	140	23	a	a	DET
ap-1189	140	24	central	central	ADJ
ap-1189	140	25	extension	extension	NOUN
ap-1189	140	26	p̂	p̂	NOUN
ap-1189	140	27	of	of	ADP
ap-1189	140	28	the	the	DET
ap-1189	140	29	group	group	NOUN
ap-1189	140	30	p	p	NOUN
ap-1189	140	31	of	of	ADP
ap-1189	140	32	paths	path	NOUN
ap-1189	140	33	in	in	ADP
ap-1189	140	34	g	g	PROPN
ap-1189	140	35	(	(	PUNCT
ap-1189	140	36	with	with	ADP
ap-1189	140	37	initial	initial	ADJ
ap-1189	140	38	point	point	NOUN
ap-1189	140	39	e	e	X
ap-1189	140	40	∈	∈	PROPN
ap-1189	140	41	g	g	PROPN
ap-1189	140	42	)	)	PUNCT
ap-1189	140	43	as	as	ADP
ap-1189	140	44	an	an	DET
ap-1189	140	45	extension	extension	NOUN
ap-1189	140	46	of	of	ADP
ap-1189	140	47	the	the	DET
ap-1189	140	48	central	central	ADJ
ap-1189	140	49	extension	extension	NOUN
ap-1189	140	50	over	over	ADP
ap-1189	140	51	the	the	DET
ap-1189	140	52	subgroup	subgroup	NOUN
ap-1189	140	53	ωg	ωg	PROPN
ap-1189	140	54	.	.	PUNCT
ap-1189	141	1	the	the	DET
ap-1189	141	2	failure	failure	NOUN
ap-1189	141	3	of	of	ADP
ap-1189	141	4	this	this	DET
ap-1189	141	5	central	central	ADJ
ap-1189	141	6	extension	extension	NOUN
ap-1189	141	7	is	be	AUX
ap-1189	141	8	measured	measure	VERB
ap-1189	141	9	by	by	ADP
ap-1189	141	10	the	the	DET
ap-1189	141	11	cocycle	cocycle	PROPN
ap-1189	141	12	α	α	PROPN
ap-1189	141	13	,	,	PUNCT
ap-1189	141	14	as	as	ADP
ap-1189	141	15	an	an	DET
ap-1189	141	16	obstruction	obstruction	NOUN
ap-1189	141	17	to	to	ADP
ap-1189	141	18	associativity	associativity	NOUN
ap-1189	141	19	of	of	ADP
ap-1189	141	20	p̂	p̂	X
ap-1189	141	21	.	.	PUNCT
ap-1189	142	1	on	on	ADP
ap-1189	142	2	the	the	DET
ap-1189	142	3	lie	lie	NOUN
ap-1189	142	4	algebra	algebra	NOUN
ap-1189	142	5	level	level	NOUN
ap-1189	142	6	,	,	PUNCT
ap-1189	142	7	we	we	PRON
ap-1189	142	8	have	have	VERB
ap-1189	142	9	a	a	DET
ap-1189	142	10	corresponding	correspond	VERB
ap-1189	142	11	cocycle	cocycle	NOUN
ap-1189	142	12	c3	c3	NOUN
ap-1189	142	13	=	=	PUNCT
ap-1189	142	14	dα	dα	NOUN
ap-1189	142	15	which	which	PRON
ap-1189	142	16	is	be	AUX
ap-1189	142	17	easily	easily	ADV
ap-1189	142	18	computed	compute	VERB
ap-1189	142	19	.	.	PUNCT
ap-1189	143	1	the	the	DET
ap-1189	143	2	cocycle	cocycle	PROPN
ap-1189	143	3	c	c	PROPN
ap-1189	143	4	of	of	ADP
ap-1189	143	5	ωg	ωg	PROPN
ap-1189	143	6	extends	extend	VERB
ap-1189	143	7	to	to	ADP
ap-1189	143	8	the	the	DET
ap-1189	143	9	path	path	NOUN
ap-1189	143	10	lie	lie	NOUN
ap-1189	143	11	algebra	algebra	NOUN
ap-1189	143	12	pg	pg	NOUN
ap-1189	143	13	as	as	ADP
ap-1189	143	14	c(x	c(x	PROPN
ap-1189	143	15	,	,	PUNCT
ap-1189	143	16	y	y	PROPN
ap-1189	143	17	)	)	PUNCT
ap-1189	144	1	=	=	PUNCT
ap-1189	145	1	k	k	PROPN
ap-1189	145	2	4πi	4πi	NOUN
ap-1189	145	3	∫	∫	PROPN
ap-1189	146	1	[	[	X
ap-1189	146	2	0,2π	0,2π	NOUN
ap-1189	146	3	]	]	X
ap-1189	146	4	(	(	PUNCT
ap-1189	146	5	〈	〈	PROPN
ap-1189	146	6	x	x	X
ap-1189	146	7	,	,	PUNCT
ap-1189	146	8	dy	dy	VERB
ap-1189	146	9	〉	〉	NOUN
ap-1189	146	10	−	−	PROPN
ap-1189	146	11	〈	〈	PROPN
ap-1189	146	12	y	y	PROPN
ap-1189	146	13	,	,	PUNCT
ap-1189	146	14	dx	dx	PROPN
ap-1189	146	15	〉	〉	NUM
ap-1189	146	16	)	)	PUNCT
ap-1189	146	17	.	.	PUNCT
ap-1189	147	1	this	this	PRON
ap-1189	147	2	is	be	AUX
ap-1189	147	3	an	an	DET
ap-1189	147	4	antisymmetric	antisymmetric	ADJ
ap-1189	147	5	bilinear	bilinear	NOUN
ap-1189	147	6	form	form	NOUN
ap-1189	147	7	on	on	ADP
ap-1189	147	8	pg	pg	PROPN
ap-1189	148	1	but	but	CCONJ
ap-1189	148	2	it	it	PRON
ap-1189	148	3	fails	fail	VERB
ap-1189	148	4	to	to	PART
ap-1189	148	5	be	be	AUX
ap-1189	148	6	a	a	DET
ap-1189	148	7	lie	lie	NOUN
ap-1189	148	8	algebra	algebra	VERB
ap-1189	148	9	2	2	NUM
ap-1189	148	10	-	-	PUNCT
ap-1189	148	11	cocycle	cocycle	NOUN
ap-1189	148	12	.	.	PUNCT
ap-1189	149	1	the	the	DET
ap-1189	149	2	coboundary	coboundary	NOUN
ap-1189	149	3	is	be	AUX
ap-1189	149	4	given	give	VERB
ap-1189	149	5	by	by	ADP
ap-1189	149	6	(	(	PUNCT
ap-1189	149	7	δc)(x	δc)(x	PROPN
ap-1189	149	8	,	,	PUNCT
ap-1189	149	9	y	y	PROPN
ap-1189	149	10	,	,	PUNCT
ap-1189	149	11	z	z	NOUN
ap-1189	149	12	)	)	PUNCT
ap-1189	149	13	=	=	SYM
ap-1189	149	14	c(x	c(x	NOUN
ap-1189	149	15	,	,	PUNCT
ap-1189	149	16	[	[	X
ap-1189	149	17	y	y	X
ap-1189	149	18	,	,	PUNCT
ap-1189	149	19	z	z	NOUN
ap-1189	149	20	]	]	X
ap-1189	149	21	)	)	PUNCT
ap-1189	150	1	+	+	CCONJ
ap-1189	150	2	c(y	c(y	PROPN
ap-1189	150	3	,	,	PUNCT
ap-1189	150	4	[	[	X
ap-1189	150	5	z	z	X
ap-1189	150	6	,	,	PUNCT
ap-1189	150	7	x	x	X
ap-1189	150	8	]	]	PUNCT
ap-1189	150	9	)	)	PUNCT
ap-1189	151	1	+	+	CCONJ
ap-1189	151	2	c(z	c(z	NUM
ap-1189	151	3	,	,	PUNCT
ap-1189	151	4	[	[	X
ap-1189	151	5	x	x	X
ap-1189	151	6	,	,	PUNCT
ap-1189	151	7	y	y	PROPN
ap-1189	151	8	]	]	PUNCT
ap-1189	151	9	)	)	PUNCT
ap-1189	151	10	=	=	SYM
ap-1189	152	1	−	−	PROPN
ap-1189	153	1	k	k	PROPN
ap-1189	153	2	4πi	4πi	PROPN
ap-1189	153	3	〈	〈	PROPN
ap-1189	153	4	x	x	PRON
ap-1189	153	5	,	,	PUNCT
ap-1189	153	6	[	[	X
ap-1189	153	7	y	y	NOUN
ap-1189	153	8	,	,	PUNCT
ap-1189	153	9	z]〉|2π	z]〉|2π	X
ap-1189	153	10	=	=	SYM
ap-1189	153	11	dα(x	dα(x	PROPN
ap-1189	153	12	,	,	PUNCT
ap-1189	153	13	y	y	PROPN
ap-1189	153	14	,	,	PUNCT
ap-1189	153	15	z	z	NOUN
ap-1189	153	16	)	)	PUNCT
ap-1189	153	17	.	.	PUNCT
ap-1189	154	1	thus	thus	ADV
ap-1189	154	2	δc	δc	PRON
ap-1189	154	3	reduces	reduce	VERB
ap-1189	154	4	to	to	ADP
ap-1189	154	5	a	a	DET
ap-1189	154	6	3	3	NUM
ap-1189	154	7	-	-	PUNCT
ap-1189	154	8	cocycle	cocycle	NOUN
ap-1189	154	9	of	of	ADP
ap-1189	154	10	the	the	DET
ap-1189	154	11	lie	lie	NOUN
ap-1189	154	12	algebra	algebra	NOUN
ap-1189	154	13	g	g	PROPN
ap-1189	154	14	ofg	ofg	PROPN
ap-1189	154	15	on	on	ADP
ap-1189	154	16	the	the	DET
ap-1189	154	17	boundary	boundary	NOUN
ap-1189	154	18	x	x	X
ap-1189	155	1	=	=	PUNCT
ap-1189	155	2	2π	2π	NOUN
ap-1189	155	3	.	.	PUNCT
ap-1189	156	1	assuming	assume	VERB
ap-1189	156	2	that	that	SCONJ
ap-1189	156	3	the	the	DET
ap-1189	156	4	bilinear	bilinear	NOUN
ap-1189	156	5	form	form	NOUN
ap-1189	156	6	is	be	AUX
ap-1189	156	7	normalized	normalize	VERB
ap-1189	156	8	as	as	ADP
ap-1189	156	9	〈	〈	PROPN
ap-1189	156	10	x	x	X
ap-1189	156	11	,	,	PUNCT
ap-1189	156	12	y	y	PROPN
ap-1189	156	13	〉	〉	PROPN
ap-1189	156	14	=	=	PUNCT
ap-1189	156	15	trxy	trxy	NOUN
ap-1189	156	16	,	,	PUNCT
ap-1189	156	17	trace	trace	NOUN
ap-1189	156	18	in	in	ADP
ap-1189	156	19	the	the	DET
ap-1189	156	20	defining	define	VERB
ap-1189	156	21	representation	representation	NOUN
ap-1189	156	22	of	of	ADP
ap-1189	156	23	g	g	NOUN
ap-1189	156	24	,	,	PUNCT
ap-1189	156	25	then	then	ADV
ap-1189	156	26	the	the	DET
ap-1189	156	27	above	above	ADJ
ap-1189	156	28	3	3	NUM
ap-1189	156	29	-	-	PUNCT
ap-1189	156	30	cocycle	cocycle	NOUN
ap-1189	156	31	defines	define	NOUN
ap-1189	156	32	by	by	ADP
ap-1189	156	33	left	left	ADJ
ap-1189	156	34	translations	translation	NOUN
ap-1189	156	35	on	on	ADP
ap-1189	156	36	g	g	ADP
ap-1189	156	37	the	the	DET
ap-1189	156	38	left	left	ADJ
ap-1189	156	39	-	-	PUNCT
ap-1189	156	40	invariant	invariant	ADJ
ap-1189	156	41	de	de	PROPN
ap-1189	156	42	rham	rham	PROPN
ap-1189	156	43	form	form	NOUN
ap-1189	156	44	−	−	PROPN
ap-1189	156	45	1	1	NUM
ap-1189	156	46	12πi	12πi	NOUN
ap-1189	156	47	tr	tr	PUNCT
ap-1189	156	48	(	(	PUNCT
ap-1189	156	49	g−1dg)3	g−1dg)3	PROPN
ap-1189	156	50	;	;	PUNCT
ap-1189	156	51	this	this	PRON
ap-1189	156	52	is	be	AUX
ap-1189	156	53	normalized	normalize	VERB
ap-1189	156	54	as	as	ADP
ap-1189	156	55	2πi	2πi	NOUN
ap-1189	156	56	times	time	NOUN
ap-1189	156	57	an	an	DET
ap-1189	156	58	integral	integral	ADJ
ap-1189	156	59	3	3	NUM
ap-1189	156	60	-	-	PUNCT
ap-1189	156	61	form	form	NOUN
ap-1189	156	62	on	on	ADP
ap-1189	156	63	g	g	PROPN
ap-1189	156	64	and	and	CCONJ
ap-1189	156	65	is	be	AUX
ap-1189	156	66	the	the	DET
ap-1189	156	67	generator	generator	NOUN
ap-1189	156	68	of	of	ADP
ap-1189	156	69	h3(g	h3(g	PROPN
ap-1189	156	70	,	,	PUNCT
ap-1189	156	71	z	z	NOUN
ap-1189	156	72	)	)	PUNCT
ap-1189	156	73	for	for	ADP
ap-1189	156	74	g	g	NOUN
ap-1189	156	75	=	=	SYM
ap-1189	156	76	su(n	su(n	X
ap-1189	156	77	)	)	PUNCT
ap-1189	156	78	.	.	PUNCT
ap-1189	157	1	5	5	NUM
ap-1189	157	2	cocycles	cocycle	NOUN
ap-1189	157	3	and	and	CCONJ
ap-1189	157	4	associated	associate	VERB
ap-1189	157	5	vector	vector	NOUN
ap-1189	157	6	bundles	bundle	NOUN
ap-1189	157	7	let	let	VERB
ap-1189	157	8	us	we	PRON
ap-1189	157	9	recall	recall	VERB
ap-1189	157	10	the	the	DET
ap-1189	157	11	standard	standard	ADJ
ap-1189	157	12	construction	construction	NOUN
ap-1189	157	13	of	of	ADP
ap-1189	157	14	a	a	DET
ap-1189	157	15	vector	vector	NOUN
ap-1189	157	16	bundle	bundle	NOUN
ap-1189	157	17	associated	associate	VERB
ap-1189	157	18	to	to	ADP
ap-1189	157	19	a	a	DET
ap-1189	157	20	principal	principal	NOUN
ap-1189	157	21	g	g	PROPN
ap-1189	157	22	bundle	bundle	NOUN
ap-1189	157	23	π	π	NOUN
ap-1189	157	24	:p	:p	X
ap-1189	157	25	→m	→m	X
ap-1189	157	26	over	over	ADP
ap-1189	157	27	a	a	DET
ap-1189	157	28	base	base	NOUN
ap-1189	157	29	m	m	NOUN
ap-1189	157	30	.	.	PUNCT
ap-1189	158	1	fix	fix	VERB
ap-1189	158	2	a	a	DET
ap-1189	158	3	representation	representation	NOUN
ap-1189	158	4	ρ	ρ	NOUN
ap-1189	158	5	:	:	PUNCT
ap-1189	158	6	g	g	PROPN
ap-1189	158	7	→	→	SYM
ap-1189	158	8	aut(v	aut(v	PROPN
ap-1189	158	9	)	)	PUNCT
ap-1189	158	10	,	,	PUNCT
ap-1189	158	11	in	in	ADP
ap-1189	158	12	a	a	DET
ap-1189	158	13	vector	vector	NOUN
ap-1189	158	14	space	space	NOUN
ap-1189	158	15	v	v	NOUN
ap-1189	158	16	.	.	PUNCT
ap-1189	159	1	define	define	VERB
ap-1189	159	2	the	the	DET
ap-1189	159	3	total	total	ADJ
ap-1189	159	4	space	space	NOUN
ap-1189	159	5	of	of	ADP
ap-1189	159	6	a	a	DET
ap-1189	159	7	vector	vector	NOUN
ap-1189	159	8	bundle	bundle	NOUN
ap-1189	159	9	as	as	ADP
ap-1189	159	10	e	e	X
ap-1189	159	11	=	=	NOUN
ap-1189	159	12	p	p	X
ap-1189	159	13	×ρ	×ρ	NOUN
ap-1189	159	14	v	v	NOUN
ap-1189	159	15	,	,	PUNCT
ap-1189	159	16	with	with	ADP
ap-1189	159	17	the	the	DET
ap-1189	159	18	equivalence	equivalence	NOUN
ap-1189	159	19	(	(	PUNCT
ap-1189	159	20	p	p	X
ap-1189	159	21	,	,	PUNCT
ap-1189	159	22	v	v	NOUN
ap-1189	159	23	)	)	PUNCT
ap-1189	159	24	≡	≡	PROPN
ap-1189	159	25	(	(	PUNCT
ap-1189	159	26	pg	pg	INTJ
ap-1189	159	27	,	,	PUNCT
ap-1189	159	28	ρ(g)−1v	ρ(g)−1v	PROPN
ap-1189	159	29	)	)	PUNCT
ap-1189	159	30	.	.	PUNCT
ap-1189	160	1	the	the	DET
ap-1189	160	2	projection	projection	NOUN
ap-1189	160	3	onto	onto	ADP
ap-1189	160	4	the	the	DET
ap-1189	160	5	basem	basem	NOUN
ap-1189	160	6	is	be	AUX
ap-1189	160	7	(	(	PUNCT
ap-1189	160	8	p	p	X
ap-1189	160	9	,	,	PUNCT
ap-1189	160	10	v	v	NOUN
ap-1189	160	11	)	)	PUNCT
ap-1189	160	12	�	�	PROPN
ap-1189	160	13	→	→	SYM
ap-1189	160	14	π(p	π(p	PROPN
ap-1189	160	15	)	)	PUNCT
ap-1189	160	16	.	.	PUNCT
ap-1189	161	1	consider	consider	VERB
ap-1189	161	2	the	the	DET
ap-1189	161	3	following	follow	VERB
ap-1189	161	4	generalization	generalization	NOUN
ap-1189	161	5	of	of	ADP
ap-1189	161	6	this	this	DET
ap-1189	161	7	construction	construction	NOUN
ap-1189	161	8	:	:	PUNCT
ap-1189	161	9	fix	fix	VERB
ap-1189	161	10	a	a	DET
ap-1189	161	11	1	1	NUM
ap-1189	161	12	-	-	PUNCT
ap-1189	161	13	cocycle	cocycle	NOUN
ap-1189	161	14	ω	ω	PROPN
ap-1189	161	15	:p	:p	NOUN
ap-1189	161	16	×g	×g	PROPN
ap-1189	161	17	→	→	SYM
ap-1189	161	18	aut(v	aut(v	PROPN
ap-1189	161	19	)	)	PUNCT
ap-1189	161	20	and	and	CCONJ
ap-1189	161	21	set	set	VERB
ap-1189	161	22	e	e	NOUN
ap-1189	161	23	=	=	PUNCT
ap-1189	161	24	p	p	PROPN
ap-1189	161	25	×ω	×ω	ADV
ap-1189	161	26	v	v	NOUN
ap-1189	161	27	,	,	PUNCT
ap-1189	161	28	with	with	ADP
ap-1189	161	29	(	(	PUNCT
ap-1189	161	30	pg	pg	INTJ
ap-1189	161	31	,	,	PUNCT
ap-1189	161	32	ω(p	ω(p	PROPN
ap-1189	161	33	;	;	PUNCT
ap-1189	162	1	g)−1v	g)−1v	NOUN
ap-1189	162	2	)	)	PUNCT
ap-1189	162	3	≡	≡	PROPN
ap-1189	162	4	(	(	PUNCT
ap-1189	162	5	p	p	X
ap-1189	162	6	,	,	PUNCT
ap-1189	162	7	v	v	NOUN
ap-1189	162	8	)	)	PUNCT
ap-1189	162	9	.	.	PUNCT
ap-1189	163	1	the	the	DET
ap-1189	163	2	transitivity	transitivity	NOUN
ap-1189	163	3	of	of	ADP
ap-1189	163	4	the	the	DET
ap-1189	163	5	relation	relation	NOUN
ap-1189	163	6	is	be	AUX
ap-1189	163	7	given	give	VERB
ap-1189	163	8	by	by	ADP
ap-1189	163	9	the	the	DET
ap-1189	163	10	cocycle	cocycle	NOUN
ap-1189	163	11	condition	condition	NOUN
ap-1189	163	12	ω(p	ω(p	NOUN
ap-1189	163	13	;	;	PUNCT
ap-1189	163	14	gg′	gg′	NOUN
ap-1189	163	15	)	)	PUNCT
ap-1189	163	16	=	=	PUNCT
ap-1189	164	1	ω(p	ω(p	NOUN
ap-1189	164	2	;	;	PUNCT
ap-1189	164	3	g)ω(pg	g)ω(pg	NUM
ap-1189	164	4	;	;	PUNCT
ap-1189	164	5	g′	g′	NOUN
ap-1189	164	6	)	)	PUNCT
ap-1189	164	7	.	.	PUNCT
ap-1189	165	1	an	an	DET
ap-1189	165	2	example	example	NOUN
ap-1189	165	3	of	of	ADP
ap-1189	165	4	this	this	DET
ap-1189	165	5	construction	construction	NOUN
ap-1189	165	6	was	be	AUX
ap-1189	165	7	already	already	ADV
ap-1189	165	8	given	give	VERB
ap-1189	165	9	in	in	ADP
ap-1189	165	10	the	the	DET
ap-1189	165	11	construction	construction	NOUN
ap-1189	165	12	of	of	ADP
ap-1189	165	13	the	the	DET
ap-1189	165	14	determinant	determinant	ADJ
ap-1189	165	15	bundle	bundle	NOUN
ap-1189	165	16	over	over	ADP
ap-1189	165	17	the	the	DET
ap-1189	165	18	gauge	gauge	NOUN
ap-1189	165	19	orbit	orbit	NOUN
ap-1189	165	20	space	space	NOUN
ap-1189	165	21	a	a	PRON
ap-1189	165	22	/	/	SYM
ap-1189	165	23	g.	g.	NOUN
ap-1189	165	24	let	let	VERB
ap-1189	165	25	g	g	NOUN
ap-1189	165	26	be	be	AUX
ap-1189	165	27	a	a	DET
ap-1189	165	28	topological	topological	ADJ
ap-1189	165	29	group	group	NOUN
ap-1189	165	30	and	and	CCONJ
ap-1189	165	31	f	f	NOUN
ap-1189	165	32	:	:	PUNCT
ap-1189	165	33	g	g	PROPN
ap-1189	165	34	→	→	SYM
ap-1189	165	35	h	h	NOUN
ap-1189	165	36	a	a	DET
ap-1189	165	37	homotopy	homotopy	NOUN
ap-1189	165	38	to	to	ADP
ap-1189	165	39	another	another	DET
ap-1189	165	40	topological	topological	ADJ
ap-1189	165	41	group	group	NOUN
ap-1189	165	42	h	h	NOUN
ap-1189	165	43	.	.	PUNCT
ap-1189	166	1	morally	morally	ADV
ap-1189	166	2	,	,	PUNCT
ap-1189	166	3	representation	representation	NOUN
ap-1189	166	4	theory	theory	NOUN
ap-1189	166	5	of	of	ADP
ap-1189	166	6	h	h	NOUN
ap-1189	166	7	should	should	AUX
ap-1189	166	8	encode	encode	VERB
ap-1189	166	9	information	information	NOUN
ap-1189	166	10	about	about	ADP
ap-1189	166	11	representations	representation	NOUN
ap-1189	166	12	of	of	ADP
ap-1189	166	13	g.	g.	PROPN
ap-1189	166	14	however	however	ADV
ap-1189	166	15	,	,	PUNCT
ap-1189	166	16	it	it	PRON
ap-1189	166	17	can	can	AUX
ap-1189	166	18	happen	happen	VERB
ap-1189	166	19	that	that	SCONJ
ap-1189	166	20	h	h	NOUN
ap-1189	166	21	has	have	VERB
ap-1189	166	22	a	a	DET
ap-1189	166	23	good	good	ADJ
ap-1189	166	24	representation	representation	NOUN
ap-1189	166	25	theory	theory	NOUN
ap-1189	166	26	but	but	CCONJ
ap-1189	166	27	g	g	NOUN
ap-1189	166	28	lacks	lack	VERB
ap-1189	166	29	unitary	unitary	ADJ
ap-1189	166	30	faithful	faithful	ADJ
ap-1189	166	31	hilbert	hilbert	NOUN
ap-1189	166	32	space	space	NOUN
ap-1189	166	33	representations	representation	NOUN
ap-1189	166	34	.	.	PUNCT
ap-1189	167	1	but	but	CCONJ
ap-1189	167	2	we	we	PRON
ap-1189	167	3	can	can	AUX
ap-1189	167	4	define	define	VERB
ap-1189	167	5	a	a	DET
ap-1189	167	6	cocycle	cocycle	NOUN
ap-1189	167	7	ω(b	ω(b	NOUN
ap-1189	167	8	;	;	PUNCT
ap-1189	167	9	g	g	X
ap-1189	167	10	)	)	PUNCT
ap-1189	167	11	=	=	SYM
ap-1189	167	12	f(b)−1f(bg	f(b)−1f(bg	PROPN
ap-1189	167	13	)	)	PUNCT
ap-1189	167	14	with	with	ADP
ap-1189	167	15	values	value	NOUN
ap-1189	167	16	in	in	ADP
ap-1189	167	17	h	h	PROPN
ap-1189	167	18	.	.	PUNCT
ap-1189	168	1	selecting	select	VERB
ap-1189	168	2	a	a	DET
ap-1189	168	3	representation	representation	NOUN
ap-1189	168	4	ρ	ρ	NOUN
ap-1189	168	5	of	of	ADP
ap-1189	168	6	h	h	NOUN
ap-1189	168	7	in	in	ADP
ap-1189	168	8	v	v	NUM
ap-1189	168	9	we	we	PRON
ap-1189	168	10	obtain	obtain	VERB
ap-1189	168	11	a	a	DET
ap-1189	168	12	1	1	NUM
ap-1189	168	13	-	-	PUNCT
ap-1189	168	14	cocycle	cocycle	NOUN
ap-1189	168	15	ρ(ω(b	ρ(ω(b	NOUN
ap-1189	168	16	;	;	PUNCT
ap-1189	168	17	g	g	NOUN
ap-1189	168	18	)	)	PUNCT
ap-1189	168	19	)	)	PUNCT
ap-1189	168	20	for	for	ADP
ap-1189	168	21	the	the	DET
ap-1189	168	22	right	right	ADJ
ap-1189	168	23	action	action	NOUN
ap-1189	168	24	of	of	ADP
ap-1189	168	25	g	g	NOUN
ap-1189	168	26	on	on	ADP
ap-1189	168	27	itself	itself	PRON
ap-1189	168	28	,	,	PUNCT
ap-1189	168	29	with	with	ADP
ap-1189	168	30	values	value	NOUN
ap-1189	168	31	in	in	ADP
ap-1189	168	32	aut(v	aut(v	PROPN
ap-1189	168	33	)	)	PUNCT
ap-1189	168	34	.	.	PUNCT
ap-1189	169	1	we	we	PRON
ap-1189	169	2	can	can	AUX
ap-1189	169	3	view	view	VERB
ap-1189	169	4	this	this	PRON
ap-1189	169	5	as	as	ADP
ap-1189	169	6	a	a	DET
ap-1189	169	7	representation	representation	NOUN
ap-1189	169	8	of	of	ADP
ap-1189	169	9	g	g	NOUN
ap-1189	169	10	in	in	ADP
ap-1189	169	11	a	a	DET
ap-1189	169	12	group	group	NOUN
ap-1189	169	13	of	of	ADP
ap-1189	169	14	matrices	matrix	NOUN
ap-1189	169	15	with	with	ADP
ap-1189	169	16	entries	entry	NOUN
ap-1189	169	17	in	in	ADP
ap-1189	169	18	the	the	DET
ap-1189	169	19	algebra	algebra	NOUN
ap-1189	169	20	of	of	ADP
ap-1189	169	21	complex	complex	ADJ
ap-1189	169	22	functions	function	NOUN
ap-1189	169	23	on	on	ADP
ap-1189	169	24	g	g	PROPN
ap-1189	169	25	(	(	PUNCT
ap-1189	169	26	but	but	CCONJ
ap-1189	169	27	with	with	ADP
ap-1189	169	28	an	an	DET
ap-1189	169	29	action	action	NOUN
ap-1189	169	30	of	of	ADP
ap-1189	169	31	g	g	NOUN
ap-1189	169	32	on	on	ADP
ap-1189	169	33	functions	function	NOUN
ap-1189	169	34	through	through	ADP
ap-1189	169	35	right	right	ADJ
ap-1189	169	36	translation	translation	NOUN
ap-1189	169	37	)	)	PUNCT
ap-1189	169	38	.	.	PUNCT
ap-1189	170	1	example	example	NOUN
ap-1189	170	2	1	1	NUM
ap-1189	170	3	the	the	DET
ap-1189	170	4	loop	loop	NOUN
ap-1189	170	5	group	group	NOUN
ap-1189	170	6	lg	lg	NOUN
ap-1189	170	7	of	of	ADP
ap-1189	170	8	smooth	smooth	ADJ
ap-1189	170	9	maps	map	NOUN
ap-1189	170	10	f	f	NOUN
ap-1189	171	1	:	:	PUNCT
ap-1189	171	2	s1	s1	PROPN
ap-1189	171	3	→	→	SYM
ap-1189	171	4	g	g	PROPN
ap-1189	171	5	,	,	PUNCT
ap-1189	171	6	g	g	PROPN
ap-1189	171	7	a	a	DET
ap-1189	171	8	compact	compact	ADJ
ap-1189	171	9	lie	lie	NOUN
ap-1189	171	10	group	group	NOUN
ap-1189	171	11	,	,	PUNCT
ap-1189	171	12	has	have	VERB
ap-1189	171	13	a	a	DET
ap-1189	171	14	beautiful	beautiful	ADJ
ap-1189	171	15	theory	theory	NOUN
ap-1189	171	16	of	of	ADP
ap-1189	171	17	projective	projective	ADJ
ap-1189	171	18	highest	high	ADJ
ap-1189	171	19	weight	weight	NOUN
ap-1189	171	20	representations	representation	NOUN
ap-1189	171	21	,	,	PUNCT
ap-1189	171	22	[	[	X
ap-1189	171	23	11	11	NUM
ap-1189	171	24	,	,	PUNCT
ap-1189	171	25	10	10	NUM
ap-1189	171	26	]	]	PUNCT
ap-1189	171	27	.	.	PUNCT
ap-1189	172	1	these	these	PRON
ap-1189	172	2	are	be	AUX
ap-1189	172	3	representations	representation	NOUN
ap-1189	172	4	of	of	ADP
ap-1189	172	5	a	a	DET
ap-1189	172	6	central	central	ADJ
ap-1189	172	7	extension	extension	NOUN
ap-1189	172	8	l̂g	l̂g	PROPN
ap-1189	172	9	.	.	PUNCT
ap-1189	173	1	on	on	ADP
ap-1189	173	2	the	the	DET
ap-1189	173	3	lie	lie	NOUN
ap-1189	173	4	algebra	algebra	NOUN
ap-1189	173	5	level	level	NOUN
ap-1189	173	6	,	,	PUNCT
ap-1189	173	7	the	the	DET
ap-1189	173	8	central	central	ADJ
ap-1189	173	9	extension	extension	NOUN
ap-1189	173	10	is	be	AUX
ap-1189	173	11	given	give	VERB
ap-1189	173	12	as	as	ADP
ap-1189	173	13	in	in	ADP
ap-1189	173	14	sect	sect	NOUN
ap-1189	173	15	.	.	PUNCT
ap-1189	174	1	3	3	X
ap-1189	174	2	.	.	X
ap-1189	174	3	one	one	PRON
ap-1189	174	4	can	can	AUX
ap-1189	174	5	show	show	VERB
ap-1189	174	6	that	that	SCONJ
ap-1189	174	7	lg	lg	PROPN
ap-1189	174	8	is	be	AUX
ap-1189	174	9	homotopy	homotopy	NOUN
ap-1189	174	10	equivalent	equivalent	ADJ
ap-1189	174	11	to	to	ADP
ap-1189	174	12	the	the	DET
ap-1189	174	13	banach	banach	ADV
ap-1189	174	14	-	-	PUNCT
ap-1189	174	15	lie	lie	NOUN
ap-1189	174	16	group	group	NOUN
ap-1189	174	17	lcg	lcg	NOUN
ap-1189	174	18	of	of	ADP
ap-1189	174	19	continuous	continuous	ADJ
ap-1189	174	20	loops	loop	NOUN
ap-1189	174	21	,	,	PUNCT
ap-1189	174	22	[	[	X
ap-1189	174	23	4	4	NUM
ap-1189	174	24	]	]	PUNCT
ap-1189	174	25	.	.	PUNCT
ap-1189	175	1	however	however	ADV
ap-1189	175	2	,	,	PUNCT
ap-1189	175	3	no	no	DET
ap-1189	175	4	representations	representation	NOUN
ap-1189	175	5	of	of	ADP
ap-1189	175	6	lcg	lcg	NOUN
ap-1189	175	7	analogous	analogous	ADJ
ap-1189	175	8	to	to	ADP
ap-1189	175	9	the	the	DET
ap-1189	175	10	highest	high	ADJ
ap-1189	175	11	weight	weight	NOUN
ap-1189	175	12	representations	representation	NOUN
ap-1189	175	13	are	be	AUX
ap-1189	175	14	known	know	VERB
ap-1189	175	15	.	.	PUNCT
ap-1189	176	1	instead	instead	ADV
ap-1189	176	2	,	,	PUNCT
ap-1189	176	3	we	we	PRON
ap-1189	176	4	can	can	AUX
ap-1189	176	5	use	use	VERB
ap-1189	176	6	the	the	DET
ap-1189	176	7	cocycle	cocycle	NOUN
ap-1189	176	8	ω	ω	PROPN
ap-1189	176	9	:	:	PUNCT
ap-1189	176	10	lcg×	lcg×	ADJ
ap-1189	176	11	lcg	lcg	PROPN
ap-1189	176	12	→	→	SYM
ap-1189	176	13	lg	lg	PROPN
ap-1189	176	14	45	45	NUM
ap-1189	176	15	acta	acta	PROPN
ap-1189	176	16	polytechnica	polytechnica	PROPN
ap-1189	176	17	vol	vol	NOUN
ap-1189	176	18	.	.	PROPN
ap-1189	177	1	50	50	NUM
ap-1189	177	2	no	no	NOUN
ap-1189	177	3	.	.	PUNCT
ap-1189	178	1	3/2010	3/2010	NUM
ap-1189	178	2	to	to	PART
ap-1189	178	3	tranfer	tranfer	VERB
ap-1189	178	4	representations	representation	NOUN
ap-1189	178	5	of	of	ADP
ap-1189	178	6	lg	lg	NOUN
ap-1189	178	7	to	to	ADP
ap-1189	178	8	hilbert	hilbert	NOUN
ap-1189	178	9	space	space	NOUN
ap-1189	178	10	operator	operator	NOUN
ap-1189	178	11	cocycles	cocycle	NOUN
ap-1189	178	12	on	on	ADP
ap-1189	178	13	lcg	lcg	PROPN
ap-1189	178	14	,	,	PUNCT
ap-1189	178	15	[	[	X
ap-1189	178	16	8	8	NUM
ap-1189	178	17	]	]	PUNCT
ap-1189	178	18	.	.	PUNCT
ap-1189	179	1	example	example	NOUN
ap-1189	179	2	2	2	NUM
ap-1189	179	3	let	let	VERB
ap-1189	179	4	h	h	NOUN
ap-1189	179	5	=	=	SYM
ap-1189	179	6	h−	h−	PROPN
ap-1189	179	7	⊕	⊕	PROPN
ap-1189	179	8	h+	h+	X
ap-1189	179	9	be	be	AUX
ap-1189	179	10	a	a	DET
ap-1189	179	11	polarized	polarize	VERB
ap-1189	179	12	hilbert	hilbert	NOUN
ap-1189	179	13	space	space	NOUN
ap-1189	179	14	and	and	CCONJ
ap-1189	179	15	up	up	ADP
ap-1189	179	16	the	the	DET
ap-1189	179	17	group	group	NOUN
ap-1189	179	18	of	of	ADP
ap-1189	179	19	unitaries	unitarie	NOUN
ap-1189	179	20	in	in	ADP
ap-1189	179	21	h	h	PRON
ap-1189	179	22	such	such	ADJ
ap-1189	179	23	that	that	SCONJ
ap-1189	179	24	the	the	DET
ap-1189	179	25	off	off	ADV
ap-1189	179	26	-	-	PUNCT
ap-1189	179	27	diagonal	diagonal	ADJ
ap-1189	179	28	blocks	block	NOUN
ap-1189	179	29	with	with	ADP
ap-1189	179	30	respect	respect	NOUN
ap-1189	179	31	to	to	ADP
ap-1189	179	32	the	the	DET
ap-1189	179	33	polarization	polarization	NOUN
ap-1189	179	34	are	be	AUX
ap-1189	179	35	in	in	ADP
ap-1189	179	36	the	the	DET
ap-1189	179	37	schatten	schatten	ADJ
ap-1189	179	38	ideal	ideal	NOUN
ap-1189	179	39	lp	lp	PROPN
ap-1189	179	40	of	of	ADP
ap-1189	179	41	bounded	bounded	PROPN
ap-1189	179	42	operators	operator	NOUN
ap-1189	180	1	a	a	DET
ap-1189	180	2	with	with	ADP
ap-1189	180	3	tr|a|p	tr|a|p	PROPN
ap-1189	180	4	<	<	X
ap-1189	180	5	∞.	∞.	PROPN
ap-1189	180	6	the	the	DET
ap-1189	180	7	case	case	NOUN
ap-1189	180	8	p	p	X
ap-1189	180	9	=	=	SYM
ap-1189	180	10	2	2	NUM
ap-1189	180	11	is	be	AUX
ap-1189	180	12	important	important	ADJ
ap-1189	180	13	since	since	SCONJ
ap-1189	180	14	the	the	DET
ap-1189	180	15	highest	high	ADJ
ap-1189	180	16	weight	weight	NOUN
ap-1189	180	17	representations	representation	NOUN
ap-1189	180	18	of	of	ADP
ap-1189	180	19	l̂g	l̂g	PROPN
ap-1189	180	20	can	can	AUX
ap-1189	180	21	be	be	AUX
ap-1189	180	22	constructed	construct	VERB
ap-1189	180	23	from	from	ADP
ap-1189	180	24	representations	representation	NOUN
ap-1189	180	25	of	of	ADP
ap-1189	180	26	a	a	DET
ap-1189	180	27	central	central	ADJ
ap-1189	180	28	extension	extension	NOUN
ap-1189	180	29	û2	û2	NOUN
ap-1189	180	30	,	,	PUNCT
ap-1189	180	31	[	[	X
ap-1189	180	32	11	11	NUM
ap-1189	180	33	]	]	PUNCT
ap-1189	180	34	.	.	PUNCT
ap-1189	181	1	the	the	DET
ap-1189	181	2	lie	lie	NOUN
ap-1189	181	3	algebra	algebra	VERB
ap-1189	181	4	central	central	ADJ
ap-1189	181	5	extension	extension	NOUN
ap-1189	181	6	is	be	AUX
ap-1189	181	7	defined	define	VERB
ap-1189	181	8	by	by	ADP
ap-1189	181	9	the	the	DET
ap-1189	181	10	2	2	NUM
ap-1189	181	11	-	-	PUNCT
ap-1189	181	12	cocycle	cocycle	NOUN
ap-1189	181	13	c(x	c(x	NOUN
ap-1189	181	14	,	,	PUNCT
ap-1189	181	15	y	y	PROPN
ap-1189	181	16	)	)	PUNCT
ap-1189	181	17	=	=	SYM
ap-1189	182	1	1	1	NUM
ap-1189	182	2	2	2	NUM
ap-1189	182	3	trc	trc	X
ap-1189	182	4	x	x	PUNCT
ap-1189	182	5	[	[	X
ap-1189	182	6	ε	ε	PROPN
ap-1189	182	7	,	,	PUNCT
ap-1189	182	8	y	y	PROPN
ap-1189	182	9	]	]	PUNCT
ap-1189	182	10	where	where	SCONJ
ap-1189	182	11	ε	ε	PROPN
ap-1189	182	12	is	be	AUX
ap-1189	182	13	the	the	DET
ap-1189	182	14	grading	grade	VERB
ap-1189	182	15	operator	operator	NOUN
ap-1189	182	16	in	in	ADP
ap-1189	182	17	h	h	NOUN
ap-1189	182	18	and	and	CCONJ
ap-1189	182	19	the	the	DET
ap-1189	182	20	condition	condition	NOUN
ap-1189	182	21	trace	trace	NOUN
ap-1189	182	22	trc	trc	PROPN
ap-1189	182	23	is	be	AUX
ap-1189	182	24	defined	define	VERB
ap-1189	182	25	as	as	ADP
ap-1189	182	26	trc	trc	PROPN
ap-1189	182	27	x	x	PUNCT
ap-1189	182	28	=	=	SYM
ap-1189	182	29	1	1	NUM
ap-1189	182	30	2	2	NUM
ap-1189	182	31	trtr	trtr	NOUN
ap-1189	182	32	(	(	PUNCT
ap-1189	182	33	x	x	PROPN
ap-1189	182	34	+	+	X
ap-1189	182	35	εxε	εxε	ADJ
ap-1189	182	36	)	)	PUNCT
ap-1189	182	37	.	.	PUNCT
ap-1189	183	1	the	the	DET
ap-1189	183	2	groups	group	NOUN
ap-1189	183	3	up	up	ADP
ap-1189	183	4	are	be	AUX
ap-1189	183	5	important	important	ADJ
ap-1189	183	6	because	because	SCONJ
ap-1189	183	7	one	one	NUM
ap-1189	183	8	has	have	VERB
ap-1189	183	9	an	an	DET
ap-1189	183	10	embedding	embed	VERB
ap-1189	183	11	map(m	map(m	PROPN
ap-1189	183	12	,	,	PUNCT
ap-1189	183	13	g	g	NOUN
ap-1189	183	14	)	)	PUNCT
ap-1189	183	15	⊂	⊂	PROPN
ap-1189	183	16	up	up	ADV
ap-1189	183	17	when	when	SCONJ
ap-1189	183	18	m	m	PROPN
ap-1189	183	19	is	be	AUX
ap-1189	183	20	a	a	DET
ap-1189	183	21	compact	compact	ADJ
ap-1189	183	22	spin	spin	NOUN
ap-1189	183	23	manifold	manifold	ADJ
ap-1189	183	24	and	and	CCONJ
ap-1189	183	25	g	g	PROPN
ap-1189	183	26	compact	compact	ADJ
ap-1189	183	27	lie	lie	NOUN
ap-1189	183	28	group	group	NOUN
ap-1189	183	29	,	,	PUNCT
ap-1189	183	30	for	for	ADP
ap-1189	183	31	p	p	NOUN
ap-1189	183	32	>	>	X
ap-1189	183	33	dimm	dimm	NOUN
ap-1189	183	34	,	,	PUNCT
ap-1189	183	35	[	[	X
ap-1189	183	36	15	15	NUM
ap-1189	183	37	]	]	PUNCT
ap-1189	183	38	.	.	PUNCT
ap-1189	184	1	according	accord	VERB
ap-1189	184	2	to	to	ADP
ap-1189	184	3	richard	richard	PROPN
ap-1189	184	4	palais	palais	PROPN
ap-1189	184	5	,	,	PUNCT
ap-1189	184	6	up	up	ADV
ap-1189	184	7	is	be	AUX
ap-1189	184	8	homotopy	homotopy	NOUN
ap-1189	184	9	equivalent	equivalent	ADJ
ap-1189	184	10	to	to	ADP
ap-1189	184	11	u2	u2	NOUN
ap-1189	184	12	for	for	ADP
ap-1189	184	13	all	all	DET
ap-1189	184	14	p	p	PRON
ap-1189	184	15	≥	≥	NOUN
ap-1189	184	16	1	1	NUM
ap-1189	184	17	,	,	PUNCT
ap-1189	184	18	[	[	X
ap-1189	184	19	16	16	NUM
ap-1189	184	20	]	]	PUNCT
ap-1189	184	21	,	,	PUNCT
ap-1189	184	22	so	so	SCONJ
ap-1189	184	23	we	we	PRON
ap-1189	184	24	can	can	AUX
ap-1189	184	25	define	define	VERB
ap-1189	184	26	generalized	generalized	ADJ
ap-1189	184	27	representations	representation	NOUN
ap-1189	184	28	of	of	ADP
ap-1189	184	29	map(m	map(m	PROPN
ap-1189	184	30	,	,	PUNCT
ap-1189	184	31	g	g	NOUN
ap-1189	184	32	)	)	PUNCT
ap-1189	184	33	from	from	ADP
ap-1189	184	34	this	this	DET
ap-1189	184	35	equivalence	equivalence	NOUN
ap-1189	184	36	and	and	CCONJ
ap-1189	184	37	the	the	DET
ap-1189	184	38	embebding	embebding	NOUN
ap-1189	184	39	to	to	ADP
ap-1189	184	40	up	up	ADP
ap-1189	184	41	.	.	PUNCT
ap-1189	185	1	6	6	NUM
ap-1189	185	2	application	application	NOUN
ap-1189	185	3	to	to	PART
ap-1189	185	4	gauge	gauge	VERB
ap-1189	185	5	theory	theory	NOUN
ap-1189	185	6	letda	letda	PROPN
ap-1189	185	7	dirac	dirac	NOUN
ap-1189	185	8	hamiltonian	hamiltonian	NOUN
ap-1189	185	9	on	on	ADP
ap-1189	185	10	an	an	DET
ap-1189	185	11	odd	odd	ADJ
ap-1189	185	12	dimensional	dimensional	ADJ
ap-1189	185	13	compact	compact	ADJ
ap-1189	185	14	spin	spin	NOUN
ap-1189	185	15	manifold	manifold	NOUN
ap-1189	185	16	coupled	couple	VERB
ap-1189	185	17	to	to	ADP
ap-1189	185	18	a	a	DET
ap-1189	185	19	gauge	gauge	ADJ
ap-1189	185	20	potential	potential	ADJ
ap-1189	185	21	a.	a.	NOUN
ap-1189	185	22	the	the	DET
ap-1189	185	23	quantization	quantization	NOUN
ap-1189	185	24	d̂a	d̂a	NOUN
ap-1189	185	25	of	of	ADP
ap-1189	185	26	da	da	PROPN
ap-1189	185	27	acts	act	NOUN
ap-1189	185	28	in	in	ADP
ap-1189	185	29	a	a	DET
ap-1189	185	30	fermionic	fermionic	NOUN
ap-1189	185	31	fock	fock	ADJ
ap-1189	185	32	space	space	NOUN
ap-1189	185	33	.	.	PUNCT
ap-1189	186	1	for	for	ADP
ap-1189	186	2	different	different	ADJ
ap-1189	186	3	potentials	potential	NOUN
ap-1189	186	4	the	the	DET
ap-1189	186	5	representations	representation	NOUN
ap-1189	186	6	of	of	ADP
ap-1189	186	7	the	the	DET
ap-1189	186	8	fermion	fermion	NOUN
ap-1189	186	9	algebra	algebra	NOUN
ap-1189	186	10	are	be	AUX
ap-1189	186	11	inequivalent	inequivalent	ADJ
ap-1189	186	12	[	[	X
ap-1189	186	13	17	17	NUM
ap-1189	186	14	]	]	PUNCT
ap-1189	186	15	.	.	PUNCT
ap-1189	187	1	in	in	ADP
ap-1189	187	2	scattering	scatter	VERB
ap-1189	187	3	problems	problem	NOUN
ap-1189	187	4	one	one	PRON
ap-1189	187	5	would	would	AUX
ap-1189	187	6	like	like	VERB
ap-1189	187	7	to	to	PART
ap-1189	187	8	realize	realize	VERB
ap-1189	187	9	the	the	DET
ap-1189	187	10	operators	operator	NOUN
ap-1189	187	11	d̂a	d̂a	PROPN
ap-1189	187	12	in	in	ADP
ap-1189	187	13	a	a	DET
ap-1189	187	14	single	single	ADJ
ap-1189	187	15	fock	fock	ADJ
ap-1189	187	16	space	space	NOUN
ap-1189	187	17	f	f	PROPN
ap-1189	187	18	,	,	PUNCT
ap-1189	187	19	the	the	DET
ap-1189	187	20	fock	fock	ADJ
ap-1189	187	21	space	space	NOUN
ap-1189	187	22	of	of	ADP
ap-1189	187	23	free	free	ADJ
ap-1189	187	24	fermions	fermion	NOUN
ap-1189	187	25	,	,	PUNCT
ap-1189	187	26	a	a	DET
ap-1189	187	27	=	=	NOUN
ap-1189	187	28	0	0	NUM
ap-1189	187	29	.	.	PUNCT
ap-1189	188	1	this	this	PRON
ap-1189	188	2	can	can	AUX
ap-1189	188	3	be	be	AUX
ap-1189	188	4	achieved	achieve	VERB
ap-1189	188	5	by	by	ADP
ap-1189	188	6	choosing	choose	VERB
ap-1189	188	7	for	for	ADP
ap-1189	188	8	each	each	PRON
ap-1189	188	9	a	a	DET
ap-1189	188	10	a	a	DET
ap-1189	188	11	unitary	unitary	ADJ
ap-1189	188	12	operator	operator	NOUN
ap-1189	188	13	ta	ta	PART
ap-1189	188	14	which	which	PRON
ap-1189	188	15	reduces	reduce	VERB
ap-1189	188	16	the	the	DET
ap-1189	188	17	offdiagonal	offdiagonal	ADJ
ap-1189	188	18	blocks	block	NOUN
ap-1189	188	19	of	of	ADP
ap-1189	188	20	da	da	NOUN
ap-1189	188	21	to	to	ADP
ap-1189	188	22	hilbert	hilbert	NOUN
ap-1189	188	23	-	-	PUNCT
ap-1189	188	24	schmidt	schmidt	PROPN
ap-1189	188	25	operators	operator	NOUN
ap-1189	188	26	,	,	PUNCT
ap-1189	188	27	for	for	ADP
ap-1189	188	28	the	the	DET
ap-1189	188	29	‘	'	PUNCT
ap-1189	188	30	free	free	ADJ
ap-1189	188	31	’	'	PUNCT
ap-1189	188	32	polarization	polarization	NOUN
ap-1189	188	33	ε	ε	PROPN
ap-1189	188	34	=	=	SYM
ap-1189	188	35	d0/|d0|	d0/|d0|	PROPN
ap-1189	188	36	.	.	PUNCT
ap-1189	189	1	then	then	ADV
ap-1189	189	2	each	each	DET
ap-1189	189	3	d′	d′	PRON
ap-1189	189	4	a	a	DET
ap-1189	189	5	=	=	SYM
ap-1189	189	6	t−1	t−1	PROPN
ap-1189	189	7	a	a	DET
ap-1189	189	8	data	datum	NOUN
ap-1189	189	9	can	can	AUX
ap-1189	189	10	be	be	AUX
ap-1189	189	11	quantized	quantize	VERB
ap-1189	189	12	in	in	ADP
ap-1189	189	13	the	the	DET
ap-1189	189	14	free	free	ADJ
ap-1189	189	15	fock	fock	ADJ
ap-1189	189	16	space	space	NOUN
ap-1189	189	17	,	,	PUNCT
ap-1189	189	18	[	[	X
ap-1189	189	19	12	12	NUM
ap-1189	189	20	]	]	PUNCT
ap-1189	189	21	,	,	PUNCT
ap-1189	189	22	[	[	X
ap-1189	189	23	13	13	NUM
ap-1189	189	24	]	]	PUNCT
ap-1189	189	25	.	.	PUNCT
ap-1189	190	1	this	this	PRON
ap-1189	190	2	has	have	VERB
ap-1189	190	3	a	a	DET
ap-1189	190	4	consequence	consequence	NOUN
ap-1189	190	5	for	for	ADP
ap-1189	190	6	the	the	DET
ap-1189	190	7	implementation	implementation	NOUN
ap-1189	190	8	of	of	ADP
ap-1189	190	9	the	the	DET
ap-1189	190	10	gauge	gauge	ADJ
ap-1189	190	11	action	action	NOUN
ap-1189	190	12	a	a	DET
ap-1189	190	13	�	�	PROPN
ap-1189	190	14	→	→	SYM
ap-1189	190	15	ag	ag	NOUN
ap-1189	190	16	=	=	PROPN
ap-1189	190	17	g−1ag	g−1ag	PROPN
ap-1189	190	18	+	+	CCONJ
ap-1189	190	19	g−1dg	g−1dg	NOUN
ap-1189	190	20	in	in	ADP
ap-1189	190	21	the	the	DET
ap-1189	190	22	fock	fock	ADJ
ap-1189	190	23	space	space	NOUN
ap-1189	190	24	.	.	PUNCT
ap-1189	191	1	in	in	ADP
ap-1189	191	2	the	the	DET
ap-1189	191	3	1	1	NUM
ap-1189	191	4	-	-	PUNCT
ap-1189	191	5	particle	particle	NOUN
ap-1189	191	6	space	space	NOUN
ap-1189	191	7	the	the	DET
ap-1189	191	8	action	action	NOUN
ap-1189	191	9	of	of	ADP
ap-1189	191	10	g	g	PROPN
ap-1189	191	11	is	be	AUX
ap-1189	191	12	replaced	replace	VERB
ap-1189	191	13	by	by	ADP
ap-1189	191	14	ω(a	ω(a	PROPN
ap-1189	191	15	;	;	PUNCT
ap-1189	191	16	g	g	X
ap-1189	191	17	)	)	PUNCT
ap-1189	191	18	=	=	SYM
ap-1189	192	1	t−1	t−1	PROPN
ap-1189	192	2	a	a	DET
ap-1189	192	3	gtag	gtag	NOUN
ap-1189	192	4	with	with	ADP
ap-1189	192	5	ω(a	ω(a	PROPN
ap-1189	192	6	;	;	PUNCT
ap-1189	192	7	gg′	gg′	NOUN
ap-1189	192	8	)	)	PUNCT
ap-1189	192	9	=	=	SYM
ap-1189	193	1	ω(a	ω(a	PROPN
ap-1189	193	2	;	;	PUNCT
ap-1189	193	3	g)ω(ag	g)ω(ag	X
ap-1189	193	4	;	;	PUNCT
ap-1189	193	5	g′	g′	NOUN
ap-1189	193	6	)	)	PUNCT
ap-1189	193	7	.	.	PUNCT
ap-1189	194	1	now	now	ADV
ap-1189	194	2	the	the	DET
ap-1189	194	3	shale	shale	NOUN
ap-1189	194	4	-	-	PUNCT
ap-1189	194	5	stinespring	stinespre	VERB
ap-1189	194	6	condition	condition	NOUN
ap-1189	194	7	[	[	X
ap-1189	194	8	ε	ε	PROPN
ap-1189	194	9	,	,	PUNCT
ap-1189	194	10	ω(a	ω(a	PROPN
ap-1189	194	11	;	;	PUNCT
ap-1189	194	12	g	g	NOUN
ap-1189	194	13	)	)	PUNCT
ap-1189	194	14	]	]	PUNCT
ap-1189	195	1	∈	∈	PROPN
ap-1189	195	2	l2	l2	NOUN
ap-1189	195	3	is	be	AUX
ap-1189	195	4	satisfied	satisfied	ADJ
ap-1189	195	5	and	and	CCONJ
ap-1189	195	6	we	we	PRON
ap-1189	195	7	can	can	AUX
ap-1189	195	8	quantize	quantize	VERB
ap-1189	195	9	in	in	ADP
ap-1189	195	10	f	f	PROPN
ap-1189	195	11	,	,	PUNCT
ap-1189	195	12	ω(a	ω(a	PROPN
ap-1189	195	13	;	;	PUNCT
ap-1189	195	14	g	g	NOUN
ap-1189	195	15	)	)	PUNCT
ap-1189	195	16	�	�	PROPN
ap-1189	195	17	→	→	SYM
ap-1189	195	18	ω̂(a	ω̂(a	NUM
ap-1189	195	19	;	;	PUNCT
ap-1189	195	20	g′	g′	NUM
ap-1189	195	21	)	)	PUNCT
ap-1189	195	22	.	.	PUNCT
ap-1189	196	1	for	for	ADP
ap-1189	196	2	the	the	DET
ap-1189	196	3	lie	lie	NOUN
ap-1189	196	4	algebra	algebra	NOUN
ap-1189	196	5	of	of	ADP
ap-1189	196	6	the	the	DET
ap-1189	196	7	gauge	gauge	ADJ
ap-1189	196	8	group	group	NOUN
ap-1189	196	9	we	we	PRON
ap-1189	196	10	have	have	VERB
ap-1189	196	11	the	the	DET
ap-1189	196	12	lie	lie	NOUN
ap-1189	196	13	algebra	algebra	PROPN
ap-1189	196	14	cocycle	cocycle	NOUN
ap-1189	196	15	dω(a;x	dω(a;x	PROPN
ap-1189	196	16	)	)	PUNCT
ap-1189	197	1	=	=	PUNCT
ap-1189	198	1	t−1	t−1	PROPN
ap-1189	198	2	a	a	DET
ap-1189	198	3	xta	xta	PROPN
ap-1189	199	1	+	+	CCONJ
ap-1189	199	2	t−1	t−1	PROPN
ap-1189	199	3	a	a	DET
ap-1189	199	4	lxta	lxta	NOUN
ap-1189	199	5	with	with	ADP
ap-1189	199	6	quantization	quantization	NOUN
ap-1189	199	7	d̂ω(a;x	d̂ω(a;x	PROPN
ap-1189	199	8	)	)	PUNCT
ap-1189	199	9	.	.	PUNCT
ap-1189	200	1	let	let	VERB
ap-1189	200	2	x	x	PRON
ap-1189	200	3	be	be	AUX
ap-1189	200	4	an	an	DET
ap-1189	200	5	element	element	NOUN
ap-1189	200	6	in	in	ADP
ap-1189	200	7	the	the	DET
ap-1189	200	8	lie	lie	NOUN
ap-1189	200	9	algebramap(m	algebramap(m	ADP
ap-1189	200	10	,	,	PUNCT
ap-1189	200	11	g	g	NOUN
ap-1189	200	12	)	)	PUNCT
ap-1189	200	13	of	of	ADP
ap-1189	200	14	the	the	DET
ap-1189	200	15	gauge	gauge	ADJ
ap-1189	200	16	group	group	NOUN
ap-1189	200	17	g	g	PROPN
ap-1189	200	18	=	=	SYM
ap-1189	200	19	map(m	map(m	PROPN
ap-1189	200	20	,	,	PUNCT
ap-1189	200	21	g	g	NOUN
ap-1189	200	22	)	)	PUNCT
ap-1189	200	23	.	.	PUNCT
ap-1189	201	1	its	its	PRON
ap-1189	201	2	quantization	quantization	NOUN
ap-1189	201	3	is	be	AUX
ap-1189	201	4	then	then	ADV
ap-1189	201	5	gx	gx	PROPN
ap-1189	201	6	=	=	PUNCT
ap-1189	201	7	lx	lx	PROPN
ap-1189	201	8	+	+	X
ap-1189	201	9	d̂ω(a;x	d̂ω(a;x	PROPN
ap-1189	201	10	)	)	PUNCT
ap-1189	201	11	where	where	SCONJ
ap-1189	201	12	lx	lx	NOUN
ap-1189	201	13	is	be	AUX
ap-1189	201	14	the	the	DET
ap-1189	201	15	lie	lie	NOUN
ap-1189	201	16	derivative	derivative	NOUN
ap-1189	201	17	in	in	ADP
ap-1189	201	18	the	the	DET
ap-1189	201	19	direction	direction	NOUN
ap-1189	201	20	of	of	ADP
ap-1189	201	21	x	x	PRON
ap-1189	201	22	,	,	PUNCT
ap-1189	201	23	corresponding	correspond	VERB
ap-1189	201	24	to	to	ADP
ap-1189	201	25	the	the	DET
ap-1189	201	26	infinitesimal	infinitesimal	ADJ
ap-1189	201	27	gauge	gauge	NOUN
ap-1189	201	28	action	action	NOUN
ap-1189	201	29	a	a	DET
ap-1189	201	30	�	�	PROPN
ap-1189	201	31	→	→	SYM
ap-1189	201	32	[	[	X
ap-1189	201	33	a	a	X
ap-1189	201	34	,	,	PUNCT
ap-1189	201	35	x	x	SYM
ap-1189	201	36	]	]	PUNCT
ap-1189	202	1	+	+	CCONJ
ap-1189	202	2	dx	dx	PROPN
ap-1189	202	3	.	.	PUNCT
ap-1189	203	1	the	the	DET
ap-1189	203	2	commutation	commutation	NOUN
ap-1189	203	3	relations	relation	NOUN
ap-1189	203	4	are	be	AUX
ap-1189	203	5	now	now	ADV
ap-1189	203	6	modified	modify	VERB
ap-1189	203	7	by	by	ADP
ap-1189	203	8	a	a	DET
ap-1189	203	9	cocycle	cocycle	NOUN
ap-1189	203	10	c	c	NOUN
ap-1189	203	11	,	,	PUNCT
ap-1189	203	12	[	[	X
ap-1189	203	13	gx	gx	X
ap-1189	203	14	,	,	PUNCT
ap-1189	203	15	gy	gy	INTJ
ap-1189	203	16	]	]	PUNCT
ap-1189	203	17	=	=	SYM
ap-1189	203	18	g[x	g[x	PROPN
ap-1189	203	19	,	,	PUNCT
ap-1189	203	20	y	y	PROPN
ap-1189	203	21	]	]	PUNCT
ap-1189	204	1	+	+	CCONJ
ap-1189	204	2	c(a;x	c(a;x	PROPN
ap-1189	204	3	,	,	PUNCT
ap-1189	204	4	y	y	PROPN
ap-1189	204	5	)	)	PUNCT
ap-1189	204	6	lxc(a	lxc(a	PROPN
ap-1189	204	7	;	;	PUNCT
ap-1189	204	8	[	[	X
ap-1189	204	9	y	y	PROPN
ap-1189	204	10	,	,	PUNCT
ap-1189	204	11	z])+c(a	z])+c(a	PROPN
ap-1189	204	12	;	;	PUNCT
ap-1189	204	13	[	[	X
ap-1189	204	14	x	x	X
ap-1189	204	15	,	,	PUNCT
ap-1189	204	16	[	[	X
ap-1189	204	17	y	y	NOUN
ap-1189	204	18	,	,	PUNCT
ap-1189	204	19	z]])+	z]])+	PROPN
ap-1189	204	20	cyclic	cyclic	PROPN
ap-1189	204	21	combin	combin	NOUN
ap-1189	204	22	.	.	PUNCT
ap-1189	205	1	=	=	PUNCT
ap-1189	205	2	0	0	X
ap-1189	205	3	.	.	PUNCT
ap-1189	206	1	the	the	DET
ap-1189	206	2	lie	lie	NOUN
ap-1189	206	3	derivative	derivative	NOUN
ap-1189	206	4	lx	lx	NOUN
ap-1189	206	5	is	be	AUX
ap-1189	206	6	needed	need	VERB
ap-1189	206	7	since	since	SCONJ
ap-1189	206	8	the	the	DET
ap-1189	206	9	fock	fock	ADJ
ap-1189	206	10	spaces	space	NOUN
ap-1189	206	11	f	f	PROPN
ap-1189	206	12	depend	depend	VERB
ap-1189	206	13	on	on	ADP
ap-1189	206	14	the	the	DET
ap-1189	206	15	external	external	ADJ
ap-1189	206	16	gauge	gauge	NOUN
ap-1189	206	17	field	field	NOUN
ap-1189	207	1	a	a	PRON
ap-1189	207	2	:	:	PUNCT
ap-1189	207	3	although	although	SCONJ
ap-1189	207	4	as	as	SCONJ
ap-1189	207	5	hilbert	hilbert	NOUN
ap-1189	207	6	spaces	space	NOUN
ap-1189	207	7	fa	fa	INTJ
ap-1189	207	8	are	be	AUX
ap-1189	207	9	all	all	DET
ap-1189	207	10	the	the	DET
ap-1189	207	11	same	same	ADJ
ap-1189	207	12	,	,	PUNCT
ap-1189	207	13	the	the	DET
ap-1189	207	14	gauge	gauge	NOUN
ap-1189	207	15	action	action	NOUN
ap-1189	207	16	explicitly	explicitly	ADV
ap-1189	207	17	depends	depend	VERB
ap-1189	207	18	on	on	ADP
ap-1189	207	19	a.	a.	NOUN
ap-1189	207	20	the	the	DET
ap-1189	207	21	2	2	NUM
ap-1189	207	22	-	-	PUNCT
ap-1189	207	23	cocycle	cocycle	NOUN
ap-1189	207	24	property	property	NOUN
ap-1189	207	25	quarantees	quarantee	NOUN
ap-1189	207	26	the	the	DET
ap-1189	207	27	jacobi	jacobi	PROPN
ap-1189	207	28	identity	identity	NOUN
ap-1189	207	29	for	for	ADP
ap-1189	207	30	the	the	DET
ap-1189	207	31	extension	extension	NOUN
ap-1189	207	32	lie(ĝ	lie(ĝ	NOUN
ap-1189	207	33	)	)	PUNCT
ap-1189	207	34	=	=	SYM
ap-1189	207	35	map(m	map(m	X
ap-1189	207	36	,	,	PUNCT
ap-1189	207	37	g)⊕map(a	g)⊕map(a	PROPN
ap-1189	207	38	,	,	PUNCT
ap-1189	207	39	c	c	NOUN
ap-1189	207	40	)	)	PUNCT
ap-1189	207	41	.	.	PUNCT
ap-1189	208	1	in	in	ADP
ap-1189	208	2	the	the	DET
ap-1189	208	3	case	case	NOUN
ap-1189	208	4	whenm	whenm	NOUN
ap-1189	208	5	=	=	SYM
ap-1189	208	6	s1	s1	NOUN
ap-1189	208	7	one	one	NOUN
ap-1189	208	8	can	can	AUX
ap-1189	208	9	take	take	VERB
ap-1189	208	10	ta	ta	ADP
ap-1189	208	11	=	=	SYM
ap-1189	208	12	1	1	NUM
ap-1189	208	13	and	and	CCONJ
ap-1189	208	14	we	we	PRON
ap-1189	208	15	obtain	obtain	VERB
ap-1189	208	16	the	the	DET
ap-1189	208	17	standard	standard	ADJ
ap-1189	208	18	central	central	ADJ
ap-1189	208	19	extension	extension	NOUN
ap-1189	208	20	of	of	ADP
ap-1189	208	21	the	the	DET
ap-1189	208	22	loop	loop	NOUN
ap-1189	208	23	algebra	algebra	PROPN
ap-1189	208	24	map(s1	map(s1	PROPN
ap-1189	208	25	,	,	PUNCT
ap-1189	208	26	g	g	NOUN
ap-1189	208	27	)	)	PUNCT
ap-1189	208	28	.	.	PUNCT
ap-1189	209	1	in	in	ADP
ap-1189	209	2	the	the	DET
ap-1189	209	3	case	case	NOUN
ap-1189	209	4	when	when	SCONJ
ap-1189	209	5	dimm	dimm	NOUN
ap-1189	209	6	=	=	SYM
ap-1189	209	7	3	3	NUM
ap-1189	209	8	one	one	NOUN
ap-1189	209	9	can	can	AUX
ap-1189	209	10	show	show	VERB
ap-1189	209	11	that	that	SCONJ
ap-1189	209	12	the	the	DET
ap-1189	209	13	2	2	NUM
ap-1189	209	14	-	-	PUNCT
ap-1189	209	15	cocycle	cocycle	NOUN
ap-1189	209	16	c	c	PROPN
ap-1189	209	17	is	be	AUX
ap-1189	209	18	equivalent	equivalent	ADJ
ap-1189	209	19	to	to	ADP
ap-1189	209	20	the	the	DET
ap-1189	209	21	local	local	ADJ
ap-1189	209	22	form	form	NOUN
ap-1189	209	23	c	c	PROPN
ap-1189	209	24	≡	≡	PROPN
ap-1189	209	25	const	const	PROPN
ap-1189	209	26	.	.	PUNCT
ap-1189	210	1	∫	∫	PROPN
ap-1189	210	2	m	m	PROPN
ap-1189	210	3	tra[dx	tra[dx	PROPN
ap-1189	210	4	,	,	PUNCT
ap-1189	210	5	dy	dy	X
ap-1189	210	6	]	]	PUNCT
ap-1189	210	7	where	where	SCONJ
ap-1189	210	8	the	the	DET
ap-1189	210	9	trace	trace	NOUN
ap-1189	210	10	under	under	ADP
ap-1189	210	11	the	the	DET
ap-1189	210	12	integral	integral	ADJ
ap-1189	210	13	sign	sign	NOUN
ap-1189	210	14	is	be	AUX
ap-1189	210	15	computed	compute	VERB
ap-1189	210	16	in	in	ADP
ap-1189	210	17	a	a	DET
ap-1189	210	18	finite	finite	ADJ
ap-1189	210	19	-	-	ADJ
ap-1189	210	20	dimensional	dimensional	ADJ
ap-1189	210	21	representation	representation	NOUN
ap-1189	210	22	of	of	ADP
ap-1189	210	23	g.	g.	PROPN
ap-1189	210	24	this	this	DET
ap-1189	210	25	representation	representation	NOUN
ap-1189	210	26	is	be	AUX
ap-1189	210	27	the	the	DET
ap-1189	210	28	same	same	ADJ
ap-1189	210	29	defined	define	VERB
ap-1189	210	30	by	by	ADP
ap-1189	210	31	the	the	DET
ap-1189	210	32	g	g	NOUN
ap-1189	210	33	-	-	PUNCT
ap-1189	210	34	action	action	NOUN
ap-1189	210	35	on	on	ADP
ap-1189	210	36	fermions	fermion	NOUN
ap-1189	210	37	in	in	ADP
ap-1189	210	38	the	the	DET
ap-1189	210	39	1	1	NUM
ap-1189	210	40	-	-	PUNCT
ap-1189	210	41	particle	particle	NOUN
ap-1189	210	42	space	space	NOUN
ap-1189	210	43	.	.	PUNCT
ap-1189	211	1	actually	actually	ADV
ap-1189	211	2	,	,	PUNCT
ap-1189	211	3	the	the	DET
ap-1189	211	4	coefficient	coefficient	NOUN
ap-1189	211	5	in	in	ADP
ap-1189	211	6	the	the	DET
ap-1189	211	7	front	front	NOUN
ap-1189	211	8	of	of	ADP
ap-1189	211	9	the	the	DET
ap-1189	211	10	integral	integral	ADJ
ap-1189	211	11	is	be	AUX
ap-1189	211	12	nonzero	nonzero	ADJ
ap-1189	211	13	only	only	ADV
ap-1189	211	14	for	for	ADP
ap-1189	211	15	chiral	chiral	ADJ
ap-1189	211	16	fermions	fermion	NOUN
ap-1189	211	17	(	(	PUNCT
ap-1189	211	18	the	the	DET
ap-1189	211	19	schwinger	schwinger	NOUN
ap-1189	211	20	terms	term	NOUN
ap-1189	211	21	from	from	ADP
ap-1189	211	22	left	left	ADJ
ap-1189	211	23	and	and	CCONJ
ap-1189	211	24	right	right	ADJ
ap-1189	211	25	chiral	chiral	ADJ
ap-1189	211	26	sectors	sector	NOUN
ap-1189	211	27	cancel	cancel	VERB
ap-1189	211	28	)	)	PUNCT
ap-1189	211	29	.	.	PUNCT
ap-1189	212	1	references	reference	NOUN
ap-1189	212	2	[	[	X
ap-1189	212	3	1	1	NUM
ap-1189	212	4	]	]	X
ap-1189	212	5	bargmann	bargmann	PROPN
ap-1189	212	6	,	,	PUNCT
ap-1189	212	7	v.	v.	ADV
ap-1189	212	8	:	:	PUNCT
ap-1189	212	9	on	on	ADP
ap-1189	212	10	unitary	unitary	ADJ
ap-1189	212	11	ray	ray	NOUN
ap-1189	212	12	representations	representation	NOUN
ap-1189	212	13	of	of	ADP
ap-1189	212	14	continuous	continuous	ADJ
ap-1189	212	15	groups	group	NOUN
ap-1189	212	16	.	.	PUNCT
ap-1189	213	1	ann	ann	PROPN
ap-1189	213	2	.	.	PROPN
ap-1189	213	3	of	of	ADP
ap-1189	213	4	math	math	NOUN
ap-1189	213	5	.	.	PUNCT
ap-1189	214	1	(	(	PUNCT
ap-1189	214	2	2	2	NUM
ap-1189	214	3	)	)	PUNCT
ap-1189	214	4	59	59	NUM
ap-1189	214	5	,	,	PUNCT
ap-1189	214	6	(	(	PUNCT
ap-1189	214	7	1954	1954	NUM
ap-1189	214	8	)	)	PUNCT
ap-1189	214	9	,	,	PUNCT
ap-1189	214	10	1–46	1–46	PROPN
ap-1189	214	11	.	.	PUNCT
ap-1189	215	1	[	[	X
ap-1189	215	2	2	2	NUM
ap-1189	215	3	]	]	SYM
ap-1189	215	4	carey	carey	NOUN
ap-1189	215	5	,	,	PUNCT
ap-1189	215	6	a.	a.	PROPN
ap-1189	215	7	l.	l.	PROPN
ap-1189	215	8	:	:	PUNCT
ap-1189	215	9	the	the	DET
ap-1189	215	10	origin	origin	NOUN
ap-1189	215	11	of	of	ADP
ap-1189	215	12	three	three	NUM
ap-1189	215	13	-	-	PUNCT
ap-1189	215	14	cocycles	cocycle	NOUN
ap-1189	215	15	in	in	ADP
ap-1189	215	16	quantum	quantum	ADJ
ap-1189	215	17	field	field	NOUN
ap-1189	215	18	theory	theory	NOUN
ap-1189	215	19	.	.	PUNCT
ap-1189	216	1	phys	phy	NOUN
ap-1189	216	2	.	.	PUNCT
ap-1189	217	1	lett	lett	PROPN
ap-1189	217	2	.	.	PUNCT
ap-1189	218	1	b	b	PROPN
ap-1189	218	2	194	194	NUM
ap-1189	218	3	,	,	PUNCT
ap-1189	218	4	(	(	PUNCT
ap-1189	218	5	1987	1987	NUM
ap-1189	218	6	)	)	PUNCT
ap-1189	218	7	,	,	PUNCT
ap-1189	218	8	267–270	267–270	NUM
ap-1189	218	9	.	.	PUNCT
ap-1189	219	1	[	[	X
ap-1189	219	2	3	3	NUM
ap-1189	219	3	]	]	X
ap-1189	219	4	carey	carey	PROPN
ap-1189	219	5	,	,	PUNCT
ap-1189	219	6	a.	a.	PROPN
ap-1189	219	7	l.	l.	PROPN
ap-1189	219	8	,	,	PUNCT
ap-1189	219	9	grundling	grundling	NOUN
ap-1189	219	10	,	,	PUNCT
ap-1189	219	11	h.	h.	PROPN
ap-1189	219	12	,	,	PUNCT
ap-1189	219	13	raeburn	raeburn	NOUN
ap-1189	219	14	,	,	PUNCT
ap-1189	219	15	i.	i.	PROPN
ap-1189	219	16	,	,	PUNCT
ap-1189	219	17	sutherland	sutherland	PROPN
ap-1189	219	18	,	,	PUNCT
ap-1189	219	19	c.	c.	PROPN
ap-1189	219	20	:	:	PUNCT
ap-1189	219	21	group	group	NOUN
ap-1189	219	22	actions	action	NOUN
ap-1189	219	23	on	on	ADP
ap-1189	219	24	c∗-algebras	c∗-algebra	NOUN
ap-1189	219	25	,	,	PUNCT
ap-1189	219	26	3cocycles	3cocycles	NUM
ap-1189	219	27	and	and	CCONJ
ap-1189	219	28	quantum	quantum	ADJ
ap-1189	219	29	field	field	NOUN
ap-1189	219	30	theory	theory	NOUN
ap-1189	219	31	.	.	PUNCT
ap-1189	220	1	commun	commun	PROPN
ap-1189	220	2	.	.	PUNCT
ap-1189	221	1	math	math	NOUN
ap-1189	221	2	.	.	PUNCT
ap-1189	222	1	phys	phy	NOUN
ap-1189	222	2	.	.	PUNCT
ap-1189	223	1	168	168	NUM
ap-1189	223	2	,	,	PUNCT
ap-1189	223	3	(	(	PUNCT
ap-1189	223	4	1995	1995	NUM
ap-1189	223	5	)	)	PUNCT
ap-1189	223	6	,	,	PUNCT
ap-1189	224	1	389–416	389–416	NUM
ap-1189	224	2	.	.	PUNCT
ap-1189	225	1	[	[	X
ap-1189	225	2	4	4	NUM
ap-1189	225	3	]	]	X
ap-1189	225	4	carey	carey	PROPN
ap-1189	225	5	,	,	PUNCT
ap-1189	225	6	a.	a.	PROPN
ap-1189	225	7	l.	l.	PROPN
ap-1189	225	8	,	,	PUNCT
ap-1189	225	9	crowley	crowley	PROPN
ap-1189	225	10	,	,	PUNCT
ap-1189	225	11	d.	d.	PROPN
ap-1189	225	12	,	,	PUNCT
ap-1189	225	13	murray	murray	PROPN
ap-1189	225	14	,	,	PUNCT
ap-1189	225	15	m.	m.	PROPN
ap-1189	225	16	k.	k.	PROPN
ap-1189	225	17	:	:	PUNCT
ap-1189	225	18	principal	principal	ADJ
ap-1189	225	19	bundles	bundle	NOUN
ap-1189	225	20	and	and	CCONJ
ap-1189	225	21	the	the	DET
ap-1189	225	22	dixmier	dixmier	NOUN
ap-1189	225	23	douady	douady	PROPN
ap-1189	225	24	class	class	PROPN
ap-1189	225	25	.	.	PUNCT
ap-1189	226	1	comm	comm	NOUN
ap-1189	226	2	.	.	PUNCT
ap-1189	227	1	math	math	NOUN
ap-1189	227	2	.	.	PUNCT
ap-1189	228	1	phys	phy	NOUN
ap-1189	228	2	.	.	PUNCT
ap-1189	229	1	193	193	NUM
ap-1189	229	2	,	,	PUNCT
ap-1189	229	3	(	(	PUNCT
ap-1189	229	4	1998	1998	NUM
ap-1189	229	5	)	)	PUNCT
ap-1189	229	6	,	,	PUNCT
ap-1189	229	7	no	no	INTJ
ap-1189	229	8	.	.	NOUN
ap-1189	229	9	1	1	NUM
ap-1189	229	10	,	,	PUNCT
ap-1189	229	11	171–196	171–196	NUM
ap-1189	229	12	.	.	PUNCT
ap-1189	230	1	[	[	X
ap-1189	230	2	5	5	NUM
ap-1189	230	3	]	]	SYM
ap-1189	230	4	carey	carey	PROPN
ap-1189	230	5	,	,	PUNCT
ap-1189	230	6	a.	a.	PROPN
ap-1189	230	7	l.	l.	PROPN
ap-1189	230	8	,	,	PUNCT
ap-1189	230	9	mickelsson	mickelsson	PROPN
ap-1189	230	10	,	,	PUNCT
ap-1189	230	11	j.	j.	PROPN
ap-1189	230	12	,	,	PUNCT
ap-1189	230	13	murray	murray	PROPN
ap-1189	230	14	,	,	PUNCT
ap-1189	230	15	m.	m.	NOUN
ap-1189	230	16	k.	k.	PROPN
ap-1189	230	17	:	:	PUNCT
ap-1189	230	18	bundle	bundle	NOUN
ap-1189	230	19	gerbes	gerbe	NOUN
ap-1189	230	20	applied	apply	VERB
ap-1189	230	21	to	to	ADP
ap-1189	230	22	quantum	quantum	ADJ
ap-1189	230	23	field	field	NOUN
ap-1189	230	24	theory	theory	NOUN
ap-1189	230	25	.	.	PUNCT
ap-1189	231	1	rev	rev	PROPN
ap-1189	231	2	.	.	PROPN
ap-1189	231	3	math	math	NOUN
ap-1189	231	4	.	.	PUNCT
ap-1189	232	1	phys	phy	NOUN
ap-1189	232	2	.	.	PUNCT
ap-1189	233	1	12	12	NUM
ap-1189	233	2	,	,	PUNCT
ap-1189	233	3	(	(	PUNCT
ap-1189	233	4	2000	2000	NUM
ap-1189	233	5	)	)	PUNCT
ap-1189	233	6	,	,	PUNCT
ap-1189	233	7	no	no	INTJ
ap-1189	233	8	.	.	NOUN
ap-1189	233	9	1	1	NUM
ap-1189	233	10	,	,	PUNCT
ap-1189	233	11	65–90	65–90	NOUN
ap-1189	233	12	.	.	PUNCT
ap-1189	234	1	46	46	NUM
ap-1189	234	2	acta	acta	PROPN
ap-1189	234	3	polytechnica	polytechnica	PROPN
ap-1189	234	4	vol	vol	NOUN
ap-1189	234	5	.	.	PROPN
ap-1189	235	1	50	50	NUM
ap-1189	235	2	no	no	NOUN
ap-1189	235	3	.	.	PUNCT
ap-1189	236	1	3/2010	3/2010	NUM
ap-1189	236	2	[	[	X
ap-1189	236	3	6	6	NUM
ap-1189	236	4	]	]	X
ap-1189	236	5	grossman	grossman	NOUN
ap-1189	236	6	,	,	PUNCT
ap-1189	236	7	b.	b.	PROPN
ap-1189	236	8	:	:	PUNCT
ap-1189	236	9	the	the	DET
ap-1189	236	10	meaning	meaning	NOUN
ap-1189	236	11	of	of	ADP
ap-1189	236	12	the	the	DET
ap-1189	236	13	third	third	ADJ
ap-1189	236	14	cocycle	cocycle	NOUN
ap-1189	236	15	in	in	ADP
ap-1189	236	16	the	the	DET
ap-1189	236	17	group	group	NOUN
ap-1189	236	18	cohomology	cohomology	NOUN
ap-1189	236	19	of	of	ADP
ap-1189	236	20	nonabelian	nonabelian	PROPN
ap-1189	236	21	gauge	gauge	NOUN
ap-1189	236	22	theories	theory	NOUN
ap-1189	236	23	.	.	PUNCT
ap-1189	237	1	phys	phy	NOUN
ap-1189	237	2	.	.	PUNCT
ap-1189	238	1	lett	lett	PROPN
ap-1189	238	2	.	.	PUNCT
ap-1189	239	1	b	b	PROPN
ap-1189	239	2	160	160	NUM
ap-1189	239	3	,	,	PUNCT
ap-1189	239	4	(	(	PUNCT
ap-1189	239	5	1985	1985	NUM
ap-1189	239	6	)	)	PUNCT
ap-1189	239	7	,	,	PUNCT
ap-1189	239	8	94–100	94–100	PROPN
ap-1189	239	9	.	.	PUNCT
ap-1189	240	1	jackiw	jackiw	PROPN
ap-1189	240	2	,	,	PUNCT
ap-1189	240	3	r.	r.	PROPN
ap-1189	240	4	:	:	PUNCT
ap-1189	240	5	three	three	NUM
ap-1189	240	6	-	-	PUNCT
ap-1189	240	7	cocycle	cocycle	NOUN
ap-1189	240	8	in	in	ADP
ap-1189	240	9	mathematics	mathematics	PROPN
ap-1189	240	10	and	and	CCONJ
ap-1189	240	11	physics	physic	NOUN
ap-1189	240	12	.	.	PUNCT
ap-1189	241	1	phys	phy	NOUN
ap-1189	241	2	.	.	PUNCT
ap-1189	242	1	rev	rev	PROPN
ap-1189	242	2	.	.	PROPN
ap-1189	242	3	lett	lett	PROPN
ap-1189	242	4	.	.	PROPN
ap-1189	243	1	54	54	NUM
ap-1189	243	2	,	,	PUNCT
ap-1189	243	3	(	(	PUNCT
ap-1189	243	4	1985	1985	NUM
ap-1189	243	5	)	)	PUNCT
ap-1189	243	6	,	,	PUNCT
ap-1189	244	1	159–162	159–162	NUM
ap-1189	244	2	.	.	PUNCT
ap-1189	245	1	jo	jo	PROPN
ap-1189	245	2	,	,	PUNCT
ap-1189	245	3	s.	s.	PROPN
ap-1189	245	4	g.	g.	PROPN
ap-1189	245	5	:	:	PUNCT
ap-1189	245	6	commutator	commutator	NOUN
ap-1189	245	7	of	of	ADP
ap-1189	245	8	gauge	gauge	ADJ
ap-1189	245	9	generators	generator	NOUN
ap-1189	245	10	in	in	ADP
ap-1189	245	11	nonabelian	nonabelian	ADJ
ap-1189	245	12	chiral	chiral	ADJ
ap-1189	245	13	theory	theory	NOUN
ap-1189	245	14	.	.	PUNCT
ap-1189	246	1	nuclear	nuclear	ADJ
ap-1189	246	2	phys	phy	NOUN
ap-1189	246	3	.	.	PUNCT
ap-1189	247	1	b	b	PROPN
ap-1189	247	2	259	259	NUM
ap-1189	247	3	,	,	PUNCT
ap-1189	247	4	(	(	PUNCT
ap-1189	247	5	1985	1985	NUM
ap-1189	247	6	)	)	PUNCT
ap-1189	247	7	,	,	PUNCT
ap-1189	247	8	616–636	616–636	NUM
ap-1189	247	9	.	.	PUNCT
ap-1189	248	1	[	[	X
ap-1189	248	2	7	7	NUM
ap-1189	248	3	]	]	SYM
ap-1189	248	4	frenkel	frenkel	NOUN
ap-1189	248	5	,	,	PUNCT
ap-1189	248	6	e.	e.	PROPN
ap-1189	248	7	,	,	PUNCT
ap-1189	248	8	xinwen	xinwen	PROPN
ap-1189	248	9	zhu	zhu	PROPN
ap-1189	248	10	:	:	PUNCT
ap-1189	248	11	gerbal	gerbal	ADJ
ap-1189	248	12	representations	representation	NOUN
ap-1189	248	13	of	of	ADP
ap-1189	248	14	double	double	ADJ
ap-1189	248	15	loop	loop	NOUN
ap-1189	248	16	groups	group	NOUN
ap-1189	248	17	.	.	PUNCT
ap-1189	249	1	arxiv.math/0810.1487	arxiv.math/0810.1487	X
ap-1189	250	1	[	[	X
ap-1189	250	2	8	8	NUM
ap-1189	250	3	]	]	X
ap-1189	250	4	hekmati	hekmati	NOUN
ap-1189	250	5	,	,	PUNCT
ap-1189	250	6	p.	p.	PROPN
ap-1189	250	7	,	,	PUNCT
ap-1189	250	8	mickelsson	mickelsson	PROPN
ap-1189	250	9	,	,	PUNCT
ap-1189	250	10	j.	j.	PROPN
ap-1189	250	11	:	:	PUNCT
ap-1189	250	12	fractional	fractional	PROPN
ap-1189	250	13	loop	loop	NOUN
ap-1189	250	14	group	group	NOUN
ap-1189	250	15	and	and	CCONJ
ap-1189	250	16	twisted	twisted	ADJ
ap-1189	250	17	k	k	NOUN
ap-1189	250	18	-	-	NOUN
ap-1189	250	19	theory	theory	NOUN
ap-1189	250	20	.	.	PUNCT
ap-1189	251	1	arxiv:0801.2522	arxiv:0801.2522	NOUN
ap-1189	251	2	.	.	PUNCT
ap-1189	252	1	[	[	X
ap-1189	252	2	9	9	NUM
ap-1189	252	3	]	]	SYM
ap-1189	252	4	mac	mac	PROPN
ap-1189	252	5	lane	lane	NOUN
ap-1189	252	6	,	,	PUNCT
ap-1189	252	7	saunders	saunder	NOUN
ap-1189	252	8	:	:	PUNCT
ap-1189	252	9	homology.die	homology.die	X
ap-1189	252	10	grundlehren	grundlehren	PROPN
ap-1189	252	11	der	der	ADJ
ap-1189	252	12	mathematischen	mathematischen	PROPN
ap-1189	252	13	wissenschaften	wissenschaften	VERB
ap-1189	252	14	,	,	PUNCT
ap-1189	252	15	band	band	NOUN
ap-1189	252	16	114	114	NUM
ap-1189	252	17	.	.	PUNCT
ap-1189	252	18	springer	springer	NOUN
ap-1189	252	19	verlag	verlag	PROPN
ap-1189	252	20	(	(	PUNCT
ap-1189	252	21	1963	1963	NUM
ap-1189	252	22	)	)	PUNCT
ap-1189	252	23	.	.	PUNCT
ap-1189	253	1	[	[	X
ap-1189	253	2	10	10	NUM
ap-1189	253	3	]	]	X
ap-1189	253	4	kac	kac	PROPN
ap-1189	253	5	,	,	PUNCT
ap-1189	253	6	victor	victor	PROPN
ap-1189	253	7	:	:	PUNCT
ap-1189	253	8	infinite	infinite	ADJ
ap-1189	253	9	-	-	PUNCT
ap-1189	253	10	dimensional	dimensional	ADJ
ap-1189	253	11	lie	lie	NOUN
ap-1189	253	12	algebras	algebra	NOUN
ap-1189	253	13	.	.	PUNCT
ap-1189	253	14	third	third	PROPN
ap-1189	253	15	edition	edition	PROPN
ap-1189	253	16	.	.	PUNCT
ap-1189	254	1	cambridge	cambridge	PROPN
ap-1189	254	2	university	university	PROPN
ap-1189	254	3	press	press	PROPN
ap-1189	254	4	,	,	PUNCT
ap-1189	254	5	cambridge	cambridge	PROPN
ap-1189	254	6	,	,	PUNCT
ap-1189	254	7	(	(	PUNCT
ap-1189	254	8	1990	1990	NUM
ap-1189	254	9	)	)	PUNCT
ap-1189	254	10	.	.	PUNCT
ap-1189	255	1	[	[	X
ap-1189	255	2	11	11	NUM
ap-1189	255	3	]	]	X
ap-1189	255	4	pressley	pressley	NOUN
ap-1189	255	5	,	,	PUNCT
ap-1189	255	6	a.	a.	PROPN
ap-1189	255	7	,	,	PUNCT
ap-1189	255	8	segal	segal	PROPN
ap-1189	255	9	,	,	PUNCT
ap-1189	255	10	g.	g.	PROPN
ap-1189	255	11	:	:	PUNCT
ap-1189	255	12	loop	loop	NOUN
ap-1189	255	13	groups	group	NOUN
ap-1189	255	14	.	.	PUNCT
ap-1189	256	1	oxford	oxford	PROPN
ap-1189	256	2	mathematical	mathematical	ADJ
ap-1189	256	3	monographs	monograph	NOUN
ap-1189	256	4	.	.	PUNCT
ap-1189	257	1	the	the	DET
ap-1189	257	2	clarendon	clarendon	PROPN
ap-1189	257	3	press	press	NOUN
ap-1189	257	4	,	,	PUNCT
ap-1189	257	5	oxford	oxford	PROPN
ap-1189	257	6	university	university	PROPN
ap-1189	257	7	press	press	NOUN
ap-1189	257	8	,	,	PUNCT
ap-1189	257	9	new	new	PROPN
ap-1189	257	10	york	york	PROPN
ap-1189	257	11	,	,	PUNCT
ap-1189	257	12	(	(	PUNCT
ap-1189	257	13	1986	1986	NUM
ap-1189	257	14	)	)	PUNCT
ap-1189	257	15	.	.	PUNCT
ap-1189	258	1	[	[	X
ap-1189	258	2	12	12	NUM
ap-1189	258	3	]	]	X
ap-1189	258	4	mickelsson	mickelsson	NOUN
ap-1189	258	5	,	,	PUNCT
ap-1189	258	6	j.	j.	PROPN
ap-1189	258	7	:	:	PUNCT
ap-1189	258	8	wodzicki	wodzicki	PROPN
ap-1189	258	9	residue	residue	NOUN
ap-1189	258	10	and	and	CCONJ
ap-1189	258	11	anomalies	anomaly	NOUN
ap-1189	258	12	of	of	ADP
ap-1189	258	13	current	current	ADJ
ap-1189	258	14	algebras	algebra	NOUN
ap-1189	258	15	.	.	PUNCT
ap-1189	259	1	integrable	integrable	ADJ
ap-1189	259	2	models	model	NOUN
ap-1189	259	3	and	and	CCONJ
ap-1189	259	4	strings	string	NOUN
ap-1189	259	5	(	(	PUNCT
ap-1189	259	6	espoo	espoo	PROPN
ap-1189	259	7	,	,	PUNCT
ap-1189	259	8	1993	1993	NUM
ap-1189	259	9	)	)	PUNCT
ap-1189	259	10	,	,	PUNCT
ap-1189	259	11	123–135	123–135	NUM
ap-1189	259	12	,	,	PUNCT
ap-1189	259	13	lecture	lecture	NOUN
ap-1189	259	14	notes	note	NOUN
ap-1189	259	15	in	in	ADP
ap-1189	259	16	phys	phy	NOUN
ap-1189	259	17	.	.	PUNCT
ap-1189	259	18	,	,	PUNCT
ap-1189	259	19	436	436	NUM
ap-1189	259	20	,	,	PUNCT
ap-1189	259	21	springer	springer	NOUN
ap-1189	259	22	,	,	PUNCT
ap-1189	259	23	berlin	berlin	PROPN
ap-1189	259	24	,	,	PUNCT
ap-1189	259	25	(	(	PUNCT
ap-1189	259	26	1994	1994	NUM
ap-1189	259	27	)	)	PUNCT
ap-1189	259	28	.	.	PUNCT
ap-1189	260	1	[	[	X
ap-1189	260	2	13	13	NUM
ap-1189	260	3	]	]	X
ap-1189	260	4	langmann	langmann	PROPN
ap-1189	260	5	,	,	PUNCT
ap-1189	260	6	e.	e.	PROPN
ap-1189	260	7	,	,	PUNCT
ap-1189	260	8	mickelsson	mickelsson	PROPN
ap-1189	260	9	,	,	PUNCT
ap-1189	260	10	j.	j.	PROPN
ap-1189	260	11	:	:	PUNCT
ap-1189	260	12	scattering	scatter	VERB
ap-1189	260	13	matrix	matrix	NOUN
ap-1189	260	14	in	in	ADP
ap-1189	260	15	external	external	ADJ
ap-1189	260	16	field	field	NOUN
ap-1189	260	17	problems	problem	NOUN
ap-1189	260	18	.	.	PUNCT
ap-1189	261	1	j.	j.	PROPN
ap-1189	261	2	math	math	PROPN
ap-1189	261	3	.	.	PUNCT
ap-1189	262	1	phys	phy	NOUN
ap-1189	262	2	.	.	PUNCT
ap-1189	263	1	37	37	NUM
ap-1189	263	2	,	,	PUNCT
ap-1189	263	3	(	(	PUNCT
ap-1189	263	4	1996	1996	NUM
ap-1189	263	5	)	)	PUNCT
ap-1189	263	6	,	,	PUNCT
ap-1189	263	7	no	no	INTJ
ap-1189	263	8	.	.	NOUN
ap-1189	263	9	8	8	NUM
ap-1189	263	10	,	,	PUNCT
ap-1189	263	11	3	3	NUM
ap-1189	263	12	933–3	933–3	NUM
ap-1189	263	13	953	953	NUM
ap-1189	263	14	.	.	PUNCT
ap-1189	264	1	[	[	X
ap-1189	264	2	14	14	NUM
ap-1189	264	3	]	]	X
ap-1189	264	4	mickelsson	mickelsson	NOUN
ap-1189	264	5	,	,	PUNCT
ap-1189	264	6	j.	j.	PROPN
ap-1189	264	7	:	:	PUNCT
ap-1189	264	8	from	from	ADP
ap-1189	264	9	gauge	gauge	ADJ
ap-1189	264	10	anomalies	anomaly	NOUN
ap-1189	264	11	to	to	ADP
ap-1189	264	12	gerbes	gerbe	NOUN
ap-1189	264	13	and	and	CCONJ
ap-1189	264	14	gerbal	gerbal	ADJ
ap-1189	264	15	actions	action	NOUN
ap-1189	264	16	.	.	PUNCT
ap-1189	265	1	arxiv:0812.1640	arxiv:0812.1640	VERB
ap-1189	265	2	.	.	PUNCT
ap-1189	266	1	to	to	PART
ap-1189	266	2	be	be	AUX
ap-1189	266	3	publ	publ	NOUN
ap-1189	266	4	.	.	PUNCT
ap-1189	267	1	in	in	ADP
ap-1189	267	2	the	the	DET
ap-1189	267	3	proceedings	proceeding	NOUN
ap-1189	267	4	of	of	ADP
ap-1189	267	5	“	"	PUNCT
ap-1189	267	6	motives	motive	NOUN
ap-1189	267	7	,	,	PUNCT
ap-1189	267	8	quantum	quantum	ADJ
ap-1189	267	9	field	field	NOUN
ap-1189	267	10	theory	theory	NOUN
ap-1189	267	11	,	,	PUNCT
ap-1189	267	12	and	and	CCONJ
ap-1189	267	13	pseudodifferential	pseudodifferential	ADJ
ap-1189	267	14	operators	operator	NOUN
ap-1189	267	15	”	"	PUNCT
ap-1189	267	16	,	,	PUNCT
ap-1189	267	17	boston	boston	PROPN
ap-1189	267	18	university	university	PROPN
ap-1189	267	19	,	,	PUNCT
ap-1189	267	20	june	june	PROPN
ap-1189	267	21	2–13	2–13	PROPN
ap-1189	267	22	,	,	PUNCT
ap-1189	267	23	2008	2008	NUM
ap-1189	267	24	.	.	PUNCT
ap-1189	268	1	[	[	X
ap-1189	268	2	15	15	NUM
ap-1189	268	3	]	]	X
ap-1189	268	4	mickelsson	mickelsson	NOUN
ap-1189	268	5	,	,	PUNCT
ap-1189	268	6	j.	j.	PROPN
ap-1189	268	7	,	,	PUNCT
ap-1189	268	8	rajeev	rajeev	PROPN
ap-1189	268	9	,	,	PUNCT
ap-1189	268	10	s.	s.	PROPN
ap-1189	268	11	g.	g.	PROPN
ap-1189	268	12	:	:	PUNCT
ap-1189	268	13	current	current	ADJ
ap-1189	268	14	algebras	algebra	NOUN
ap-1189	268	15	in	in	ADP
ap-1189	268	16	d	d	PROPN
ap-1189	268	17	+	+	CCONJ
ap-1189	268	18	1	1	NUM
ap-1189	268	19	-	-	PUNCT
ap-1189	268	20	dimensions	dimension	NOUN
ap-1189	268	21	and	and	CCONJ
ap-1189	268	22	determinant	determinant	ADJ
ap-1189	268	23	bundles	bundle	NOUN
ap-1189	268	24	over	over	ADP
ap-1189	268	25	infinite	infinite	ADJ
ap-1189	268	26	-	-	PUNCT
ap-1189	268	27	dimensional	dimensional	ADJ
ap-1189	268	28	grassmannians	grassmannian	NOUN
ap-1189	268	29	.	.	PUNCT
ap-1189	269	1	comm	comm	NOUN
ap-1189	269	2	.	.	PUNCT
ap-1189	269	3	math	math	NOUN
ap-1189	269	4	.	.	PUNCT
ap-1189	270	1	phys	phy	NOUN
ap-1189	270	2	.	.	PUNCT
ap-1189	271	1	116	116	NUM
ap-1189	271	2	,	,	PUNCT
ap-1189	271	3	(	(	PUNCT
ap-1189	271	4	1988	1988	NUM
ap-1189	271	5	)	)	PUNCT
ap-1189	271	6	,	,	PUNCT
ap-1189	271	7	no	no	INTJ
ap-1189	271	8	.	.	NOUN
ap-1189	271	9	3	3	NUM
ap-1189	271	10	,	,	PUNCT
ap-1189	271	11	365–400	365–400	NUM
ap-1189	271	12	.	.	PUNCT
ap-1189	272	1	[	[	X
ap-1189	272	2	16	16	NUM
ap-1189	272	3	]	]	X
ap-1189	272	4	palais	palais	PROPN
ap-1189	272	5	,	,	PUNCT
ap-1189	272	6	r.	r.	PROPN
ap-1189	272	7	:	:	PUNCT
ap-1189	272	8	on	on	ADP
ap-1189	272	9	the	the	DET
ap-1189	272	10	homotopy	homotopy	NOUN
ap-1189	272	11	type	type	NOUN
ap-1189	272	12	of	of	ADP
ap-1189	272	13	certain	certain	ADJ
ap-1189	272	14	groups	group	NOUN
ap-1189	272	15	of	of	ADP
ap-1189	272	16	operators	operator	NOUN
ap-1189	272	17	.	.	PUNCT
ap-1189	273	1	topology	topology	NOUN
ap-1189	273	2	3	3	NUM
ap-1189	273	3	,	,	PUNCT
ap-1189	273	4	(	(	PUNCT
ap-1189	273	5	1965	1965	NUM
ap-1189	273	6	)	)	PUNCT
ap-1189	273	7	,	,	PUNCT
ap-1189	273	8	271–279	271–279	NUM
ap-1189	273	9	.	.	PUNCT
ap-1189	274	1	[	[	X
ap-1189	274	2	17	17	NUM
ap-1189	274	3	]	]	X
ap-1189	274	4	shale	shale	PROPN
ap-1189	274	5	,	,	PUNCT
ap-1189	274	6	david	david	PROPN
ap-1189	274	7	,	,	PUNCT
ap-1189	274	8	stinespring	stinespring	PROPN
ap-1189	274	9	,	,	PUNCT
ap-1189	274	10	w.	w.	PROPN
ap-1189	274	11	f.	f.	PROPN
ap-1189	274	12	:	:	PUNCT
ap-1189	274	13	spinor	spinor	NOUN
ap-1189	274	14	representations	representation	NOUN
ap-1189	274	15	of	of	ADP
ap-1189	274	16	infinite	infinite	ADJ
ap-1189	274	17	orthogonal	orthogonal	ADJ
ap-1189	274	18	groups	group	NOUN
ap-1189	274	19	.	.	PUNCT
ap-1189	275	1	j.	j.	PROPN
ap-1189	275	2	math	math	PROPN
ap-1189	275	3	.	.	PUNCT
ap-1189	276	1	mech	mech	PROPN
ap-1189	276	2	.	.	PUNCT
ap-1189	277	1	14	14	NUM
ap-1189	277	2	,	,	PUNCT
ap-1189	277	3	(	(	PUNCT
ap-1189	277	4	1965	1965	NUM
ap-1189	277	5	)	)	PUNCT
ap-1189	277	6	,	,	PUNCT
ap-1189	277	7	315–322	315–322	NUM
ap-1189	277	8	.	.	PUNCT
ap-1189	278	1	jouko	jouko	PROPN
ap-1189	278	2	mickelsson	mickelsson	PROPN
ap-1189	278	3	department	department	PROPN
ap-1189	278	4	of	of	ADP
ap-1189	278	5	mathematics	mathematics	PROPN
ap-1189	278	6	and	and	CCONJ
ap-1189	278	7	statistics	statistics	PROPN
ap-1189	278	8	university	university	PROPN
ap-1189	278	9	of	of	ADP
ap-1189	278	10	helsinki	helsinki	PROPN
ap-1189	278	11	department	department	PROPN
ap-1189	278	12	of	of	ADP
ap-1189	278	13	theoretical	theoretical	PROPN
ap-1189	278	14	physics	physics	PROPN
ap-1189	278	15	royal	royal	PROPN
ap-1189	278	16	institute	institute	PROPN
ap-1189	278	17	of	of	ADP
ap-1189	278	18	technology	technology	PROPN
ap-1189	278	19	,	,	PUNCT
ap-1189	278	20	stockholm	stockholm	PROPN
ap-1189	278	21	47	47	NUM