id	sid	tid	token	lemma	pos
ejpam-2608	1	1	european	european	PROPN
ejpam-2608	1	2	journal	journal	PROPN
ejpam-2608	1	3	of	of	ADP
ejpam-2608	1	4	pure	pure	ADJ
ejpam-2608	1	5	and	and	CCONJ
ejpam-2608	1	6	applied	apply	VERB
ejpam-2608	1	7	mathematics	mathematic	NOUN
ejpam-2608	1	8	vol	vol	NOUN
ejpam-2608	1	9	.	.	PROPN
ejpam-2608	2	1	10	10	NUM
ejpam-2608	2	2	,	,	PUNCT
ejpam-2608	2	3	no	no	INTJ
ejpam-2608	2	4	.	.	NOUN
ejpam-2608	2	5	3	3	NUM
ejpam-2608	2	6	,	,	PUNCT
ejpam-2608	2	7	2017	2017	NUM
ejpam-2608	2	8	,	,	PUNCT
ejpam-2608	2	9	440	440	NUM
ejpam-2608	2	10	-	-	SYM
ejpam-2608	2	11	454	454	NUM
ejpam-2608	2	12	issn	issn	PROPN
ejpam-2608	2	13	1307	1307	NUM
ejpam-2608	2	14	-	-	SYM
ejpam-2608	2	15	5543	5543	NUM
ejpam-2608	2	16	–	–	PUNCT
ejpam-2608	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2608	2	18	published	publish	VERB
ejpam-2608	2	19	by	by	ADP
ejpam-2608	2	20	new	new	PROPN
ejpam-2608	2	21	york	york	PROPN
ejpam-2608	2	22	business	business	PROPN
ejpam-2608	2	23	global	global	ADJ
ejpam-2608	2	24	narrowing	narrow	VERB
ejpam-2608	2	25	cohomology	cohomology	NOUN
ejpam-2608	2	26	for	for	ADP
ejpam-2608	2	27	complex	complex	ADJ
ejpam-2608	2	28	s6	s6	PROPN
ejpam-2608	2	29	andrew	andrew	PROPN
ejpam-2608	2	30	mchugh	mchugh	PROPN
ejpam-2608	2	31	department	department	PROPN
ejpam-2608	2	32	of	of	ADP
ejpam-2608	2	33	mathematics	mathematics	PROPN
ejpam-2608	2	34	and	and	CCONJ
ejpam-2608	2	35	statistics	statistic	NOUN
ejpam-2608	2	36	,	,	PUNCT
ejpam-2608	2	37	zayed	zayed	PROPN
ejpam-2608	2	38	university	university	PROPN
ejpam-2608	2	39	,	,	PUNCT
ejpam-2608	2	40	abu	abu	PROPN
ejpam-2608	2	41	dhabi	dhabi	PROPN
ejpam-2608	2	42	,	,	PUNCT
ejpam-2608	2	43	uae	uae	PROPN
ejpam-2608	2	44	abstract	abstract	NOUN
ejpam-2608	2	45	.	.	PUNCT
ejpam-2608	3	1	we	we	PRON
ejpam-2608	3	2	compute	compute	VERB
ejpam-2608	3	3	bott	bott	PROPN
ejpam-2608	3	4	chern	chern	PROPN
ejpam-2608	3	5	,	,	PUNCT
ejpam-2608	3	6	and	and	CCONJ
ejpam-2608	3	7	aeppli	aeppli	VERB
ejpam-2608	3	8	cohomology	cohomology	NOUN
ejpam-2608	3	9	for	for	ADP
ejpam-2608	3	10	a	a	DET
ejpam-2608	3	11	complex	complex	ADJ
ejpam-2608	3	12	structure	structure	NOUN
ejpam-2608	3	13	on	on	ADP
ejpam-2608	3	14	the	the	DET
ejpam-2608	3	15	six	six	NUM
ejpam-2608	3	16	sphere	sphere	NOUN
ejpam-2608	3	17	,	,	PUNCT
ejpam-2608	3	18	s6	s6	PROPN
ejpam-2608	3	19	.	.	PUNCT
ejpam-2608	4	1	we	we	PRON
ejpam-2608	4	2	also	also	ADV
ejpam-2608	4	3	give	give	VERB
ejpam-2608	4	4	a	a	DET
ejpam-2608	4	5	table	table	NOUN
ejpam-2608	4	6	for	for	ADP
ejpam-2608	4	7	the	the	DET
ejpam-2608	4	8	hodge	hodge	PROPN
ejpam-2608	4	9	numbers	number	NOUN
ejpam-2608	4	10	for	for	ADP
ejpam-2608	4	11	the	the	DET
ejpam-2608	4	12	bott	bott	PROPN
ejpam-2608	4	13	-	-	PUNCT
ejpam-2608	4	14	chern	chern	PROPN
ejpam-2608	4	15	(	(	PUNCT
ejpam-2608	4	16	and	and	CCONJ
ejpam-2608	4	17	thus	thus	ADV
ejpam-2608	4	18	also	also	ADV
ejpam-2608	4	19	aeppli	aeppli	ADJ
ejpam-2608	4	20	)	)	PUNCT
ejpam-2608	4	21	cohomology	cohomology	NOUN
ejpam-2608	4	22	where	where	SCONJ
ejpam-2608	4	23	hodge	hodge	PROPN
ejpam-2608	4	24	numbers	number	NOUN
ejpam-2608	4	25	are	be	AUX
ejpam-2608	4	26	given	give	VERB
ejpam-2608	4	27	in	in	ADP
ejpam-2608	4	28	terms	term	NOUN
ejpam-2608	4	29	of	of	ADP
ejpam-2608	4	30	whole	whole	ADJ
ejpam-2608	4	31	number	number	NOUN
ejpam-2608	4	32	parameters	parameter	VERB
ejpam-2608	4	33	a	a	DET
ejpam-2608	4	34	=	=	SYM
ejpam-2608	4	35	h2,0	h2,0	PROPN
ejpam-2608	4	36	∂̄	∂̄	ADP
ejpam-2608	4	37	−	−	PROPN
ejpam-2608	4	38	h1,0	h1,0	NOUN
ejpam-2608	4	39	∂̄	∂̄	NOUN
ejpam-2608	4	40	,	,	PUNCT
ejpam-2608	4	41	c	c	NOUN
ejpam-2608	4	42	=	=	SYM
ejpam-2608	4	43	h0,2	h0,2	PROPN
ejpam-2608	4	44	∂̄	∂̄	ADV
ejpam-2608	4	45	,	,	PUNCT
ejpam-2608	4	46	d	d	NOUN
ejpam-2608	4	47	=	=	SYM
ejpam-2608	4	48	h1,2	h1,2	ADJ
ejpam-2608	4	49	∂̄	∂̄	NOUN
ejpam-2608	4	50	,	,	PUNCT
ejpam-2608	4	51	h2,0	h2,0	PROPN
ejpam-2608	4	52	∂̄	∂̄	NOUN
ejpam-2608	4	53	,	,	PUNCT
ejpam-2608	4	54	h1,1	h1,1	PROPN
ejpam-2608	4	55	bc	bc	PROPN
ejpam-2608	4	56	,	,	PUNCT
ejpam-2608	4	57	and	and	CCONJ
ejpam-2608	4	58	h2,2	h2,2	PROPN
ejpam-2608	4	59	bc	bc	PROPN
ejpam-2608	4	60	.	.	PUNCT
ejpam-2608	5	1	as	as	ADP
ejpam-2608	5	2	an	an	DET
ejpam-2608	5	3	example	example	NOUN
ejpam-2608	5	4	,	,	PUNCT
ejpam-2608	5	5	we	we	PRON
ejpam-2608	5	6	work	work	VERB
ejpam-2608	5	7	out	out	ADP
ejpam-2608	5	8	the	the	DET
ejpam-2608	5	9	bott	bott	PROPN
ejpam-2608	5	10	-	-	PUNCT
ejpam-2608	5	11	chern	chern	PROPN
ejpam-2608	5	12	hodge	hodge	PROPN
ejpam-2608	5	13	numbers	number	NOUN
ejpam-2608	5	14	completely	completely	ADV
ejpam-2608	5	15	in	in	ADP
ejpam-2608	5	16	the	the	DET
ejpam-2608	5	17	hypothetical	hypothetical	ADJ
ejpam-2608	5	18	case	case	NOUN
ejpam-2608	5	19	that	that	SCONJ
ejpam-2608	5	20	the	the	DET
ejpam-2608	5	21	dolbeault	dolbeault	NOUN
ejpam-2608	5	22	cohomology	cohomology	NOUN
ejpam-2608	5	23	has	have	VERB
ejpam-2608	5	24	h2,0	h2,0	PROPN
ejpam-2608	5	25	=	=	PUNCT
ejpam-2608	5	26	a	a	PROPN
ejpam-2608	5	27	=	=	SYM
ejpam-2608	5	28	c	c	NOUN
ejpam-2608	5	29	=	=	SYM
ejpam-2608	6	1	d	d	NOUN
ejpam-2608	6	2	=	=	SYM
ejpam-2608	6	3	0	0	NUM
ejpam-2608	6	4	.	.	NUM
ejpam-2608	6	5	2010	2010	NUM
ejpam-2608	6	6	mathematics	mathematic	NOUN
ejpam-2608	6	7	subject	subject	NOUN
ejpam-2608	6	8	classifications	classification	NOUN
ejpam-2608	6	9	:	:	PUNCT
ejpam-2608	6	10	53c56,55n99,32q99	53c56,55n99,32q99	NUM
ejpam-2608	6	11	key	key	ADJ
ejpam-2608	6	12	words	word	NOUN
ejpam-2608	6	13	and	and	CCONJ
ejpam-2608	6	14	phrases	phrase	NOUN
ejpam-2608	6	15	:	:	PUNCT
ejpam-2608	6	16	six	six	NUM
ejpam-2608	6	17	sphere	sphere	ADJ
ejpam-2608	6	18	,	,	PUNCT
ejpam-2608	6	19	complex	complex	ADJ
ejpam-2608	6	20	structure	structure	NOUN
ejpam-2608	6	21	,	,	PUNCT
ejpam-2608	6	22	hodge	hodge	PROPN
ejpam-2608	6	23	numbers	number	NOUN
ejpam-2608	6	24	,	,	PUNCT
ejpam-2608	6	25	aeppli	aeppli	ADJ
ejpam-2608	6	26	cohomology	cohomology	NOUN
ejpam-2608	6	27	,	,	PUNCT
ejpam-2608	6	28	bott	bott	PROPN
ejpam-2608	6	29	-	-	PUNCT
ejpam-2608	6	30	chern	chern	PROPN
ejpam-2608	6	31	cohomology	cohomology	NOUN
ejpam-2608	7	1	1	1	X
ejpam-2608	7	2	.	.	PUNCT
ejpam-2608	7	3	introduction	introduction	NOUN
ejpam-2608	7	4	the	the	DET
ejpam-2608	7	5	existence	existence	NOUN
ejpam-2608	7	6	of	of	ADP
ejpam-2608	7	7	a	a	DET
ejpam-2608	7	8	complex	complex	ADJ
ejpam-2608	7	9	structure	structure	NOUN
ejpam-2608	7	10	on	on	ADP
ejpam-2608	7	11	s6	s6	PROPN
ejpam-2608	7	12	has	have	AUX
ejpam-2608	7	13	been	be	AUX
ejpam-2608	7	14	a	a	DET
ejpam-2608	7	15	persistent	persistent	ADJ
ejpam-2608	7	16	question	question	NOUN
ejpam-2608	7	17	for	for	ADP
ejpam-2608	7	18	many	many	ADJ
ejpam-2608	7	19	years	year	NOUN
ejpam-2608	7	20	.	.	PUNCT
ejpam-2608	8	1	in	in	ADP
ejpam-2608	8	2	1954	1954	NUM
ejpam-2608	8	3	,	,	PUNCT
ejpam-2608	8	4	hirzebruch[6	hirzebruch[6	PROPN
ejpam-2608	8	5	]	]	PUNCT
ejpam-2608	8	6	showed	show	VERB
ejpam-2608	8	7	that	that	SCONJ
ejpam-2608	8	8	if	if	SCONJ
ejpam-2608	8	9	a	a	DET
ejpam-2608	8	10	complex	complex	ADJ
ejpam-2608	8	11	structure	structure	NOUN
ejpam-2608	8	12	on	on	ADP
ejpam-2608	8	13	s6	s6	PROPN
ejpam-2608	8	14	does	do	AUX
ejpam-2608	8	15	exist	exist	VERB
ejpam-2608	8	16	,	,	PUNCT
ejpam-2608	8	17	then	then	ADV
ejpam-2608	8	18	by	by	ADP
ejpam-2608	8	19	blowing	blow	VERB
ejpam-2608	8	20	up	up	ADP
ejpam-2608	8	21	a	a	DET
ejpam-2608	8	22	point	point	NOUN
ejpam-2608	8	23	,	,	PUNCT
ejpam-2608	8	24	one	one	PRON
ejpam-2608	8	25	obtains	obtain	VERB
ejpam-2608	8	26	an	an	DET
ejpam-2608	8	27	exotic	exotic	ADJ
ejpam-2608	8	28	complex	complex	ADJ
ejpam-2608	8	29	structure	structure	NOUN
ejpam-2608	8	30	on	on	ADP
ejpam-2608	8	31	cp3	cp3	PROPN
ejpam-2608	8	32	.	.	PUNCT
ejpam-2608	9	1	in	in	ADP
ejpam-2608	9	2	fact	fact	NOUN
ejpam-2608	9	3	,	,	PUNCT
ejpam-2608	9	4	these	these	DET
ejpam-2608	9	5	complex	complex	ADJ
ejpam-2608	9	6	structures	structure	NOUN
ejpam-2608	9	7	on	on	ADP
ejpam-2608	9	8	s6	s6	PROPN
ejpam-2608	9	9	and	and	CCONJ
ejpam-2608	9	10	cp3	cp3	PROPN
ejpam-2608	9	11	are	be	AUX
ejpam-2608	9	12	non	non	ADJ
ejpam-2608	9	13	-	-	NOUN
ejpam-2608	9	14	kahler	kahler	NOUN
ejpam-2608	9	15	.	.	PUNCT
ejpam-2608	10	1	in	in	ADP
ejpam-2608	10	2	1987	1987	NUM
ejpam-2608	10	3	lebrun[8	lebrun[8	NUM
ejpam-2608	10	4	]	]	PUNCT
ejpam-2608	10	5	showed	show	VERB
ejpam-2608	10	6	that	that	SCONJ
ejpam-2608	10	7	a	a	DET
ejpam-2608	10	8	complex	complex	ADJ
ejpam-2608	10	9	structure	structure	NOUN
ejpam-2608	10	10	on	on	ADP
ejpam-2608	10	11	s6	s6	PROPN
ejpam-2608	10	12	can	can	AUX
ejpam-2608	10	13	not	not	PART
ejpam-2608	10	14	be	be	AUX
ejpam-2608	10	15	compatible	compatible	ADJ
ejpam-2608	10	16	with	with	ADP
ejpam-2608	10	17	the	the	DET
ejpam-2608	10	18	standard	standard	ADJ
ejpam-2608	10	19	metric	metric	NOUN
ejpam-2608	10	20	on	on	ADP
ejpam-2608	10	21	s6	s6	PROPN
ejpam-2608	10	22	.	.	PUNCT
ejpam-2608	11	1	in	in	ADP
ejpam-2608	11	2	1998	1998	NUM
ejpam-2608	11	3	,	,	PUNCT
ejpam-2608	11	4	campana	campana	NOUN
ejpam-2608	11	5	,	,	PUNCT
ejpam-2608	11	6	demailly	demailly	ADV
ejpam-2608	11	7	,	,	PUNCT
ejpam-2608	11	8	and	and	CCONJ
ejpam-2608	11	9	pertenell[3	pertenell[3	NOUN
ejpam-2608	11	10	]	]	PUNCT
ejpam-2608	11	11	showed	show	VERB
ejpam-2608	11	12	that	that	SCONJ
ejpam-2608	11	13	a	a	DET
ejpam-2608	11	14	complex	complex	ADJ
ejpam-2608	11	15	s6	s6	PROPN
ejpam-2608	11	16	has	have	VERB
ejpam-2608	11	17	no	no	DET
ejpam-2608	11	18	global	global	ADJ
ejpam-2608	11	19	non	non	ADJ
ejpam-2608	11	20	-	-	ADJ
ejpam-2608	11	21	constant	constant	ADJ
ejpam-2608	11	22	meromorphic	meromorphic	ADJ
ejpam-2608	11	23	functions	function	NOUN
ejpam-2608	11	24	.	.	PUNCT
ejpam-2608	12	1	in	in	ADP
ejpam-2608	12	2	2000	2000	NUM
ejpam-2608	12	3	,	,	PUNCT
ejpam-2608	12	4	huckleberry	huckleberry	NOUN
ejpam-2608	12	5	,	,	PUNCT
ejpam-2608	12	6	kebekus	kebekus	PROPN
ejpam-2608	12	7	,	,	PUNCT
ejpam-2608	12	8	and	and	CCONJ
ejpam-2608	12	9	peternell	peternell	NOUN
ejpam-2608	12	10	showed	show	VERB
ejpam-2608	12	11	it	it	PRON
ejpam-2608	12	12	is	be	AUX
ejpam-2608	12	13	not	not	PART
ejpam-2608	12	14	almost	almost	ADV
ejpam-2608	12	15	homogeneous	homogeneous	ADJ
ejpam-2608	12	16	.	.	PUNCT
ejpam-2608	13	1	recently	recently	ADV
ejpam-2608	13	2	in	in	ADP
ejpam-2608	13	3	2015	2015	NUM
ejpam-2608	13	4	,	,	PUNCT
ejpam-2608	13	5	etesi[4	etesi[4	X
ejpam-2608	13	6	]	]	PUNCT
ejpam-2608	13	7	has	have	AUX
ejpam-2608	13	8	published	publish	VERB
ejpam-2608	13	9	an	an	DET
ejpam-2608	13	10	article	article	NOUN
ejpam-2608	13	11	which	which	PRON
ejpam-2608	13	12	constructs	construct	VERB
ejpam-2608	13	13	a	a	DET
ejpam-2608	13	14	complex	complex	ADJ
ejpam-2608	13	15	structure	structure	NOUN
ejpam-2608	13	16	on	on	ADP
ejpam-2608	13	17	s6	s6	PROPN
ejpam-2608	13	18	.	.	PUNCT
ejpam-2608	14	1	in	in	ADP
ejpam-2608	14	2	this	this	DET
ejpam-2608	14	3	paper	paper	NOUN
ejpam-2608	14	4	,	,	PUNCT
ejpam-2608	14	5	we	we	PRON
ejpam-2608	14	6	search	search	VERB
ejpam-2608	14	7	for	for	ADP
ejpam-2608	14	8	the	the	DET
ejpam-2608	14	9	dolbeault	dolbeault	NOUN
ejpam-2608	14	10	,	,	PUNCT
ejpam-2608	14	11	bott	bott	PROPN
ejpam-2608	14	12	-	-	PUNCT
ejpam-2608	14	13	chern	chern	PROPN
ejpam-2608	14	14	and	and	CCONJ
ejpam-2608	14	15	aeppli	aeppli	VERB
ejpam-2608	14	16	cohomology	cohomology	NOUN
ejpam-2608	14	17	hodge	hodge	PROPN
ejpam-2608	14	18	numbers	number	NOUN
ejpam-2608	14	19	for	for	ADP
ejpam-2608	14	20	a	a	DET
ejpam-2608	14	21	complex	complex	ADJ
ejpam-2608	14	22	s6	s6	PROPN
ejpam-2608	14	23	.	.	PUNCT
ejpam-2608	15	1	in	in	ADP
ejpam-2608	15	2	1997	1997	NUM
ejpam-2608	15	3	,	,	PUNCT
ejpam-2608	15	4	gray[5	gray[5	X
ejpam-2608	15	5	]	]	PUNCT
ejpam-2608	15	6	showed	show	VERB
ejpam-2608	15	7	that	that	SCONJ
ejpam-2608	15	8	for	for	ADP
ejpam-2608	15	9	the	the	DET
ejpam-2608	15	10	dolbeault	dolbeault	PROPN
ejpam-2608	15	11	hodge	hodge	PROPN
ejpam-2608	15	12	numbers	number	NOUN
ejpam-2608	15	13	,	,	PUNCT
ejpam-2608	15	14	we	we	PRON
ejpam-2608	15	15	have	have	VERB
ejpam-2608	15	16	h3,0	h3,0	PROPN
ejpam-2608	15	17	=	=	SYM
ejpam-2608	16	1	h0,3	h0,3	PROPN
ejpam-2608	16	2	=	=	SYM
ejpam-2608	16	3	0	0	NUM
ejpam-2608	16	4	and	and	CCONJ
ejpam-2608	16	5	h0,1	h0,1	PROPN
ejpam-2608	16	6	≥	≥	NOUN
ejpam-2608	16	7	1	1	NUM
ejpam-2608	16	8	.	.	PUNCT
ejpam-2608	17	1	in	in	ADP
ejpam-2608	17	2	2000	2000	NUM
ejpam-2608	17	3	,	,	PUNCT
ejpam-2608	17	4	ugarte	ugarte	NOUN
ejpam-2608	17	5	essentially	essentially	ADV
ejpam-2608	17	6	gave	give	VERB
ejpam-2608	17	7	the	the	DET
ejpam-2608	17	8	following	following	NOUN
ejpam-2608	17	9	for	for	ADP
ejpam-2608	17	10	the	the	DET
ejpam-2608	17	11	dolbeault	dolbeault	NOUN
ejpam-2608	17	12	cohomology	cohomology	NOUN
ejpam-2608	17	13	on	on	ADP
ejpam-2608	17	14	s6	s6	PROPN
ejpam-2608	17	15	which	which	PRON
ejpam-2608	17	16	we	we	PRON
ejpam-2608	17	17	shall	shall	AUX
ejpam-2608	17	18	summarise	summarise	VERB
ejpam-2608	17	19	shortly	shortly	ADV
ejpam-2608	17	20	in	in	ADP
ejpam-2608	17	21	a	a	DET
ejpam-2608	17	22	table	table	NOUN
ejpam-2608	17	23	.	.	PUNCT
ejpam-2608	18	1	let	let	VERB
ejpam-2608	18	2	a	a	DET
ejpam-2608	18	3	=	=	PUNCT
ejpam-2608	18	4	h2,0	h2,0	PROPN
ejpam-2608	18	5	2	2	NUM
ejpam-2608	18	6	where	where	SCONJ
ejpam-2608	18	7	h2,0	h2,0	PROPN
ejpam-2608	18	8	2	2	NUM
ejpam-2608	18	9	=	=	SYM
ejpam-2608	18	10	dimce	dimce	NOUN
ejpam-2608	18	11	2,0	2,0	NUM
ejpam-2608	18	12	2	2	NUM
ejpam-2608	18	13	from	from	ADP
ejpam-2608	18	14	the	the	DET
ejpam-2608	18	15	frohlicher	frohlicher	PROPN
ejpam-2608	18	16	spectral	spectral	ADJ
ejpam-2608	18	17	sequence	sequence	NOUN
ejpam-2608	18	18	.	.	PUNCT
ejpam-2608	19	1	ugarte	ugarte	NOUN
ejpam-2608	19	2	shows	show	VERB
ejpam-2608	19	3	that	that	SCONJ
ejpam-2608	19	4	h2,0	h2,0	PROPN
ejpam-2608	19	5	2	2	X
ejpam-2608	19	6	=	=	SYM
ejpam-2608	19	7	h2,0	h2,0	NOUN
ejpam-2608	19	8	−	−	NOUN
ejpam-2608	19	9	h1,0	h1,0	PROPN
ejpam-2608	19	10	.	.	PUNCT
ejpam-2608	20	1	now	now	ADV
ejpam-2608	20	2	,	,	PUNCT
ejpam-2608	20	3	let	let	VERB
ejpam-2608	20	4	c	c	NOUN
ejpam-2608	20	5	=	=	SYM
ejpam-2608	20	6	h0,2	h0,2	PROPN
ejpam-2608	20	7	,	,	PUNCT
ejpam-2608	20	8	and	and	CCONJ
ejpam-2608	20	9	d	d	PROPN
ejpam-2608	20	10	=	=	SYM
ejpam-2608	20	11	h2,1	h2,1	PROPN
ejpam-2608	20	12	.	.	PUNCT
ejpam-2608	21	1	we	we	PRON
ejpam-2608	21	2	have	have	VERB
ejpam-2608	21	3	ugarte	ugarte	NOUN
ejpam-2608	21	4	’s	’s	PART
ejpam-2608	21	5	results	result	NOUN
ejpam-2608	21	6	in	in	ADP
ejpam-2608	21	7	the	the	DET
ejpam-2608	21	8	following	following	NOUN
ejpam-2608	21	9	:	:	PUNCT
ejpam-2608	21	10	email	email	NOUN
ejpam-2608	21	11	addresses	address	NOUN
ejpam-2608	21	12	:	:	PUNCT
ejpam-2608	21	13	andrew.mchugh@zu.ac.ae	andrew.mchugh@zu.ac.ae	ADJ
ejpam-2608	21	14	,	,	PUNCT
ejpam-2608	22	1	andrewmchugh@snet.net	andrewmchugh@snet.net	PROPN
ejpam-2608	22	2	(	(	PUNCT
ejpam-2608	22	3	a.	a.	PROPN
ejpam-2608	22	4	mchugh	mchugh	PROPN
ejpam-2608	22	5	)	)	PUNCT
ejpam-2608	22	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2608	23	1	440	440	NUM
ejpam-2608	23	2	c	c	X
ejpam-2608	23	3	©	©	PROPN
ejpam-2608	23	4	2017	2017	NUM
ejpam-2608	23	5	ejpam	ejpam	VERB
ejpam-2608	23	6	all	all	DET
ejpam-2608	23	7	rights	right	NOUN
ejpam-2608	23	8	reserved	reserve	VERB
ejpam-2608	23	9	.	.	PUNCT
ejpam-2608	24	1	a.	a.	PROPN
ejpam-2608	24	2	mchugh	mchugh	PROPN
ejpam-2608	24	3	/	/	SYM
ejpam-2608	24	4	eur	eur	PROPN
ejpam-2608	24	5	.	.	PUNCT
ejpam-2608	25	1	j.	j.	PROPN
ejpam-2608	25	2	pure	pure	PROPN
ejpam-2608	25	3	appl	appl	PROPN
ejpam-2608	25	4	.	.	PROPN
ejpam-2608	25	5	math	math	PROPN
ejpam-2608	25	6	,	,	PUNCT
ejpam-2608	25	7	10	10	NUM
ejpam-2608	25	8	(	(	PUNCT
ejpam-2608	25	9	3	3	NUM
ejpam-2608	25	10	)	)	PUNCT
ejpam-2608	25	11	(	(	PUNCT
ejpam-2608	25	12	2017	2017	NUM
ejpam-2608	25	13	)	)	PUNCT
ejpam-2608	25	14	,	,	PUNCT
ejpam-2608	25	15	440	440	NUM
ejpam-2608	25	16	-	-	SYM
ejpam-2608	25	17	454	454	NUM
ejpam-2608	25	18	441	441	NUM
ejpam-2608	25	19	table	table	NOUN
ejpam-2608	25	20	1	1	NUM
ejpam-2608	25	21	:	:	PUNCT
ejpam-2608	25	22	ugarte	ugarte	NOUN
ejpam-2608	25	23	:	:	PUNCT
ejpam-2608	25	24	hp	hp	PROPN
ejpam-2608	25	25	,	,	PUNCT
ejpam-2608	25	26	q	q	NOUN
ejpam-2608	25	27	for	for	ADP
ejpam-2608	25	28	a	a	DET
ejpam-2608	25	29	complex	complex	ADJ
ejpam-2608	25	30	structure	structure	NOUN
ejpam-2608	25	31	on	on	ADP
ejpam-2608	25	32	s6	s6	PROPN
ejpam-2608	25	33	0	0	PUNCT
ejpam-2608	26	1	h1,0	h1,0	X
ejpam-2608	26	2	+	+	CCONJ
ejpam-2608	26	3	a	a	DET
ejpam-2608	26	4	h1,0	h1,0	PROPN
ejpam-2608	26	5	1	1	NUM
ejpam-2608	26	6	c	c	NOUN
ejpam-2608	26	7	d	d	SYM
ejpam-2608	26	8	d−	d−	PROPN
ejpam-2608	26	9	a+	a+	PUNCT
ejpam-2608	26	10	1	1	NUM
ejpam-2608	26	11	c+	c+	NOUN
ejpam-2608	26	12	1	1	NUM
ejpam-2608	26	13	c+	c+	NOUN
ejpam-2608	26	14	1	1	NUM
ejpam-2608	26	15	d−	d−	PROPN
ejpam-2608	26	16	a+	a+	PUNCT
ejpam-2608	26	17	1	1	NUM
ejpam-2608	26	18	d	d	SYM
ejpam-2608	26	19	c	c	NOUN
ejpam-2608	26	20	1	1	NUM
ejpam-2608	26	21	h1,0	h1,0	VERB
ejpam-2608	26	22	h1,0	h1,0	PROPN
ejpam-2608	26	23	+	+	CCONJ
ejpam-2608	26	24	a	a	DET
ejpam-2608	26	25	0	0	NUM
ejpam-2608	26	26	where	where	SCONJ
ejpam-2608	26	27	0	0	NUM
ejpam-2608	26	28	≤	≤	NOUN
ejpam-2608	26	29	a	a	DET
ejpam-2608	26	30	≤	≤	NUM
ejpam-2608	26	31	c+	c+	NOUN
ejpam-2608	26	32	1	1	NUM
ejpam-2608	26	33	,	,	PUNCT
ejpam-2608	26	34	and	and	CCONJ
ejpam-2608	26	35	c	c	PROPN
ejpam-2608	26	36	≤	≤	X
ejpam-2608	26	37	d.	d.	PROPN
ejpam-2608	26	38	2	2	NUM
ejpam-2608	26	39	.	.	PUNCT
ejpam-2608	27	1	some	some	DET
ejpam-2608	27	2	results	result	NOUN
ejpam-2608	27	3	on	on	ADP
ejpam-2608	27	4	the	the	DET
ejpam-2608	27	5	dolbeault	dolbeault	NOUN
ejpam-2608	27	6	cohomology	cohomology	NOUN
ejpam-2608	27	7	of	of	ADP
ejpam-2608	27	8	compact	compact	ADJ
ejpam-2608	27	9	complex	complex	ADJ
ejpam-2608	27	10	manifolds	manifold	NOUN
ejpam-2608	27	11	and	and	CCONJ
ejpam-2608	27	12	of	of	ADP
ejpam-2608	27	13	complex	complex	ADJ
ejpam-2608	27	14	s6	s6	PROPN
ejpam-2608	27	15	.	.	PUNCT
ejpam-2608	28	1	we	we	PRON
ejpam-2608	28	2	begin	begin	VERB
ejpam-2608	28	3	with	with	ADP
ejpam-2608	28	4	the	the	DET
ejpam-2608	28	5	result	result	NOUN
ejpam-2608	28	6	of	of	ADP
ejpam-2608	28	7	gray[5	gray[5	NOUN
ejpam-2608	28	8	]	]	X
ejpam-2608	28	9	,	,	PUNCT
ejpam-2608	28	10	(	(	PUNCT
ejpam-2608	28	11	see	see	VERB
ejpam-2608	28	12	also	also	ADV
ejpam-2608	28	13	ugarte[11	ugarte[11	VERB
ejpam-2608	28	14	]	]	X
ejpam-2608	28	15	and	and	CCONJ
ejpam-2608	28	16	brown[2	brown[2	NOUN
ejpam-2608	28	17	]	]	PRON
ejpam-2608	28	18	):	):	PUNCT
ejpam-2608	28	19	theorem	theorem	NOUN
ejpam-2608	28	20	1	1	NUM
ejpam-2608	28	21	.	.	PUNCT
ejpam-2608	29	1	(	(	PUNCT
ejpam-2608	29	2	gray	gray	ADJ
ejpam-2608	29	3	)	)	PUNCT
ejpam-2608	29	4	let	let	VERB
ejpam-2608	29	5	x	x	PRON
ejpam-2608	29	6	be	be	AUX
ejpam-2608	29	7	a	a	DET
ejpam-2608	29	8	compact	compact	ADJ
ejpam-2608	29	9	complex	complex	ADJ
ejpam-2608	29	10	manifold	manifold	NOUN
ejpam-2608	29	11	of	of	ADP
ejpam-2608	29	12	complex	complex	ADJ
ejpam-2608	29	13	dimension	dimension	NOUN
ejpam-2608	29	14	n	n	CCONJ
ejpam-2608	29	15	such	such	ADJ
ejpam-2608	29	16	that	that	PRON
ejpam-2608	29	17	bn(x	bn(x	ADJ
ejpam-2608	29	18	)	)	PUNCT
ejpam-2608	29	19	=	=	SYM
ejpam-2608	30	1	0	0	X
ejpam-2608	30	2	.	.	PUNCT
ejpam-2608	31	1	any	any	DET
ejpam-2608	31	2	complex	complex	ADJ
ejpam-2608	31	3	structure	structure	NOUN
ejpam-2608	31	4	on	on	ADP
ejpam-2608	31	5	x	x	PUNCT
ejpam-2608	31	6	has	have	VERB
ejpam-2608	31	7	the	the	DET
ejpam-2608	31	8	property	property	NOUN
ejpam-2608	31	9	hn,0	hn,0	PROPN
ejpam-2608	31	10	=	=	PUNCT
ejpam-2608	32	1	h0,n	h0,n	PROPN
ejpam-2608	32	2	=	=	SYM
ejpam-2608	32	3	0	0	X
ejpam-2608	32	4	.	.	PUNCT
ejpam-2608	33	1	we	we	PRON
ejpam-2608	33	2	will	will	AUX
ejpam-2608	33	3	be	be	AUX
ejpam-2608	33	4	supposing	suppose	VERB
ejpam-2608	33	5	that	that	SCONJ
ejpam-2608	33	6	x	x	PRON
ejpam-2608	33	7	is	be	AUX
ejpam-2608	33	8	a	a	DET
ejpam-2608	33	9	complex	complex	ADJ
ejpam-2608	33	10	manifold	manifold	NOUN
ejpam-2608	33	11	with	with	ADP
ejpam-2608	33	12	h1(x	h1(x	NOUN
ejpam-2608	33	13	,	,	PUNCT
ejpam-2608	33	14	z	z	NOUN
ejpam-2608	33	15	)	)	PUNCT
ejpam-2608	33	16	=	=	SYM
ejpam-2608	33	17	h2(x	h2(x	PROPN
ejpam-2608	33	18	,	,	PUNCT
ejpam-2608	33	19	z	z	NOUN
ejpam-2608	33	20	)	)	PUNCT
ejpam-2608	33	21	=	=	SYM
ejpam-2608	33	22	hn(x	hn(x	X
ejpam-2608	33	23	,	,	PUNCT
ejpam-2608	33	24	c	c	NOUN
ejpam-2608	33	25	)	)	PUNCT
ejpam-2608	33	26	=	=	SYM
ejpam-2608	34	1	0	0	X
ejpam-2608	34	2	.	.	PUNCT
ejpam-2608	34	3	(	(	PUNCT
ejpam-2608	34	4	for	for	ADP
ejpam-2608	34	5	example	example	NOUN
ejpam-2608	34	6	s6	s6	PROPN
ejpam-2608	34	7	with	with	ADP
ejpam-2608	34	8	a	a	DET
ejpam-2608	34	9	complex	complex	ADJ
ejpam-2608	34	10	structure	structure	NOUN
ejpam-2608	34	11	)	)	PUNCT
ejpam-2608	34	12	.	.	PUNCT
ejpam-2608	35	1	by	by	ADP
ejpam-2608	35	2	above	above	ADV
ejpam-2608	35	3	we	we	PRON
ejpam-2608	35	4	have	have	VERB
ejpam-2608	35	5	of	of	ADP
ejpam-2608	35	6	course	course	NOUN
ejpam-2608	35	7	,	,	PUNCT
ejpam-2608	35	8	hn,0	hn,0	PROPN
ejpam-2608	35	9	=	=	PUNCT
ejpam-2608	36	1	h0,n	h0,n	PROPN
ejpam-2608	36	2	=	=	SYM
ejpam-2608	36	3	0	0	X
ejpam-2608	36	4	.	.	X
ejpam-2608	37	1	note	note	VERB
ejpam-2608	37	2	that	that	SCONJ
ejpam-2608	37	3	this	this	PRON
ejpam-2608	37	4	implies	imply	VERB
ejpam-2608	37	5	that	that	SCONJ
ejpam-2608	37	6	the	the	DET
ejpam-2608	37	7	associated	associated	ADJ
ejpam-2608	37	8	canonical	canonical	ADJ
ejpam-2608	37	9	bundle	bundle	NOUN
ejpam-2608	37	10	to	to	ADP
ejpam-2608	37	11	the	the	DET
ejpam-2608	37	12	complex	complex	ADJ
ejpam-2608	37	13	structure	structure	NOUN
ejpam-2608	37	14	,	,	PUNCT
ejpam-2608	37	15	k	k	NOUN
ejpam-2608	37	16	,	,	PUNCT
ejpam-2608	37	17	is	be	AUX
ejpam-2608	37	18	not	not	PART
ejpam-2608	37	19	holomorphically	holomorphically	ADV
ejpam-2608	37	20	trivial	trivial	ADJ
ejpam-2608	37	21	.	.	PUNCT
ejpam-2608	38	1	we	we	PRON
ejpam-2608	38	2	also	also	ADV
ejpam-2608	38	3	note	note	VERB
ejpam-2608	38	4	that	that	SCONJ
ejpam-2608	38	5	because	because	SCONJ
ejpam-2608	38	6	h2(x	h2(x	PROPN
ejpam-2608	38	7	,	,	PUNCT
ejpam-2608	38	8	z	z	NOUN
ejpam-2608	38	9	)	)	PUNCT
ejpam-2608	38	10	=	=	SYM
ejpam-2608	38	11	0	0	NUM
ejpam-2608	38	12	,	,	PUNCT
ejpam-2608	38	13	we	we	PRON
ejpam-2608	38	14	have	have	VERB
ejpam-2608	38	15	that	that	SCONJ
ejpam-2608	38	16	the	the	DET
ejpam-2608	38	17	first	first	ADJ
ejpam-2608	38	18	chern	chern	PROPN
ejpam-2608	38	19	class	class	NOUN
ejpam-2608	38	20	of	of	ADP
ejpam-2608	38	21	k	k	PROPN
ejpam-2608	38	22	(	(	PUNCT
ejpam-2608	38	23	and	and	CCONJ
ejpam-2608	38	24	for	for	ADP
ejpam-2608	38	25	that	that	DET
ejpam-2608	38	26	matter	matter	NOUN
ejpam-2608	38	27	any	any	DET
ejpam-2608	38	28	complex	complex	ADJ
ejpam-2608	38	29	line	line	NOUN
ejpam-2608	38	30	bundle	bundle	NOUN
ejpam-2608	38	31	on	on	ADP
ejpam-2608	38	32	x	x	NOUN
ejpam-2608	38	33	)	)	PUNCT
ejpam-2608	38	34	is	be	AUX
ejpam-2608	38	35	0	0	NUM
ejpam-2608	38	36	.	.	PUNCT
ejpam-2608	39	1	it	it	PRON
ejpam-2608	39	2	is	be	AUX
ejpam-2608	39	3	straight	straight	ADV
ejpam-2608	39	4	forward	forward	ADV
ejpam-2608	39	5	to	to	PART
ejpam-2608	39	6	show	show	VERB
ejpam-2608	39	7	for	for	ADP
ejpam-2608	39	8	such	such	ADJ
ejpam-2608	39	9	complex	complex	ADJ
ejpam-2608	39	10	n	n	CCONJ
ejpam-2608	39	11	-	-	ADJ
ejpam-2608	39	12	fold	fold	ADJ
ejpam-2608	39	13	x	x	NOUN
ejpam-2608	39	14	,	,	PUNCT
ejpam-2608	39	15	a	a	DET
ejpam-2608	39	16	result	result	NOUN
ejpam-2608	39	17	of	of	ADP
ejpam-2608	39	18	gray	gray	ADJ
ejpam-2608	39	19	on	on	ADP
ejpam-2608	39	20	complex	complex	ADJ
ejpam-2608	39	21	s6	s6	PROPN
ejpam-2608	39	22	(	(	PUNCT
ejpam-2608	39	23	see	see	VERB
ejpam-2608	39	24	also	also	ADV
ejpam-2608	39	25	brown[2	brown[2	PROPN
ejpam-2608	39	26	]	]	X
ejpam-2608	39	27	.	.	PUNCT
ejpam-2608	39	28	)	)	PUNCT
ejpam-2608	39	29	theorem	theorem	VERB
ejpam-2608	39	30	2	2	NUM
ejpam-2608	39	31	.	.	PUNCT
ejpam-2608	40	1	h0,1	h0,1	NOUN
ejpam-2608	40	2	≥	≥	NUM
ejpam-2608	40	3	1	1	NUM
ejpam-2608	40	4	(	(	PUNCT
ejpam-2608	40	5	gray	gray	ADJ
ejpam-2608	40	6	)	)	PUNCT
ejpam-2608	40	7	proof	proof	NOUN
ejpam-2608	40	8	.	.	PUNCT
ejpam-2608	41	1	this	this	PRON
ejpam-2608	41	2	can	can	AUX
ejpam-2608	41	3	be	be	AUX
ejpam-2608	41	4	seen	see	VERB
ejpam-2608	41	5	by	by	ADP
ejpam-2608	41	6	considering	consider	VERB
ejpam-2608	41	7	the	the	DET
ejpam-2608	41	8	short	short	ADJ
ejpam-2608	41	9	exact	exact	ADJ
ejpam-2608	41	10	sequence	sequence	NOUN
ejpam-2608	41	11	of	of	ADP
ejpam-2608	41	12	sheaves	sheaf	NOUN
ejpam-2608	41	13	:	:	PUNCT
ejpam-2608	41	14	0→	0→	NUM
ejpam-2608	41	15	z→	z→	NUM
ejpam-2608	41	16	o	o	PROPN
ejpam-2608	41	17	→	→	X
ejpam-2608	41	18	o∗	o∗	PROPN
ejpam-2608	41	19	→	→	SYM
ejpam-2608	41	20	0	0	NUM
ejpam-2608	41	21	and	and	CCONJ
ejpam-2608	41	22	(	(	PUNCT
ejpam-2608	41	23	the	the	DET
ejpam-2608	41	24	portion	portion	NOUN
ejpam-2608	41	25	of	of	ADP
ejpam-2608	41	26	)	)	PUNCT
ejpam-2608	41	27	the	the	DET
ejpam-2608	41	28	resulting	result	VERB
ejpam-2608	41	29	long	long	ADJ
ejpam-2608	41	30	exact	exact	ADJ
ejpam-2608	41	31	sequence	sequence	NOUN
ejpam-2608	41	32	.	.	PUNCT
ejpam-2608	41	33	.	.	PUNCT
ejpam-2608	42	1	.→	.→	PUNCT
ejpam-2608	43	1	h1(x	h1(x	NOUN
ejpam-2608	43	2	,	,	PUNCT
ejpam-2608	43	3	z)→	z)→	PROPN
ejpam-2608	43	4	h1(x	h1(x	NOUN
ejpam-2608	43	5	,	,	PUNCT
ejpam-2608	43	6	o)→	o)→	NOUN
ejpam-2608	43	7	h1(x	h1(x	NOUN
ejpam-2608	43	8	,	,	PUNCT
ejpam-2608	43	9	o∗)→	o∗)→	NOUN
ejpam-2608	43	10	h1(x	h1(x	NOUN
ejpam-2608	43	11	,	,	PUNCT
ejpam-2608	43	12	z)→	z)→	PROPN
ejpam-2608	43	13	.	.	PUNCT
ejpam-2608	43	14	.	.	PUNCT
ejpam-2608	43	15	.	.	PUNCT
ejpam-2608	44	1	where	where	SCONJ
ejpam-2608	44	2	o	o	NOUN
ejpam-2608	44	3	denotes	denote	VERB
ejpam-2608	44	4	the	the	DET
ejpam-2608	44	5	sheaf	sheaf	NOUN
ejpam-2608	44	6	of	of	ADP
ejpam-2608	44	7	holomorphic	holomorphic	ADJ
ejpam-2608	44	8	functions	function	NOUN
ejpam-2608	44	9	on	on	ADP
ejpam-2608	44	10	x	x	PUNCT
ejpam-2608	44	11	and	and	CCONJ
ejpam-2608	44	12	o∗	o∗	PROPN
ejpam-2608	44	13	denotes	denote	VERB
ejpam-2608	44	14	the	the	DET
ejpam-2608	44	15	sheaf	sheaf	NOUN
ejpam-2608	44	16	of	of	ADP
ejpam-2608	44	17	nowhere	nowhere	PRON
ejpam-2608	44	18	zero	zero	NUM
ejpam-2608	44	19	holomorphic	holomorphic	ADJ
ejpam-2608	44	20	functions	function	NOUN
ejpam-2608	44	21	on	on	ADP
ejpam-2608	44	22	x	x	X
ejpam-2608	44	23	.	.	PUNCT
ejpam-2608	45	1	also	also	ADV
ejpam-2608	45	2	,	,	PUNCT
ejpam-2608	45	3	the	the	DET
ejpam-2608	45	4	map	map	NOUN
ejpam-2608	45	5	z→	z→	PROPN
ejpam-2608	45	6	o	o	PROPN
ejpam-2608	45	7	is	be	AUX
ejpam-2608	45	8	the	the	DET
ejpam-2608	45	9	map	map	NOUN
ejpam-2608	45	10	,	,	PUNCT
ejpam-2608	45	11	k	k	PROPN
ejpam-2608	45	12	7→	7→	NUM
ejpam-2608	45	13	ik	ik	PROPN
ejpam-2608	45	14	and	and	CCONJ
ejpam-2608	45	15	the	the	DET
ejpam-2608	45	16	map	map	NOUN
ejpam-2608	45	17	o	o	PROPN
ejpam-2608	45	18	→	→	X
ejpam-2608	45	19	o∗	o∗	PROPN
ejpam-2608	45	20	is	be	AUX
ejpam-2608	45	21	the	the	DET
ejpam-2608	45	22	exponential	exponential	ADJ
ejpam-2608	45	23	map	map	NOUN
ejpam-2608	45	24	,	,	PUNCT
ejpam-2608	45	25	f	f	PROPN
ejpam-2608	45	26	7→	7→	NUM
ejpam-2608	45	27	exp(f	exp(f	PROPN
ejpam-2608	45	28	)	)	PUNCT
ejpam-2608	45	29	.	.	PUNCT
ejpam-2608	46	1	since	since	SCONJ
ejpam-2608	46	2	h1(x	h1(x	NOUN
ejpam-2608	46	3	,	,	PUNCT
ejpam-2608	46	4	z	z	NOUN
ejpam-2608	46	5	)	)	PUNCT
ejpam-2608	46	6	=	=	SYM
ejpam-2608	46	7	h2(x	h2(x	PROPN
ejpam-2608	46	8	,	,	PUNCT
ejpam-2608	46	9	z	z	NOUN
ejpam-2608	46	10	)	)	PUNCT
ejpam-2608	46	11	=	=	SYM
ejpam-2608	46	12	0	0	NUM
ejpam-2608	47	1	we	we	PRON
ejpam-2608	47	2	have	have	VERB
ejpam-2608	47	3	h1(x	h1(x	NOUN
ejpam-2608	47	4	,	,	PUNCT
ejpam-2608	47	5	o	o	NOUN
ejpam-2608	47	6	)	)	PUNCT
ejpam-2608	48	1	=	=	SYM
ejpam-2608	48	2	h1(x	h1(x	PROPN
ejpam-2608	48	3	,	,	PUNCT
ejpam-2608	48	4	o∗	o∗	PROPN
ejpam-2608	48	5	)	)	PUNCT
ejpam-2608	48	6	.	.	PUNCT
ejpam-2608	49	1	note	note	VERB
ejpam-2608	49	2	that	that	SCONJ
ejpam-2608	49	3	1	1	X
ejpam-2608	49	4	6=	6=	ADP
ejpam-2608	49	5	k	k	PROPN
ejpam-2608	49	6	∈	∈	PROPN
ejpam-2608	49	7	h1(x	h1(x	NOUN
ejpam-2608	49	8	,	,	PUNCT
ejpam-2608	49	9	o∗	o∗	PROPN
ejpam-2608	49	10	)	)	PUNCT
ejpam-2608	49	11	and	and	CCONJ
ejpam-2608	49	12	thus	thus	ADV
ejpam-2608	49	13	h0,1	h0,1	X
ejpam-2608	49	14	6=	6=	PROPN
ejpam-2608	49	15	0	0	NUM
ejpam-2608	49	16	.	.	PUNCT
ejpam-2608	50	1	we	we	PRON
ejpam-2608	50	2	now	now	ADV
ejpam-2608	50	3	specialize	specialize	VERB
ejpam-2608	50	4	to	to	ADP
ejpam-2608	50	5	x	x	SYM
ejpam-2608	50	6	being	be	AUX
ejpam-2608	50	7	a	a	DET
ejpam-2608	50	8	three	three	NUM
ejpam-2608	50	9	dimensional	dimensional	ADJ
ejpam-2608	50	10	complex	complex	NOUN
ejpam-2608	50	11	manifold	manifold	NOUN
ejpam-2608	50	12	with	with	ADP
ejpam-2608	50	13	h1(x	h1(x	NOUN
ejpam-2608	50	14	,	,	PUNCT
ejpam-2608	50	15	z	z	NOUN
ejpam-2608	50	16	)	)	PUNCT
ejpam-2608	50	17	=	=	SYM
ejpam-2608	50	18	h2(x	h2(x	PROPN
ejpam-2608	50	19	,	,	PUNCT
ejpam-2608	50	20	z	z	NOUN
ejpam-2608	50	21	)	)	PUNCT
ejpam-2608	50	22	=	=	SYM
ejpam-2608	50	23	h3(x	h3(x	PROPN
ejpam-2608	50	24	,	,	PUNCT
ejpam-2608	50	25	c	c	NOUN
ejpam-2608	50	26	)	)	PUNCT
ejpam-2608	50	27	=	=	SYM
ejpam-2608	50	28	0	0	NUM
ejpam-2608	50	29	,	,	PUNCT
ejpam-2608	50	30	i.e.	i.e.	X
ejpam-2608	50	31	topologically	topologically	ADV
ejpam-2608	50	32	equivalent	equivalent	ADJ
ejpam-2608	50	33	to	to	ADP
ejpam-2608	50	34	s6	s6	PROPN
ejpam-2608	50	35	.	.	PUNCT
ejpam-2608	51	1	lemma	lemma	PROPN
ejpam-2608	51	2	1	1	NUM
ejpam-2608	51	3	.	.	PUNCT
ejpam-2608	52	1	h1,0	h1,0	VERB
ejpam-2608	52	2	≤	≤	NUM
ejpam-2608	52	3	h2,0	h2,0	PROPN
ejpam-2608	52	4	a.	a.	PROPN
ejpam-2608	52	5	mchugh	mchugh	PROPN
ejpam-2608	52	6	/	/	SYM
ejpam-2608	52	7	eur	eur	PROPN
ejpam-2608	52	8	.	.	PUNCT
ejpam-2608	53	1	j.	j.	PROPN
ejpam-2608	53	2	pure	pure	PROPN
ejpam-2608	53	3	appl	appl	PROPN
ejpam-2608	53	4	.	.	PROPN
ejpam-2608	53	5	math	math	PROPN
ejpam-2608	53	6	,	,	PUNCT
ejpam-2608	53	7	10	10	NUM
ejpam-2608	53	8	(	(	PUNCT
ejpam-2608	53	9	3	3	NUM
ejpam-2608	53	10	)	)	PUNCT
ejpam-2608	53	11	(	(	PUNCT
ejpam-2608	53	12	2017	2017	NUM
ejpam-2608	53	13	)	)	PUNCT
ejpam-2608	53	14	,	,	PUNCT
ejpam-2608	53	15	440	440	NUM
ejpam-2608	53	16	-	-	SYM
ejpam-2608	53	17	454	454	NUM
ejpam-2608	53	18	442	442	NUM
ejpam-2608	53	19	proof	proof	NOUN
ejpam-2608	53	20	.	.	PUNCT
ejpam-2608	54	1	we	we	PRON
ejpam-2608	54	2	consider	consider	VERB
ejpam-2608	54	3	the	the	DET
ejpam-2608	54	4	portion	portion	NOUN
ejpam-2608	54	5	of	of	ADP
ejpam-2608	54	6	the	the	DET
ejpam-2608	54	7	frohlicher	frohlicher	PROPN
ejpam-2608	54	8	spectral	spectral	ADJ
ejpam-2608	54	9	sequence	sequence	NOUN
ejpam-2608	54	10	:	:	PUNCT
ejpam-2608	54	11	∂	∂	NUM
ejpam-2608	54	12	:	:	PUNCT
ejpam-2608	54	13	h1,0(x)→	h1,0(x)→	X
ejpam-2608	54	14	h2,0(x	h2,0(x	NOUN
ejpam-2608	54	15	)	)	PUNCT
ejpam-2608	54	16	we	we	PRON
ejpam-2608	54	17	shall	shall	AUX
ejpam-2608	54	18	show	show	VERB
ejpam-2608	54	19	that	that	SCONJ
ejpam-2608	54	20	this	this	PRON
ejpam-2608	54	21	is	be	AUX
ejpam-2608	54	22	an	an	DET
ejpam-2608	54	23	injective	injective	ADJ
ejpam-2608	54	24	map	map	NOUN
ejpam-2608	54	25	of	of	ADP
ejpam-2608	54	26	vector	vector	NOUN
ejpam-2608	54	27	spaces	space	NOUN
ejpam-2608	54	28	.	.	PUNCT
ejpam-2608	55	1	indeed	indeed	ADV
ejpam-2608	55	2	,	,	PUNCT
ejpam-2608	55	3	let	let	VERB
ejpam-2608	55	4	φ	φ	PROPN
ejpam-2608	55	5	be	be	AUX
ejpam-2608	55	6	a	a	DET
ejpam-2608	55	7	∂̄	∂̄	NOUN
ejpam-2608	55	8	closed	close	VERB
ejpam-2608	55	9	1	1	NUM
ejpam-2608	55	10	,	,	PUNCT
ejpam-2608	55	11	0	0	NUM
ejpam-2608	55	12	form	form	NOUN
ejpam-2608	55	13	,	,	PUNCT
ejpam-2608	55	14	such	such	ADJ
ejpam-2608	55	15	that	that	DET
ejpam-2608	55	16	∂[φ	∂[φ	NOUN
ejpam-2608	55	17	]	]	X
ejpam-2608	55	18	=	=	SYM
ejpam-2608	55	19	0	0	X
ejpam-2608	55	20	.	.	PUNCT
ejpam-2608	56	1	thus	thus	ADV
ejpam-2608	56	2	,	,	PUNCT
ejpam-2608	56	3	[	[	X
ejpam-2608	56	4	∂φ	∂φ	X
ejpam-2608	56	5	]	]	X
ejpam-2608	56	6	=	=	SYM
ejpam-2608	56	7	0	0	NUM
ejpam-2608	56	8	and	and	CCONJ
ejpam-2608	56	9	by	by	ADP
ejpam-2608	56	10	type	type	NOUN
ejpam-2608	56	11	we	we	PRON
ejpam-2608	56	12	have	have	VERB
ejpam-2608	56	13	∂φ	∂φ	PROPN
ejpam-2608	56	14	=	=	SYM
ejpam-2608	57	1	0	0	X
ejpam-2608	57	2	.	.	PUNCT
ejpam-2608	58	1	therefore	therefore	ADV
ejpam-2608	58	2	,	,	PUNCT
ejpam-2608	58	3	dφ	dφ	X
ejpam-2608	58	4	=	=	SYM
ejpam-2608	58	5	(	(	PUNCT
ejpam-2608	58	6	∂+	∂+	PROPN
ejpam-2608	58	7	∂̄)φ	∂̄)φ	NUM
ejpam-2608	58	8	=	=	SYM
ejpam-2608	58	9	0	0	X
ejpam-2608	58	10	.	.	PUNCT
ejpam-2608	58	11	since	since	ADV
ejpam-2608	58	12	,	,	PUNCT
ejpam-2608	58	13	b1	b1	NOUN
ejpam-2608	58	14	=	=	SYM
ejpam-2608	58	15	0	0	NUM
ejpam-2608	58	16	,	,	PUNCT
ejpam-2608	58	17	we	we	PRON
ejpam-2608	58	18	have	have	VERB
ejpam-2608	58	19	φ	φ	PROPN
ejpam-2608	58	20	=	=	SYM
ejpam-2608	58	21	df	df	PROPN
ejpam-2608	58	22	for	for	ADP
ejpam-2608	58	23	some	some	DET
ejpam-2608	58	24	complex	complex	NOUN
ejpam-2608	58	25	valued	value	VERB
ejpam-2608	58	26	,	,	PUNCT
ejpam-2608	58	27	c∞	c∞	PROPN
ejpam-2608	58	28	function	function	NOUN
ejpam-2608	58	29	,	,	PUNCT
ejpam-2608	58	30	f	f	X
ejpam-2608	58	31	.	.	PUNCT
ejpam-2608	59	1	considering	consider	VERB
ejpam-2608	59	2	type	type	NOUN
ejpam-2608	59	3	,	,	PUNCT
ejpam-2608	59	4	we	we	PRON
ejpam-2608	59	5	have	have	VERB
ejpam-2608	59	6	∂̄f	∂̄f	PROPN
ejpam-2608	59	7	=	=	SYM
ejpam-2608	59	8	0	0	PUNCT
ejpam-2608	59	9	and	and	CCONJ
ejpam-2608	59	10	thus	thus	ADV
ejpam-2608	59	11	f	f	X
ejpam-2608	59	12	as	as	ADP
ejpam-2608	59	13	a	a	DET
ejpam-2608	59	14	global	global	ADJ
ejpam-2608	59	15	holomorphic	holomorphic	ADJ
ejpam-2608	59	16	function	function	NOUN
ejpam-2608	59	17	is	be	AUX
ejpam-2608	59	18	a	a	DET
ejpam-2608	59	19	constant	constant	ADJ
ejpam-2608	59	20	.	.	PUNCT
ejpam-2608	60	1	thus	thus	ADV
ejpam-2608	60	2	φ	φ	PROPN
ejpam-2608	60	3	=	=	SYM
ejpam-2608	60	4	0	0	PROPN
ejpam-2608	60	5	.	.	PUNCT
ejpam-2608	61	1	this	this	PRON
ejpam-2608	61	2	shows	show	VERB
ejpam-2608	61	3	∂	∂	NUM
ejpam-2608	61	4	induces	induce	VERB
ejpam-2608	61	5	an	an	DET
ejpam-2608	61	6	injective	injective	ADJ
ejpam-2608	61	7	map	map	NOUN
ejpam-2608	61	8	from	from	ADP
ejpam-2608	61	9	h1,0(x)→	h1,0(x)→	NOUN
ejpam-2608	61	10	h2,0(x	h2,0(x	PROPN
ejpam-2608	61	11	)	)	PUNCT
ejpam-2608	61	12	.	.	PUNCT
ejpam-2608	62	1	this	this	PRON
ejpam-2608	62	2	can	can	AUX
ejpam-2608	62	3	also	also	ADV
ejpam-2608	62	4	be	be	AUX
ejpam-2608	62	5	directly	directly	ADV
ejpam-2608	62	6	deduced	deduce	VERB
ejpam-2608	62	7	from	from	ADP
ejpam-2608	62	8	the	the	DET
ejpam-2608	62	9	result	result	NOUN
ejpam-2608	62	10	of	of	ADP
ejpam-2608	62	11	ugarte[11	ugarte[11	NOUN
ejpam-2608	62	12	]	]	PUNCT
ejpam-2608	63	1	that	that	SCONJ
ejpam-2608	63	2	e1,0	e1,0	PROPN
ejpam-2608	63	3	2	2	NUM
ejpam-2608	63	4	=	=	SYM
ejpam-2608	63	5	0	0	NUM
ejpam-2608	63	6	and	and	CCONJ
ejpam-2608	63	7	e0,0	e0,0	NOUN
ejpam-2608	63	8	2	2	NUM
ejpam-2608	63	9	=	=	SYM
ejpam-2608	63	10	1	1	NUM
ejpam-2608	63	11	.	.	PUNCT
ejpam-2608	63	12	more	more	ADV
ejpam-2608	63	13	specifically	specifically	ADV
ejpam-2608	63	14	,	,	PUNCT
ejpam-2608	63	15	brown[2	brown[2	PROPN
ejpam-2608	63	16	]	]	PUNCT
ejpam-2608	63	17	gives	give	VERB
ejpam-2608	63	18	the	the	DET
ejpam-2608	63	19	following	follow	VERB
ejpam-2608	63	20	table	table	NOUN
ejpam-2608	63	21	derived	derive	VERB
ejpam-2608	63	22	by	by	ADP
ejpam-2608	63	23	ugarte	ugarte	NOUN
ejpam-2608	63	24	for	for	ADP
ejpam-2608	63	25	ep	ep	PROPN
ejpam-2608	63	26	,	,	PUNCT
ejpam-2608	63	27	q	q	PROPN
ejpam-2608	63	28	2	2	NUM
ejpam-2608	63	29	of	of	ADP
ejpam-2608	63	30	the	the	DET
ejpam-2608	63	31	frohlicher	frohlicher	PROPN
ejpam-2608	63	32	spectral	spectral	ADJ
ejpam-2608	63	33	sequence	sequence	NOUN
ejpam-2608	63	34	for	for	ADP
ejpam-2608	63	35	a	a	DET
ejpam-2608	63	36	complex	complex	ADJ
ejpam-2608	63	37	structure	structure	NOUN
ejpam-2608	63	38	on	on	ADP
ejpam-2608	63	39	s6	s6	PROPN
ejpam-2608	63	40	:	:	PUNCT
ejpam-2608	63	41	table	table	NOUN
ejpam-2608	63	42	2	2	NUM
ejpam-2608	63	43	:	:	PUNCT
ejpam-2608	63	44	ep	ep	PROPN
ejpam-2608	63	45	,	,	PUNCT
ejpam-2608	63	46	q	q	PROPN
ejpam-2608	63	47	2	2	NUM
ejpam-2608	63	48	for	for	ADP
ejpam-2608	63	49	a	a	DET
ejpam-2608	63	50	complex	complex	ADJ
ejpam-2608	63	51	structure	structure	NOUN
ejpam-2608	63	52	on	on	ADP
ejpam-2608	63	53	s6	s6	PROPN
ejpam-2608	63	54	0	0	NUM
ejpam-2608	63	55	a	a	DET
ejpam-2608	63	56	0	0	NUM
ejpam-2608	63	57	1	1	NUM
ejpam-2608	63	58	b	b	SYM
ejpam-2608	63	59	b	b	PROPN
ejpam-2608	63	60	0	0	PUNCT
ejpam-2608	63	61	a	a	DET
ejpam-2608	63	62	a	a	DET
ejpam-2608	63	63	0	0	NUM
ejpam-2608	63	64	b	b	NOUN
ejpam-2608	63	65	b	b	PROPN
ejpam-2608	63	66	1	1	NUM
ejpam-2608	63	67	0	0	NUM
ejpam-2608	63	68	a	a	DET
ejpam-2608	63	69	0	0	NUM
ejpam-2608	63	70	the	the	DET
ejpam-2608	63	71	bottom	bottom	NOUN
ejpam-2608	63	72	row	row	NOUN
ejpam-2608	63	73	of	of	ADP
ejpam-2608	63	74	the	the	DET
ejpam-2608	63	75	table	table	NOUN
ejpam-2608	63	76	corresponds	correspond	VERB
ejpam-2608	63	77	to	to	ADP
ejpam-2608	63	78	the	the	DET
ejpam-2608	63	79	portion	portion	NOUN
ejpam-2608	63	80	of	of	ADP
ejpam-2608	63	81	the	the	DET
ejpam-2608	63	82	frohlicher	frohlicher	NOUN
ejpam-2608	63	83	sequence	sequence	NOUN
ejpam-2608	63	84	h0,0	h0,0	NOUN
ejpam-2608	63	85	→	→	SYM
ejpam-2608	63	86	h1,0	h1,0	PROPN
ejpam-2608	63	87	→	→	SYM
ejpam-2608	63	88	h2,0	h2,0	PROPN
ejpam-2608	63	89	→	→	SYM
ejpam-2608	63	90	h3,0	h3,0	PROPN
ejpam-2608	63	91	.	.	PUNCT
ejpam-2608	64	1	since	since	SCONJ
ejpam-2608	64	2	h0,0	h0,0	NOUN
ejpam-2608	64	3	=	=	SYM
ejpam-2608	64	4	c	c	NOUN
ejpam-2608	64	5	,	,	PUNCT
ejpam-2608	64	6	e0,0	e0,0	NOUN
ejpam-2608	64	7	=	=	SYM
ejpam-2608	64	8	1	1	NUM
ejpam-2608	64	9	,	,	PUNCT
ejpam-2608	64	10	and	and	CCONJ
ejpam-2608	64	11	e1,0	e1,0	PROPN
ejpam-2608	64	12	2	2	NUM
ejpam-2608	64	13	=	=	SYM
ejpam-2608	64	14	0	0	NOUN
ejpam-2608	65	1	the	the	DET
ejpam-2608	65	2	sequence	sequence	NOUN
ejpam-2608	65	3	reduces	reduce	VERB
ejpam-2608	65	4	to	to	ADP
ejpam-2608	65	5	0→	0→	NOUN
ejpam-2608	65	6	h1,0	h1,0	PROPN
ejpam-2608	65	7	→	→	SYM
ejpam-2608	65	8	h2,0	h2,0	PROPN
ejpam-2608	65	9	→	→	SYM
ejpam-2608	65	10	0	0	NUM
ejpam-2608	65	11	.	.	PUNCT
ejpam-2608	66	1	it	it	PRON
ejpam-2608	66	2	is	be	AUX
ejpam-2608	66	3	exact	exact	ADJ
ejpam-2608	66	4	at	at	ADP
ejpam-2608	66	5	h1,0	h1,0	PROPN
ejpam-2608	66	6	and	and	CCONJ
ejpam-2608	66	7	thus	thus	ADV
ejpam-2608	66	8	∂	∂	NUM
ejpam-2608	66	9	:	:	PUNCT
ejpam-2608	66	10	h1,0(x)→	h1,0(x)→	X
ejpam-2608	66	11	h2,0(x	h2,0(x	NOUN
ejpam-2608	66	12	)	)	PUNCT
ejpam-2608	66	13	is	be	AUX
ejpam-2608	66	14	injective	injective	ADJ
ejpam-2608	66	15	.	.	PUNCT
ejpam-2608	67	1	note	note	VERB
ejpam-2608	67	2	that	that	SCONJ
ejpam-2608	67	3	h1,0	h1,0	NOUN
ejpam-2608	67	4	=	=	PUNCT
ejpam-2608	67	5	h2,0	h2,0	PROPN
ejpam-2608	67	6	if	if	SCONJ
ejpam-2608	67	7	and	and	CCONJ
ejpam-2608	67	8	only	only	ADV
ejpam-2608	67	9	if	if	SCONJ
ejpam-2608	67	10	a	a	DET
ejpam-2608	67	11	=	=	NOUN
ejpam-2608	67	12	0	0	PUNCT
ejpam-2608	68	1	and	and	CCONJ
ejpam-2608	68	2	if	if	SCONJ
ejpam-2608	68	3	h1,0	h1,0	PROPN
ejpam-2608	68	4	=	=	SYM
ejpam-2608	68	5	0	0	NUM
ejpam-2608	68	6	then	then	ADV
ejpam-2608	68	7	h2,0	h2,0	PROPN
ejpam-2608	68	8	=	=	PUNCT
ejpam-2608	68	9	a	a	PRON
ejpam-2608	68	10	.	.	PUNCT
ejpam-2608	69	1	huckleberry	huckleberry	PROPN
ejpam-2608	69	2	,	,	PUNCT
ejpam-2608	69	3	kebekus	kebekus	PROPN
ejpam-2608	69	4	and	and	CCONJ
ejpam-2608	69	5	peternell	peternell	NOUN
ejpam-2608	70	1	[	[	X
ejpam-2608	70	2	7	7	NUM
ejpam-2608	70	3	]	]	PUNCT
ejpam-2608	70	4	gave	give	VERB
ejpam-2608	70	5	a	a	DET
ejpam-2608	70	6	proof	proof	NOUN
ejpam-2608	70	7	pointed	point	VERB
ejpam-2608	70	8	out	out	ADP
ejpam-2608	70	9	to	to	ADP
ejpam-2608	70	10	them	they	PRON
ejpam-2608	70	11	by	by	ADP
ejpam-2608	70	12	m.	m.	NOUN
ejpam-2608	70	13	toma	toma	PROPN
ejpam-2608	70	14	that	that	PRON
ejpam-2608	70	15	h1,0	h1,0	VERB
ejpam-2608	70	16	≤	≤	NUM
ejpam-2608	70	17	1	1	NUM
ejpam-2608	70	18	.	.	PUNCT
ejpam-2608	71	1	we	we	PRON
ejpam-2608	71	2	give	give	VERB
ejpam-2608	71	3	a	a	DET
ejpam-2608	71	4	somewhat	somewhat	ADV
ejpam-2608	71	5	different	different	ADJ
ejpam-2608	71	6	but	but	CCONJ
ejpam-2608	71	7	related	related	ADJ
ejpam-2608	71	8	proof	proof	NOUN
ejpam-2608	71	9	here	here	ADV
ejpam-2608	71	10	.	.	PUNCT
ejpam-2608	72	1	the	the	DET
ejpam-2608	72	2	present	present	ADJ
ejpam-2608	72	3	author	author	NOUN
ejpam-2608	72	4	is	be	AUX
ejpam-2608	72	5	indebted	indebte	VERB
ejpam-2608	72	6	to	to	ADP
ejpam-2608	72	7	daniel	daniel	PROPN
ejpam-2608	72	8	angella	angella	NOUN
ejpam-2608	72	9	for	for	ADP
ejpam-2608	72	10	pointing	point	VERB
ejpam-2608	72	11	out	out	ADP
ejpam-2608	72	12	the	the	DET
ejpam-2608	72	13	correct	correct	ADJ
ejpam-2608	72	14	statement	statement	NOUN
ejpam-2608	72	15	of	of	ADP
ejpam-2608	72	16	huckleberry	huckleberry	PROPN
ejpam-2608	72	17	,	,	PUNCT
ejpam-2608	72	18	kebekus	kebekus	PROPN
ejpam-2608	72	19	,	,	PUNCT
ejpam-2608	72	20	peternell	peternell	PROPN
ejpam-2608	72	21	and	and	CCONJ
ejpam-2608	72	22	toma	toma	PROPN
ejpam-2608	72	23	’s	’s	PART
ejpam-2608	72	24	result	result	NOUN
ejpam-2608	72	25	.	.	PUNCT
ejpam-2608	73	1	lemma	lemma	PROPN
ejpam-2608	73	2	2	2	NUM
ejpam-2608	73	3	.	.	PUNCT
ejpam-2608	74	1	(	(	PUNCT
ejpam-2608	74	2	huckleberry	huckleberry	PROPN
ejpam-2608	74	3	,	,	PUNCT
ejpam-2608	74	4	kebekus	kebekus	PROPN
ejpam-2608	74	5	,	,	PUNCT
ejpam-2608	74	6	peternell	peternell	PROPN
ejpam-2608	74	7	,	,	PUNCT
ejpam-2608	74	8	toma	toma	PROPN
ejpam-2608	74	9	)	)	PUNCT
ejpam-2608	75	1	h1,0	h1,0	VERB
ejpam-2608	75	2	≤	≤	NUM
ejpam-2608	75	3	1	1	NUM
ejpam-2608	75	4	,	,	PUNCT
ejpam-2608	75	5	i.e.	i.e.	X
ejpam-2608	75	6	h1,0	h1,0	X
ejpam-2608	75	7	=	=	SYM
ejpam-2608	75	8	0	0	NUM
ejpam-2608	75	9	or	or	CCONJ
ejpam-2608	75	10	1	1	NUM
ejpam-2608	75	11	proof	proof	NOUN
ejpam-2608	75	12	.	.	PUNCT
ejpam-2608	76	1	indeed	indeed	ADV
ejpam-2608	76	2	,	,	PUNCT
ejpam-2608	76	3	if	if	SCONJ
ejpam-2608	76	4	h1,0	h1,0	PROPN
ejpam-2608	76	5	=	=	SYM
ejpam-2608	76	6	2	2	NUM
ejpam-2608	76	7	,	,	PUNCT
ejpam-2608	76	8	then	then	ADV
ejpam-2608	76	9	h2,0	h2,0	PROPN
ejpam-2608	76	10	≥	≥	PROPN
ejpam-2608	76	11	2	2	NUM
ejpam-2608	76	12	.	.	PUNCT
ejpam-2608	77	1	let	let	VERB
ejpam-2608	77	2	φ1	φ1	PROPN
ejpam-2608	77	3	and	and	CCONJ
ejpam-2608	77	4	φ2	φ2	PROPN
ejpam-2608	77	5	be	be	AUX
ejpam-2608	77	6	two	two	NUM
ejpam-2608	77	7	linearly	linearly	ADV
ejpam-2608	77	8	independent	independent	ADJ
ejpam-2608	77	9	∂̄-closed	∂̄-close	VERB
ejpam-2608	77	10	global	global	ADJ
ejpam-2608	77	11	1	1	NUM
ejpam-2608	77	12	,	,	PUNCT
ejpam-2608	77	13	0	0	NUM
ejpam-2608	77	14	-	-	NOUN
ejpam-2608	77	15	forms	form	NOUN
ejpam-2608	77	16	.	.	PUNCT
ejpam-2608	78	1	let	let	VERB
ejpam-2608	78	2	φ1	φ1	PROPN
ejpam-2608	78	3	=	=	SYM
ejpam-2608	78	4	φ1	φ1	PROPN
ejpam-2608	78	5	∧	∧	PROPN
ejpam-2608	78	6	φ2	φ2	PROPN
ejpam-2608	78	7	this	this	PRON
ejpam-2608	78	8	is	be	AUX
ejpam-2608	78	9	a	a	DET
ejpam-2608	78	10	global	global	ADJ
ejpam-2608	78	11	∂̄-closed	∂̄-close	VERB
ejpam-2608	78	12	2	2	NUM
ejpam-2608	78	13	,	,	PUNCT
ejpam-2608	78	14	0	0	NUM
ejpam-2608	78	15	-	-	PUNCT
ejpam-2608	78	16	form	form	NOUN
ejpam-2608	78	17	on	on	ADP
ejpam-2608	78	18	x	x	SYM
ejpam-2608	78	19	that	that	PRON
ejpam-2608	78	20	is	be	AUX
ejpam-2608	78	21	not	not	PART
ejpam-2608	78	22	identically	identically	ADV
ejpam-2608	78	23	zero	zero	NUM
ejpam-2608	78	24	.	.	PUNCT
ejpam-2608	79	1	since	since	SCONJ
ejpam-2608	79	2	h2,0	h2,0	PROPN
ejpam-2608	79	3	≥	≥	PUNCT
ejpam-2608	79	4	2	2	NUM
ejpam-2608	79	5	we	we	PRON
ejpam-2608	79	6	can	can	AUX
ejpam-2608	79	7	select	select	VERB
ejpam-2608	79	8	φ2	φ2	PROPN
ejpam-2608	79	9	another	another	DET
ejpam-2608	79	10	∂̄-closed	∂̄-close	VERB
ejpam-2608	79	11	global	global	ADJ
ejpam-2608	79	12	2	2	NUM
ejpam-2608	79	13	,	,	PUNCT
ejpam-2608	79	14	0	0	NUM
ejpam-2608	79	15	-	-	PUNCT
ejpam-2608	79	16	form	form	NOUN
ejpam-2608	79	17	that	that	PRON
ejpam-2608	79	18	is	be	AUX
ejpam-2608	79	19	linearly	linearly	ADV
ejpam-2608	79	20	independent	independent	ADJ
ejpam-2608	79	21	of	of	ADP
ejpam-2608	79	22	φ1	φ1	PROPN
ejpam-2608	79	23	.	.	PUNCT
ejpam-2608	80	1	a.	a.	PROPN
ejpam-2608	80	2	mchugh	mchugh	PROPN
ejpam-2608	80	3	/	/	SYM
ejpam-2608	80	4	eur	eur	PROPN
ejpam-2608	80	5	.	.	PUNCT
ejpam-2608	81	1	j.	j.	PROPN
ejpam-2608	81	2	pure	pure	PROPN
ejpam-2608	81	3	appl	appl	PROPN
ejpam-2608	81	4	.	.	PROPN
ejpam-2608	81	5	math	math	PROPN
ejpam-2608	81	6	,	,	PUNCT
ejpam-2608	81	7	10	10	NUM
ejpam-2608	81	8	(	(	PUNCT
ejpam-2608	81	9	3	3	NUM
ejpam-2608	81	10	)	)	PUNCT
ejpam-2608	81	11	(	(	PUNCT
ejpam-2608	81	12	2017	2017	NUM
ejpam-2608	81	13	)	)	PUNCT
ejpam-2608	81	14	,	,	PUNCT
ejpam-2608	81	15	440	440	NUM
ejpam-2608	81	16	-	-	SYM
ejpam-2608	81	17	454	454	NUM
ejpam-2608	81	18	443	443	NUM
ejpam-2608	81	19	we	we	PRON
ejpam-2608	81	20	may	may	AUX
ejpam-2608	81	21	choose	choose	VERB
ejpam-2608	81	22	a	a	DET
ejpam-2608	81	23	point	point	NOUN
ejpam-2608	81	24	,	,	PUNCT
ejpam-2608	81	25	p	p	NOUN
ejpam-2608	81	26	∈	∈	PROPN
ejpam-2608	81	27	x	x	PUNCT
ejpam-2608	81	28	such	such	ADJ
ejpam-2608	81	29	that	that	DET
ejpam-2608	81	30	φ1	φ1	NOUN
ejpam-2608	81	31	and	and	CCONJ
ejpam-2608	81	32	φ2	φ2	PROPN
ejpam-2608	81	33	are	be	AUX
ejpam-2608	81	34	non	non	ADJ
ejpam-2608	81	35	-	-	ADJ
ejpam-2608	81	36	zero	zero	NUM
ejpam-2608	81	37	and	and	CCONJ
ejpam-2608	81	38	linearly	linearly	ADV
ejpam-2608	81	39	independent	independent	ADJ
ejpam-2608	81	40	at	at	ADP
ejpam-2608	81	41	p.	p.	NOUN
ejpam-2608	81	42	note	note	NOUN
ejpam-2608	81	43	that	that	SCONJ
ejpam-2608	81	44	φ1	φ1	NOUN
ejpam-2608	81	45	and	and	CCONJ
ejpam-2608	81	46	φ2	φ2	PROPN
ejpam-2608	81	47	are	be	AUX
ejpam-2608	81	48	also	also	ADV
ejpam-2608	81	49	non	non	ADJ
ejpam-2608	81	50	-	-	ADJ
ejpam-2608	81	51	zero	zero	NUM
ejpam-2608	81	52	and	and	CCONJ
ejpam-2608	81	53	linearly	linearly	ADV
ejpam-2608	81	54	independent	independent	ADJ
ejpam-2608	81	55	of	of	ADP
ejpam-2608	81	56	each	each	DET
ejpam-2608	81	57	other	other	ADJ
ejpam-2608	81	58	at	at	ADP
ejpam-2608	81	59	p	p	NOUN
ejpam-2608	81	60	since	since	SCONJ
ejpam-2608	81	61	φ1(p	φ1(p	NOUN
ejpam-2608	81	62	)	)	PUNCT
ejpam-2608	81	63	=	=	SYM
ejpam-2608	81	64	φ1(p	φ1(p	X
ejpam-2608	81	65	)	)	PUNCT
ejpam-2608	81	66	∧	∧	PROPN
ejpam-2608	81	67	φ2(p	φ2(p	NOUN
ejpam-2608	81	68	)	)	PUNCT
ejpam-2608	81	69	is	be	AUX
ejpam-2608	81	70	not	not	PART
ejpam-2608	81	71	zero	zero	NUM
ejpam-2608	81	72	.	.	PUNCT
ejpam-2608	82	1	let	let	VERB
ejpam-2608	82	2	ηp	ηp	ADV
ejpam-2608	82	3	∈	∈	PROPN
ejpam-2608	82	4	t	t	PROPN
ejpam-2608	82	5	1,0	1,0	NUM
ejpam-2608	82	6	p	p	NOUN
ejpam-2608	82	7	be	be	VERB
ejpam-2608	82	8	linearly	linearly	ADV
ejpam-2608	82	9	independent	independent	ADJ
ejpam-2608	82	10	of	of	ADP
ejpam-2608	82	11	φ1(p	φ1(p	NUM
ejpam-2608	82	12	)	)	PUNCT
ejpam-2608	82	13	and	and	CCONJ
ejpam-2608	82	14	φ2(2	φ2(2	NOUN
ejpam-2608	82	15	)	)	PUNCT
ejpam-2608	82	16	,	,	PUNCT
ejpam-2608	82	17	completing	complete	VERB
ejpam-2608	82	18	a	a	DET
ejpam-2608	82	19	basis	basis	NOUN
ejpam-2608	82	20	for	for	ADP
ejpam-2608	82	21	t	t	PROPN
ejpam-2608	82	22	1,0	1,0	NUM
ejpam-2608	82	23	p	p	NOUN
ejpam-2608	82	24	.	.	PUNCT
ejpam-2608	83	1	thus	thus	ADV
ejpam-2608	83	2	for	for	ADP
ejpam-2608	83	3	φ(p	φ(p	PROPN
ejpam-2608	83	4	)	)	PUNCT
ejpam-2608	83	5	and	and	CCONJ
ejpam-2608	83	6	some	some	DET
ejpam-2608	83	7	complex	complex	ADJ
ejpam-2608	83	8	numbers	number	NOUN
ejpam-2608	83	9	,	,	PUNCT
ejpam-2608	83	10	a	a	DET
ejpam-2608	83	11	,	,	PUNCT
ejpam-2608	83	12	b1	b1	NOUN
ejpam-2608	83	13	,	,	PUNCT
ejpam-2608	83	14	b2	b2	NOUN
ejpam-2608	83	15	,	,	PUNCT
ejpam-2608	83	16	we	we	PRON
ejpam-2608	83	17	have	have	VERB
ejpam-2608	83	18	,	,	PUNCT
ejpam-2608	83	19	φ2(p	φ2(p	PROPN
ejpam-2608	83	20	)	)	PUNCT
ejpam-2608	84	1	=	=	SYM
ejpam-2608	84	2	aφ1	aφ1	PROPN
ejpam-2608	84	3	∧	∧	PROPN
ejpam-2608	84	4	φ2	φ2	PROPN
ejpam-2608	84	5	+	+	CCONJ
ejpam-2608	84	6	b1η	b1η	PROPN
ejpam-2608	84	7	∧	∧	PROPN
ejpam-2608	84	8	φ1	φ1	PROPN
ejpam-2608	84	9	+	+	CCONJ
ejpam-2608	84	10	b2η	b2η	NOUN
ejpam-2608	84	11	∧	∧	PROPN
ejpam-2608	84	12	φ2	φ2	PROPN
ejpam-2608	84	13	.	.	PUNCT
ejpam-2608	85	1	now	now	ADV
ejpam-2608	85	2	b1	b1	NOUN
ejpam-2608	85	3	and	and	CCONJ
ejpam-2608	85	4	b2	b2	NOUN
ejpam-2608	85	5	are	be	AUX
ejpam-2608	85	6	not	not	PART
ejpam-2608	85	7	both	both	DET
ejpam-2608	85	8	zero	zero	NUM
ejpam-2608	85	9	.	.	PUNCT
ejpam-2608	86	1	without	without	ADP
ejpam-2608	86	2	loss	loss	NOUN
ejpam-2608	86	3	of	of	ADP
ejpam-2608	86	4	generality	generality	NOUN
ejpam-2608	86	5	,	,	PUNCT
ejpam-2608	86	6	assume	assume	VERB
ejpam-2608	86	7	b1	b1	PROPN
ejpam-2608	86	8	6=	6=	PRON
ejpam-2608	86	9	0	0	NUM
ejpam-2608	86	10	.	.	PUNCT
ejpam-2608	87	1	hence	hence	ADV
ejpam-2608	87	2	φ2(p	φ2(p	NOUN
ejpam-2608	87	3	)	)	PUNCT
ejpam-2608	87	4	∧	∧	PROPN
ejpam-2608	87	5	φ2	φ2	PROPN
ejpam-2608	87	6	6=	6=	ADP
ejpam-2608	87	7	0	0	NUM
ejpam-2608	88	1	and	and	CCONJ
ejpam-2608	88	2	φ2	φ2	PROPN
ejpam-2608	88	3	∧	∧	PROPN
ejpam-2608	88	4	φ2	φ2	PROPN
ejpam-2608	88	5	is	be	AUX
ejpam-2608	88	6	a	a	DET
ejpam-2608	88	7	non	non	ADJ
ejpam-2608	88	8	-	-	ADJ
ejpam-2608	88	9	zero	zero	ADJ
ejpam-2608	88	10	holomorphic	holomorphic	ADJ
ejpam-2608	88	11	3	3	NUM
ejpam-2608	88	12	,	,	PUNCT
ejpam-2608	88	13	0	0	NUM
ejpam-2608	88	14	-	-	PUNCT
ejpam-2608	88	15	form	form	NOUN
ejpam-2608	88	16	on	on	ADP
ejpam-2608	88	17	x.	x.	NOUN
ejpam-2608	88	18	this	this	PRON
ejpam-2608	88	19	contradicts	contradict	VERB
ejpam-2608	88	20	h3,0	h3,0	PROPN
ejpam-2608	88	21	=	=	SYM
ejpam-2608	88	22	0	0	NUM
ejpam-2608	88	23	.	.	PUNCT
ejpam-2608	89	1	we	we	PRON
ejpam-2608	89	2	must	must	AUX
ejpam-2608	89	3	then	then	ADV
ejpam-2608	89	4	have	have	VERB
ejpam-2608	89	5	h1,0	h1,0	VERB
ejpam-2608	89	6	≤	≤	NUM
ejpam-2608	89	7	1	1	NUM
ejpam-2608	89	8	.	.	PUNCT
ejpam-2608	90	1	we	we	PRON
ejpam-2608	90	2	summarize	summarize	VERB
ejpam-2608	90	3	with	with	ADP
ejpam-2608	90	4	two	two	NUM
ejpam-2608	90	5	tables	table	NOUN
ejpam-2608	90	6	of	of	ADP
ejpam-2608	90	7	the	the	DET
ejpam-2608	90	8	plausible	plausible	ADJ
ejpam-2608	90	9	hodge	hodge	NOUN
ejpam-2608	90	10	numbers	number	NOUN
ejpam-2608	90	11	(	(	PUNCT
ejpam-2608	90	12	with	with	ADP
ejpam-2608	90	13	h0,0	h0,0	NOUN
ejpam-2608	90	14	in	in	ADP
ejpam-2608	90	15	the	the	DET
ejpam-2608	90	16	bottom	bottom	ADJ
ejpam-2608	90	17	lefthand	lefthand	PROPN
ejpam-2608	90	18	corner	corner	NOUN
ejpam-2608	90	19	)	)	PUNCT
ejpam-2608	90	20	for	for	ADP
ejpam-2608	90	21	dolbeault	dolbeault	NOUN
ejpam-2608	90	22	cohomology	cohomology	NOUN
ejpam-2608	90	23	for	for	ADP
ejpam-2608	90	24	a	a	DET
ejpam-2608	90	25	complex	complex	ADJ
ejpam-2608	90	26	structure	structure	NOUN
ejpam-2608	90	27	on	on	ADP
ejpam-2608	90	28	s6	s6	PROPN
ejpam-2608	90	29	:	:	PUNCT
ejpam-2608	90	30	table	table	NOUN
ejpam-2608	90	31	3	3	NUM
ejpam-2608	90	32	:	:	PUNCT
ejpam-2608	90	33	(	(	PUNCT
ejpam-2608	90	34	h1,0	h1,0	VERB
ejpam-2608	90	35	=	=	SYM
ejpam-2608	90	36	1	1	NUM
ejpam-2608	90	37	):	):	PUNCT
ejpam-2608	90	38	hp	hp	NOUN
ejpam-2608	90	39	,	,	PUNCT
ejpam-2608	90	40	q	q	NOUN
ejpam-2608	90	41	for	for	ADP
ejpam-2608	90	42	a	a	DET
ejpam-2608	90	43	complex	complex	ADJ
ejpam-2608	90	44	structure	structure	NOUN
ejpam-2608	90	45	on	on	ADP
ejpam-2608	90	46	s6	s6	PROPN
ejpam-2608	90	47	0	0	PUNCT
ejpam-2608	90	48	a+	a+	SYM
ejpam-2608	90	49	1	1	NUM
ejpam-2608	90	50	1	1	NUM
ejpam-2608	90	51	1	1	NUM
ejpam-2608	90	52	c	c	NOUN
ejpam-2608	90	53	d	d	SYM
ejpam-2608	90	54	d−	d−	PROPN
ejpam-2608	90	55	a+	a+	PUNCT
ejpam-2608	90	56	1	1	NUM
ejpam-2608	90	57	c+	c+	NOUN
ejpam-2608	90	58	1	1	NUM
ejpam-2608	90	59	c+	c+	NOUN
ejpam-2608	90	60	1	1	NUM
ejpam-2608	90	61	d−	d−	PROPN
ejpam-2608	90	62	a+	a+	PUNCT
ejpam-2608	90	63	1	1	NUM
ejpam-2608	90	64	d	d	SYM
ejpam-2608	90	65	c	c	NOUN
ejpam-2608	90	66	1	1	NUM
ejpam-2608	90	67	1	1	NUM
ejpam-2608	90	68	a+	a+	SYM
ejpam-2608	90	69	1	1	NUM
ejpam-2608	90	70	0	0	NUM
ejpam-2608	90	71	where	where	SCONJ
ejpam-2608	90	72	0	0	NUM
ejpam-2608	90	73	≤	≤	NOUN
ejpam-2608	90	74	a	a	DET
ejpam-2608	90	75	≤	≤	NUM
ejpam-2608	90	76	c+	c+	NOUN
ejpam-2608	90	77	1	1	NUM
ejpam-2608	90	78	,	,	PUNCT
ejpam-2608	90	79	and	and	CCONJ
ejpam-2608	90	80	c	c	PROPN
ejpam-2608	90	81	≤	≤	PROPN
ejpam-2608	90	82	d.	d.	PROPN
ejpam-2608	90	83	table	table	NOUN
ejpam-2608	90	84	4	4	NUM
ejpam-2608	90	85	:	:	PUNCT
ejpam-2608	90	86	(	(	PUNCT
ejpam-2608	90	87	h1,0	h1,0	VERB
ejpam-2608	90	88	=	=	SYM
ejpam-2608	90	89	0	0	NUM
ejpam-2608	90	90	):	):	PUNCT
ejpam-2608	90	91	hp	hp	NOUN
ejpam-2608	90	92	,	,	PUNCT
ejpam-2608	90	93	q	q	NOUN
ejpam-2608	90	94	for	for	ADP
ejpam-2608	90	95	a	a	DET
ejpam-2608	90	96	complex	complex	ADJ
ejpam-2608	90	97	structure	structure	NOUN
ejpam-2608	90	98	on	on	ADP
ejpam-2608	90	99	s6	s6	PROPN
ejpam-2608	90	100	0	0	NUM
ejpam-2608	90	101	a	a	DET
ejpam-2608	90	102	0	0	NUM
ejpam-2608	90	103	1	1	NUM
ejpam-2608	90	104	c	c	NOUN
ejpam-2608	90	105	d	d	SYM
ejpam-2608	90	106	d−	d−	PROPN
ejpam-2608	90	107	a+	a+	PUNCT
ejpam-2608	90	108	1	1	NUM
ejpam-2608	90	109	c+	c+	NOUN
ejpam-2608	90	110	1	1	NUM
ejpam-2608	90	111	c+	c+	NOUN
ejpam-2608	90	112	1	1	NUM
ejpam-2608	90	113	d−	d−	PROPN
ejpam-2608	90	114	a+	a+	PUNCT
ejpam-2608	90	115	1	1	NUM
ejpam-2608	90	116	d	d	SYM
ejpam-2608	90	117	c	c	NOUN
ejpam-2608	90	118	1	1	NUM
ejpam-2608	90	119	0	0	NUM
ejpam-2608	90	120	a	a	DET
ejpam-2608	90	121	0	0	NUM
ejpam-2608	90	122	where	where	SCONJ
ejpam-2608	90	123	0	0	NUM
ejpam-2608	90	124	≤	≤	NOUN
ejpam-2608	90	125	a	a	DET
ejpam-2608	90	126	≤	≤	NUM
ejpam-2608	90	127	c+	c+	NOUN
ejpam-2608	90	128	1	1	NUM
ejpam-2608	90	129	,	,	PUNCT
ejpam-2608	90	130	and	and	CCONJ
ejpam-2608	90	131	c	c	PROPN
ejpam-2608	90	132	≤	≤	PROPN
ejpam-2608	90	133	d.	d.	PROPN
ejpam-2608	90	134	note	note	VERB
ejpam-2608	90	135	that	that	SCONJ
ejpam-2608	90	136	we	we	PRON
ejpam-2608	90	137	have	have	VERB
ejpam-2608	90	138	in	in	ADP
ejpam-2608	90	139	both	both	DET
ejpam-2608	90	140	cases	case	NOUN
ejpam-2608	90	141	,	,	PUNCT
ejpam-2608	90	142	a	a	DET
ejpam-2608	90	143	=	=	PUNCT
ejpam-2608	90	144	h2,0	h2,0	PROPN
ejpam-2608	90	145	−	−	NOUN
ejpam-2608	90	146	h1,0	h1,0	NOUN
ejpam-2608	90	147	.	.	NOUN
ejpam-2608	90	148	3	3	NUM
ejpam-2608	90	149	.	.	NOUN
ejpam-2608	90	150	aeppli	aeppli	PROPN
ejpam-2608	90	151	and	and	CCONJ
ejpam-2608	90	152	bott	bott	PROPN
ejpam-2608	90	153	-	-	PUNCT
ejpam-2608	90	154	chern	chern	PROPN
ejpam-2608	90	155	cohomology	cohomology	NOUN
ejpam-2608	90	156	on	on	ADP
ejpam-2608	90	157	complex	complex	ADJ
ejpam-2608	90	158	s6	s6	PROPN
ejpam-2608	90	159	.	.	PUNCT
ejpam-2608	91	1	the	the	DET
ejpam-2608	91	2	aeppli	aeppli	ADJ
ejpam-2608	91	3	cohomology	cohomology	NOUN
ejpam-2608	91	4	of	of	ADP
ejpam-2608	91	5	a	a	DET
ejpam-2608	91	6	complex	complex	ADJ
ejpam-2608	91	7	manifold	manifold	NOUN
ejpam-2608	91	8	is	be	AUX
ejpam-2608	91	9	defined	define	VERB
ejpam-2608	91	10	by	by	ADP
ejpam-2608	91	11	the	the	DET
ejpam-2608	91	12	vector	vector	NOUN
ejpam-2608	91	13	spaces	space	NOUN
ejpam-2608	91	14	(	(	PUNCT
ejpam-2608	91	15	see	see	VERB
ejpam-2608	91	16	popovici	popovici	ADJ
ejpam-2608	91	17	[	[	X
ejpam-2608	91	18	9	9	NUM
ejpam-2608	91	19	]	]	PUNCT
ejpam-2608	91	20	)	)	PUNCT
ejpam-2608	91	21	:	:	PUNCT
ejpam-2608	92	1	hp	hp	PROPN
ejpam-2608	92	2	,	,	PUNCT
ejpam-2608	92	3	q	q	PROPN
ejpam-2608	92	4	a	a	DET
ejpam-2608	92	5	=	=	X
ejpam-2608	92	6	ker(∂∂̄	ker(∂∂̄	NOUN
ejpam-2608	92	7	:	:	PUNCT
ejpam-2608	92	8	c∞	c∞	VERB
ejpam-2608	92	9	p	p	X
ejpam-2608	92	10	,	,	PUNCT
ejpam-2608	92	11	q	q	X
ejpam-2608	92	12	→	→	PUNCT
ejpam-2608	92	13	c∞	c∞	ADJ
ejpam-2608	92	14	p+1,q+1	p+1,q+1	PROPN
ejpam-2608	92	15	)	)	PUNCT
ejpam-2608	92	16	im(∂	im(∂	NOUN
ejpam-2608	92	17	:	:	PUNCT
ejpam-2608	92	18	c∞	c∞	PROPN
ejpam-2608	92	19	p−1,q	p−1,q	NOUN
ejpam-2608	92	20	→	→	SYM
ejpam-2608	92	21	c∞	c∞	PROPN
ejpam-2608	92	22	p	p	X
ejpam-2608	92	23	,	,	PUNCT
ejpam-2608	92	24	q	q	NOUN
ejpam-2608	92	25	)	)	PUNCT
ejpam-2608	92	26	+	+	CCONJ
ejpam-2608	92	27	im(∂̄	im(∂̄	NOUN
ejpam-2608	92	28	:	:	PUNCT
ejpam-2608	92	29	c∞	c∞	PROPN
ejpam-2608	92	30	p	p	X
ejpam-2608	92	31	,	,	PUNCT
ejpam-2608	92	32	q−1	q−1	PROPN
ejpam-2608	92	33	→	→	SYM
ejpam-2608	92	34	c∞	c∞	PROPN
ejpam-2608	92	35	p	p	X
ejpam-2608	92	36	,	,	PUNCT
ejpam-2608	92	37	q	q	NOUN
ejpam-2608	92	38	)	)	PUNCT
ejpam-2608	92	39	a.	a.	NOUN
ejpam-2608	92	40	mchugh	mchugh	PROPN
ejpam-2608	92	41	/	/	SYM
ejpam-2608	92	42	eur	eur	PROPN
ejpam-2608	92	43	.	.	PUNCT
ejpam-2608	93	1	j.	j.	PROPN
ejpam-2608	93	2	pure	pure	PROPN
ejpam-2608	93	3	appl	appl	PROPN
ejpam-2608	93	4	.	.	PROPN
ejpam-2608	93	5	math	math	PROPN
ejpam-2608	93	6	,	,	PUNCT
ejpam-2608	93	7	10	10	NUM
ejpam-2608	93	8	(	(	PUNCT
ejpam-2608	93	9	3	3	NUM
ejpam-2608	93	10	)	)	PUNCT
ejpam-2608	93	11	(	(	PUNCT
ejpam-2608	93	12	2017	2017	NUM
ejpam-2608	93	13	)	)	PUNCT
ejpam-2608	93	14	,	,	PUNCT
ejpam-2608	93	15	440	440	NUM
ejpam-2608	93	16	-	-	SYM
ejpam-2608	93	17	454	454	NUM
ejpam-2608	93	18	444	444	NUM
ejpam-2608	93	19	the	the	DET
ejpam-2608	93	20	bott	bott	PROPN
ejpam-2608	93	21	-	-	PUNCT
ejpam-2608	93	22	chern	chern	PROPN
ejpam-2608	93	23	cohomology	cohomology	NOUN
ejpam-2608	93	24	of	of	ADP
ejpam-2608	93	25	a	a	DET
ejpam-2608	93	26	complex	complex	ADJ
ejpam-2608	93	27	manifold	manifold	NOUN
ejpam-2608	93	28	is	be	AUX
ejpam-2608	93	29	defined	define	VERB
ejpam-2608	93	30	by	by	ADP
ejpam-2608	93	31	the	the	DET
ejpam-2608	93	32	vector	vector	NOUN
ejpam-2608	93	33	spaces	space	NOUN
ejpam-2608	93	34	(	(	PUNCT
ejpam-2608	93	35	again	again	ADV
ejpam-2608	93	36	see	see	VERB
ejpam-2608	93	37	popovici	popovici	ADJ
ejpam-2608	94	1	[	[	X
ejpam-2608	94	2	9	9	NUM
ejpam-2608	94	3	]	]	PUNCT
ejpam-2608	94	4	)	)	PUNCT
ejpam-2608	95	1	:	:	PUNCT
ejpam-2608	95	2	hp	hp	PROPN
ejpam-2608	95	3	,	,	PUNCT
ejpam-2608	95	4	q	q	NOUN
ejpam-2608	95	5	bc	bc	PROPN
ejpam-2608	95	6	=	=	SYM
ejpam-2608	95	7	ker(∂	ker(∂	PROPN
ejpam-2608	95	8	:	:	PUNCT
ejpam-2608	95	9	c∞	c∞	VERB
ejpam-2608	95	10	p	p	X
ejpam-2608	95	11	,	,	PUNCT
ejpam-2608	95	12	q	q	X
ejpam-2608	95	13	→	→	PUNCT
ejpam-2608	95	14	c∞	c∞	PROPN
ejpam-2608	95	15	p+1,q	p+1,q	NOUN
ejpam-2608	95	16	)	)	PUNCT
ejpam-2608	95	17	∩	∩	NOUN
ejpam-2608	95	18	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	95	19	:	:	PUNCT
ejpam-2608	95	20	c∞	c∞	VERB
ejpam-2608	95	21	p	p	X
ejpam-2608	95	22	,	,	PUNCT
ejpam-2608	95	23	q	q	X
ejpam-2608	95	24	→	→	PUNCT
ejpam-2608	95	25	c∞	c∞	PROPN
ejpam-2608	95	26	p	p	NOUN
ejpam-2608	95	27	,	,	PUNCT
ejpam-2608	95	28	q+1	q+1	NOUN
ejpam-2608	95	29	)	)	PUNCT
ejpam-2608	95	30	im(∂∂̄	im(∂∂̄	NUM
ejpam-2608	95	31	:	:	PUNCT
ejpam-2608	95	32	c∞	c∞	PROPN
ejpam-2608	95	33	p−1,q−1	p−1,q−1	X
ejpam-2608	96	1	→	→	PUNCT
ejpam-2608	96	2	c∞	c∞	PROPN
ejpam-2608	96	3	p	p	X
ejpam-2608	96	4	,	,	PUNCT
ejpam-2608	96	5	q	q	NOUN
ejpam-2608	96	6	)	)	PUNCT
ejpam-2608	96	7	on	on	ADP
ejpam-2608	96	8	compact	compact	ADJ
ejpam-2608	96	9	complex	complex	ADJ
ejpam-2608	96	10	manifolds	manifold	NOUN
ejpam-2608	96	11	,	,	PUNCT
ejpam-2608	96	12	there	there	PRON
ejpam-2608	96	13	is	be	VERB
ejpam-2608	96	14	a	a	DET
ejpam-2608	96	15	harmonic	harmonic	ADJ
ejpam-2608	96	16	theory	theory	NOUN
ejpam-2608	96	17	for	for	ADP
ejpam-2608	96	18	each	each	PRON
ejpam-2608	96	19	of	of	ADP
ejpam-2608	96	20	these	these	DET
ejpam-2608	96	21	cohomologies	cohomologie	NOUN
ejpam-2608	96	22	which	which	PRON
ejpam-2608	96	23	ensures	ensure	VERB
ejpam-2608	96	24	that	that	SCONJ
ejpam-2608	96	25	they	they	PRON
ejpam-2608	96	26	are	be	AUX
ejpam-2608	96	27	finite	finite	ADJ
ejpam-2608	96	28	dimensional	dimensional	ADJ
ejpam-2608	96	29	complex	complex	ADJ
ejpam-2608	96	30	vector	vector	NOUN
ejpam-2608	96	31	spaces	space	NOUN
ejpam-2608	96	32	.	.	PUNCT
ejpam-2608	97	1	let	let	VERB
ejpam-2608	97	2	hp	hp	PROPN
ejpam-2608	97	3	,	,	PUNCT
ejpam-2608	97	4	qa	qa	X
ejpam-2608	97	5	=	=	PUNCT
ejpam-2608	97	6	dim(hp	dim(hp	PROPN
ejpam-2608	97	7	,	,	PUNCT
ejpam-2608	97	8	q	q	PROPN
ejpam-2608	97	9	a	a	NOUN
ejpam-2608	97	10	)	)	PUNCT
ejpam-2608	97	11	and	and	CCONJ
ejpam-2608	97	12	hp	hp	PROPN
ejpam-2608	97	13	,	,	PUNCT
ejpam-2608	97	14	qbc	qbc	NOUN
ejpam-2608	97	15	=	=	PUNCT
ejpam-2608	97	16	dim(hp	dim(hp	VERB
ejpam-2608	97	17	,	,	PUNCT
ejpam-2608	97	18	q	q	PROPN
ejpam-2608	97	19	bc	bc	PROPN
ejpam-2608	97	20	)	)	PUNCT
ejpam-2608	97	21	.we	.we	PUNCT
ejpam-2608	98	1	note	note	NOUN
ejpam-2608	98	2	(	(	PUNCT
ejpam-2608	98	3	see	see	VERB
ejpam-2608	98	4	popovici[9	popovici[9	NOUN
ejpam-2608	98	5	]	]	NOUN
ejpam-2608	98	6	)	)	PUNCT
ejpam-2608	98	7	that	that	PRON
ejpam-2608	98	8	hp	hp	PROPN
ejpam-2608	98	9	,	,	PUNCT
ejpam-2608	98	10	qa	qa	PROPN
ejpam-2608	98	11	=	=	SYM
ejpam-2608	98	12	hq	hq	PROPN
ejpam-2608	98	13	,	,	PUNCT
ejpam-2608	98	14	pa	pa	PROPN
ejpam-2608	98	15	,	,	PUNCT
ejpam-2608	98	16	hp	hp	PROPN
ejpam-2608	98	17	,	,	PUNCT
ejpam-2608	98	18	qbc	qbc	NOUN
ejpam-2608	98	19	=	=	SYM
ejpam-2608	98	20	hq	hq	PROPN
ejpam-2608	98	21	,	,	PUNCT
ejpam-2608	98	22	pbc	pbc	PROPN
ejpam-2608	98	23	and	and	CCONJ
ejpam-2608	98	24	hp	hp	PROPN
ejpam-2608	98	25	,	,	PUNCT
ejpam-2608	98	26	qa	qa	NOUN
ejpam-2608	98	27	=	=	PUNCT
ejpam-2608	98	28	hn−p	hn−p	NOUN
ejpam-2608	98	29	,	,	PUNCT
ejpam-2608	98	30	n−qbc	n−qbc	NOUN
ejpam-2608	98	31	.	.	PUNCT
ejpam-2608	99	1	the	the	DET
ejpam-2608	99	2	serre	serre	PROPN
ejpam-2608	99	3	duality	duality	NOUN
ejpam-2608	99	4	of	of	ADP
ejpam-2608	99	5	bott	bott	PROPN
ejpam-2608	99	6	-	-	PUNCT
ejpam-2608	99	7	chern	chern	PROPN
ejpam-2608	99	8	and	and	CCONJ
ejpam-2608	99	9	aeppli	aeppli	VERB
ejpam-2608	99	10	cohomology	cohomology	NOUN
ejpam-2608	99	11	is	be	AUX
ejpam-2608	99	12	due	due	ADJ
ejpam-2608	99	13	to	to	ADP
ejpam-2608	99	14	schweitzer[10	schweitzer[10	PRON
ejpam-2608	99	15	]	]	PUNCT
ejpam-2608	99	16	we	we	PRON
ejpam-2608	99	17	try	try	VERB
ejpam-2608	99	18	to	to	PART
ejpam-2608	99	19	narrow	narrow	VERB
ejpam-2608	99	20	down	down	ADP
ejpam-2608	99	21	as	as	ADV
ejpam-2608	99	22	much	much	ADV
ejpam-2608	99	23	as	as	ADP
ejpam-2608	99	24	possible	possible	ADJ
ejpam-2608	99	25	the	the	DET
ejpam-2608	99	26	aeppli	aeppli	NOUN
ejpam-2608	99	27	and	and	CCONJ
ejpam-2608	99	28	bott	bott	PROPN
ejpam-2608	99	29	-	-	PUNCT
ejpam-2608	99	30	chern	chern	PROPN
ejpam-2608	99	31	cohomology	cohomology	NOUN
ejpam-2608	99	32	on	on	ADP
ejpam-2608	99	33	complex	complex	ADJ
ejpam-2608	99	34	s6	s6	PROPN
ejpam-2608	99	35	.	.	PUNCT
ejpam-2608	100	1	3.1	3.1	NUM
ejpam-2608	100	2	.	.	PUNCT
ejpam-2608	101	1	some	some	DET
ejpam-2608	101	2	long	long	ADJ
ejpam-2608	101	3	exact	exact	ADJ
ejpam-2608	101	4	sequences	sequence	NOUN
ejpam-2608	101	5	of	of	ADP
ejpam-2608	101	6	cohomology	cohomology	NOUN
ejpam-2608	101	7	consider	consider	VERB
ejpam-2608	101	8	the	the	DET
ejpam-2608	101	9	following	follow	VERB
ejpam-2608	101	10	sequence	sequence	NOUN
ejpam-2608	101	11	of	of	ADP
ejpam-2608	101	12	maps	map	NOUN
ejpam-2608	101	13	of	of	ADP
ejpam-2608	101	14	cohomology	cohomology	NOUN
ejpam-2608	101	15	on	on	ADP
ejpam-2608	101	16	a	a	DET
ejpam-2608	101	17	complex	complex	ADJ
ejpam-2608	101	18	manifold	manifold	ADJ
ejpam-2608	101	19	x	x	NOUN
ejpam-2608	101	20	:	:	PUNCT
ejpam-2608	101	21	0→	0→	NUM
ejpam-2608	101	22	hp,0	hp,0	PROPN
ejpam-2608	101	23	bc	bc	PROPN
ejpam-2608	101	24	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	102	1	hp,0	hp,0	PROPN
ejpam-2608	102	2	∂̄	∂̄	VERB
ejpam-2608	102	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	103	1	hp,0	hp,0	PROPN
ejpam-2608	103	2	a	a	DET
ejpam-2608	103	3	∂̄→	∂̄→	PROPN
ejpam-2608	103	4	hp,1	hp,1	NOUN
ejpam-2608	103	5	bc	bc	VERB
ejpam-2608	103	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	103	7	·	·	PUNCT
ejpam-2608	103	8	·	·	PUNCT
ejpam-2608	103	9	·	·	PUNCT
ejpam-2608	103	10	·	·	PUNCT
ejpam-2608	103	11	·	·	PUNCT
ejpam-2608	103	12	·	·	PUNCT
ejpam-2608	103	13	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	104	1	hp	hp	PROPN
ejpam-2608	104	2	,	,	PUNCT
ejpam-2608	104	3	n−1	n−1	PROPN
ejpam-2608	104	4	a	a	DET
ejpam-2608	104	5	∂̄→	∂̄→	PROPN
ejpam-2608	104	6	hp	hp	PROPN
ejpam-2608	104	7	,	,	PUNCT
ejpam-2608	104	8	n	n	PRON
ejpam-2608	104	9	bc	bc	PROPN
ejpam-2608	104	10	/im(∂̄)−→	/im(∂̄)−→	X
ejpam-2608	104	11	hp	hp	PROPN
ejpam-2608	104	12	,	,	PUNCT
ejpam-2608	104	13	n	n	PRON
ejpam-2608	104	14	∂̄	∂̄	X
ejpam-2608	104	15	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	105	1	hp	hp	PROPN
ejpam-2608	105	2	,	,	PUNCT
ejpam-2608	105	3	n	n	PROPN
ejpam-2608	105	4	a	a	DET
ejpam-2608	105	5	→	→	SYM
ejpam-2608	105	6	0	0	NUM
ejpam-2608	105	7	.	.	PUNCT
ejpam-2608	106	1	we	we	PRON
ejpam-2608	106	2	prove	prove	VERB
ejpam-2608	106	3	some	some	DET
ejpam-2608	106	4	claims	claim	NOUN
ejpam-2608	106	5	and	and	CCONJ
ejpam-2608	106	6	lemmas	lemma	NOUN
ejpam-2608	106	7	below	below	ADV
ejpam-2608	106	8	about	about	ADP
ejpam-2608	106	9	this	this	DET
ejpam-2608	106	10	sequence	sequence	NOUN
ejpam-2608	106	11	of	of	ADP
ejpam-2608	106	12	maps	map	NOUN
ejpam-2608	106	13	.	.	PUNCT
ejpam-2608	107	1	the	the	DET
ejpam-2608	107	2	sophisticated	sophisticated	ADJ
ejpam-2608	107	3	readers	reader	NOUN
ejpam-2608	107	4	may	may	AUX
ejpam-2608	107	5	just	just	ADV
ejpam-2608	107	6	read	read	VERB
ejpam-2608	107	7	the	the	DET
ejpam-2608	107	8	claims	claim	NOUN
ejpam-2608	107	9	and	and	CCONJ
ejpam-2608	107	10	lemmas	lemma	NOUN
ejpam-2608	107	11	skipping	skip	VERB
ejpam-2608	107	12	over	over	ADP
ejpam-2608	107	13	their	their	PRON
ejpam-2608	107	14	proofs	proof	NOUN
ejpam-2608	107	15	if	if	SCONJ
ejpam-2608	107	16	they	they	PRON
ejpam-2608	107	17	appear	appear	VERB
ejpam-2608	107	18	to	to	PART
ejpam-2608	107	19	be	be	AUX
ejpam-2608	107	20	straight	straight	ADV
ejpam-2608	107	21	forward	forward	ADV
ejpam-2608	107	22	or	or	CCONJ
ejpam-2608	107	23	obvious	obvious	ADJ
ejpam-2608	107	24	.	.	PUNCT
ejpam-2608	108	1	lemma	lemma	PROPN
ejpam-2608	108	2	3	3	NUM
ejpam-2608	108	3	.	.	PUNCT
ejpam-2608	109	1	the	the	DET
ejpam-2608	109	2	sequence	sequence	NOUN
ejpam-2608	109	3	of	of	ADP
ejpam-2608	109	4	maps	map	NOUN
ejpam-2608	109	5	above	above	ADV
ejpam-2608	109	6	is	be	AUX
ejpam-2608	109	7	exact	exact	ADJ
ejpam-2608	109	8	at	at	ADP
ejpam-2608	109	9	hp	hp	PROPN
ejpam-2608	109	10	,	,	PUNCT
ejpam-2608	109	11	q	q	NOUN
ejpam-2608	109	12	a	a	X
ejpam-2608	109	13	.	.	PUNCT
ejpam-2608	110	1	namely	namely	ADV
ejpam-2608	110	2	,	,	PUNCT
ejpam-2608	110	3	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	110	4	)	)	PUNCT
ejpam-2608	110	5	+	+	NUM
ejpam-2608	110	6	im(∂	im(∂	NOUN
ejpam-2608	110	7	)	)	PUNCT
ejpam-2608	110	8	)	)	PUNCT
ejpam-2608	110	9	:	:	PUNCT
ejpam-2608	111	1	hp	hp	PROPN
ejpam-2608	111	2	,	,	PUNCT
ejpam-2608	111	3	q	q	NOUN
ejpam-2608	111	4	∂̄	∂̄	PROPN
ejpam-2608	111	5	→	→	SYM
ejpam-2608	111	6	hp	hp	PROPN
ejpam-2608	111	7	,	,	PUNCT
ejpam-2608	111	8	q	q	NOUN
ejpam-2608	111	9	a	a	NOUN
ejpam-2608	111	10	)	)	PUNCT
ejpam-2608	111	11	=	=	SYM
ejpam-2608	111	12	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	111	13	:	:	PUNCT
ejpam-2608	111	14	hp	hp	PROPN
ejpam-2608	111	15	,	,	PUNCT
ejpam-2608	111	16	q	q	PROPN
ejpam-2608	111	17	a	a	DET
ejpam-2608	111	18	→	→	SYM
ejpam-2608	111	19	hp	hp	PROPN
ejpam-2608	111	20	,	,	PUNCT
ejpam-2608	111	21	q+1	q+1	PROPN
ejpam-2608	111	22	bc	bc	PROPN
ejpam-2608	111	23	)	)	PUNCT
ejpam-2608	111	24	.	.	PUNCT
ejpam-2608	112	1	proof	proof	NOUN
ejpam-2608	112	2	.	.	PUNCT
ejpam-2608	113	1	let	let	VERB
ejpam-2608	113	2	[	[	PUNCT
ejpam-2608	113	3	φ]a	φ]a	NOUN
ejpam-2608	113	4	∈	∈	ADJ
ejpam-2608	113	5	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	113	6	:	:	PUNCT
ejpam-2608	113	7	hp	hp	PROPN
ejpam-2608	113	8	,	,	PUNCT
ejpam-2608	113	9	q	q	PROPN
ejpam-2608	113	10	a	a	DET
ejpam-2608	113	11	→	→	SYM
ejpam-2608	113	12	hp	hp	PROPN
ejpam-2608	113	13	,	,	PUNCT
ejpam-2608	113	14	q+1	q+1	PROPN
ejpam-2608	113	15	bc	bc	PROPN
ejpam-2608	113	16	)	)	PUNCT
ejpam-2608	113	17	where	where	SCONJ
ejpam-2608	113	18	φ	φ	PROPN
ejpam-2608	113	19	is	be	AUX
ejpam-2608	113	20	some	some	DET
ejpam-2608	113	21	smooth	smooth	ADJ
ejpam-2608	113	22	p	p	NOUN
ejpam-2608	113	23	,	,	PUNCT
ejpam-2608	113	24	q	q	ADJ
ejpam-2608	113	25	-	-	PUNCT
ejpam-2608	113	26	form	form	NOUN
ejpam-2608	113	27	representative	representative	NOUN
ejpam-2608	113	28	of	of	ADP
ejpam-2608	113	29	[	[	X
ejpam-2608	113	30	φ]a	φ]a	X
ejpam-2608	113	31	.	.	PUNCT
ejpam-2608	114	1	we	we	PRON
ejpam-2608	114	2	have	have	VERB
ejpam-2608	114	3	then	then	ADV
ejpam-2608	114	4	that	that	PRON
ejpam-2608	114	5	∂̄([φ]a	∂̄([φ]a	VERB
ejpam-2608	114	6	)	)	PUNCT
ejpam-2608	114	7	=	=	PUNCT
ejpam-2608	115	1	[	[	X
ejpam-2608	115	2	∂̄(φ)]bc	∂̄(φ)]bc	PROPN
ejpam-2608	115	3	=	=	SYM
ejpam-2608	115	4	0	0	NUM
ejpam-2608	115	5	in	in	ADP
ejpam-2608	115	6	hp	hp	PROPN
ejpam-2608	115	7	,	,	PUNCT
ejpam-2608	115	8	q+1	q+1	PROPN
ejpam-2608	115	9	bc	bc	PROPN
ejpam-2608	115	10	,	,	PUNCT
ejpam-2608	115	11	i.e.	i.e.	X
ejpam-2608	115	12	∂̄(φ	∂̄(φ	X
ejpam-2608	115	13	)	)	PUNCT
ejpam-2608	116	1	=	=	NOUN
ejpam-2608	116	2	∂̄∂θ	∂̄∂θ	NOUN
ejpam-2608	116	3	for	for	ADP
ejpam-2608	116	4	some	some	DET
ejpam-2608	116	5	p−	p−	NOUN
ejpam-2608	116	6	1	1	NUM
ejpam-2608	116	7	,	,	PUNCT
ejpam-2608	116	8	q	q	ADJ
ejpam-2608	116	9	-	-	PUNCT
ejpam-2608	116	10	form	form	NOUN
ejpam-2608	116	11	θ	θ	NOUN
ejpam-2608	116	12	.	.	PUNCT
ejpam-2608	116	13	thus	thus	ADV
ejpam-2608	116	14	∂̄(φ−	∂̄(φ−	PROPN
ejpam-2608	116	15	∂θ	∂θ	PROPN
ejpam-2608	116	16	)	)	PUNCT
ejpam-2608	116	17	=	=	SYM
ejpam-2608	116	18	0	0	NUM
ejpam-2608	117	1	and	and	CCONJ
ejpam-2608	117	2	φ−	φ−	PROPN
ejpam-2608	117	3	∂θ	∂θ	PROPN
ejpam-2608	117	4	is	be	AUX
ejpam-2608	117	5	a	a	DET
ejpam-2608	117	6	∂̄-closed	∂̄-close	VERB
ejpam-2608	117	7	p	p	NOUN
ejpam-2608	117	8	,	,	PUNCT
ejpam-2608	117	9	q	q	NOUN
ejpam-2608	117	10	-	-	PUNCT
ejpam-2608	117	11	form	form	NOUN
ejpam-2608	117	12	.	.	PUNCT
ejpam-2608	118	1	we	we	PRON
ejpam-2608	118	2	conclude	conclude	VERB
ejpam-2608	118	3	then	then	ADV
ejpam-2608	118	4	that	that	SCONJ
ejpam-2608	119	1	[	[	X
ejpam-2608	119	2	φ]a	φ]a	X
ejpam-2608	119	3	=	=	PUNCT
ejpam-2608	119	4	[	[	X
ejpam-2608	119	5	φ−	φ−	PROPN
ejpam-2608	119	6	∂θ]a	∂θ]a	PROPN
ejpam-2608	119	7	∈	∈	PROPN
ejpam-2608	119	8	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	119	9	)	)	PUNCT
ejpam-2608	119	10	+	+	CCONJ
ejpam-2608	119	11	im(∂	im(∂	NOUN
ejpam-2608	119	12	)	)	PUNCT
ejpam-2608	119	13	)	)	PUNCT
ejpam-2608	119	14	:	:	PUNCT
ejpam-2608	120	1	hp	hp	PROPN
ejpam-2608	120	2	,	,	PUNCT
ejpam-2608	120	3	q	q	NOUN
ejpam-2608	120	4	∂̄	∂̄	PROPN
ejpam-2608	120	5	→	→	SYM
ejpam-2608	120	6	hp	hp	PROPN
ejpam-2608	120	7	,	,	PUNCT
ejpam-2608	120	8	q	q	NOUN
ejpam-2608	120	9	a	a	NOUN
ejpam-2608	120	10	)	)	PUNCT
ejpam-2608	120	11	a.	a.	NOUN
ejpam-2608	120	12	mchugh	mchugh	PROPN
ejpam-2608	120	13	/	/	SYM
ejpam-2608	120	14	eur	eur	PROPN
ejpam-2608	120	15	.	.	PUNCT
ejpam-2608	121	1	j.	j.	PROPN
ejpam-2608	121	2	pure	pure	PROPN
ejpam-2608	121	3	appl	appl	PROPN
ejpam-2608	121	4	.	.	PROPN
ejpam-2608	121	5	math	math	PROPN
ejpam-2608	121	6	,	,	PUNCT
ejpam-2608	121	7	10	10	NUM
ejpam-2608	121	8	(	(	PUNCT
ejpam-2608	121	9	3	3	NUM
ejpam-2608	121	10	)	)	PUNCT
ejpam-2608	121	11	(	(	PUNCT
ejpam-2608	121	12	2017	2017	NUM
ejpam-2608	121	13	)	)	PUNCT
ejpam-2608	121	14	,	,	PUNCT
ejpam-2608	121	15	440	440	NUM
ejpam-2608	121	16	-	-	SYM
ejpam-2608	121	17	454	454	NUM
ejpam-2608	121	18	445	445	NUM
ejpam-2608	121	19	and	and	CCONJ
ejpam-2608	121	20	ker(∂̄	ker(∂̄	PROPN
ejpam-2608	121	21	:	:	PUNCT
ejpam-2608	121	22	hp	hp	PROPN
ejpam-2608	121	23	,	,	PUNCT
ejpam-2608	121	24	q	q	PROPN
ejpam-2608	121	25	a	a	PRON
ejpam-2608	121	26	→	→	SYM
ejpam-2608	121	27	hp	hp	PROPN
ejpam-2608	121	28	,	,	PUNCT
ejpam-2608	121	29	q+1	q+1	PROPN
ejpam-2608	121	30	bc	bc	PROPN
ejpam-2608	121	31	)	)	PUNCT
ejpam-2608	121	32	⊆	⊆	NUM
ejpam-2608	121	33	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	121	34	)	)	PUNCT
ejpam-2608	121	35	+	+	NUM
ejpam-2608	121	36	im(∂	im(∂	NOUN
ejpam-2608	121	37	)	)	PUNCT
ejpam-2608	121	38	)	)	PUNCT
ejpam-2608	121	39	:	:	PUNCT
ejpam-2608	122	1	hp	hp	PROPN
ejpam-2608	122	2	,	,	PUNCT
ejpam-2608	122	3	q	q	NOUN
ejpam-2608	122	4	∂̄	∂̄	PROPN
ejpam-2608	122	5	→	→	SYM
ejpam-2608	122	6	hp	hp	PROPN
ejpam-2608	122	7	,	,	PUNCT
ejpam-2608	122	8	q	q	NOUN
ejpam-2608	122	9	a	a	NOUN
ejpam-2608	122	10	)	)	PUNCT
ejpam-2608	122	11	.	.	PUNCT
ejpam-2608	123	1	now	now	ADV
ejpam-2608	123	2	let	let	VERB
ejpam-2608	123	3	[	[	PUNCT
ejpam-2608	123	4	φ]a	φ]a	VERB
ejpam-2608	123	5	∈	∈	NOUN
ejpam-2608	123	6	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	123	7	)	)	PUNCT
ejpam-2608	123	8	+	+	CCONJ
ejpam-2608	123	9	im(∂	im(∂	NOUN
ejpam-2608	123	10	)	)	PUNCT
ejpam-2608	123	11	)	)	PUNCT
ejpam-2608	123	12	:	:	PUNCT
ejpam-2608	124	1	hp	hp	PROPN
ejpam-2608	124	2	,	,	PUNCT
ejpam-2608	124	3	q	q	NOUN
ejpam-2608	124	4	∂̄	∂̄	PROPN
ejpam-2608	124	5	→	→	SYM
ejpam-2608	124	6	hp	hp	PROPN
ejpam-2608	124	7	,	,	PUNCT
ejpam-2608	124	8	q	q	NOUN
ejpam-2608	124	9	a	a	NOUN
ejpam-2608	124	10	)	)	PUNCT
ejpam-2608	124	11	where	where	SCONJ
ejpam-2608	124	12	φ	φ	PROPN
ejpam-2608	124	13	is	be	AUX
ejpam-2608	124	14	some	some	DET
ejpam-2608	124	15	smooth	smooth	ADJ
ejpam-2608	124	16	p	p	NOUN
ejpam-2608	124	17	,	,	PUNCT
ejpam-2608	124	18	q	q	ADJ
ejpam-2608	124	19	-	-	PUNCT
ejpam-2608	124	20	form	form	NOUN
ejpam-2608	124	21	representative	representative	NOUN
ejpam-2608	124	22	of	of	ADP
ejpam-2608	124	23	[	[	X
ejpam-2608	124	24	φ]a	φ]a	X
ejpam-2608	124	25	.	.	PUNCT
ejpam-2608	125	1	we	we	PRON
ejpam-2608	125	2	may	may	AUX
ejpam-2608	125	3	assume	assume	VERB
ejpam-2608	125	4	that	that	SCONJ
ejpam-2608	125	5	φ	φ	PROPN
ejpam-2608	125	6	is	be	AUX
ejpam-2608	125	7	∂̄-closed	∂̄-close	VERB
ejpam-2608	125	8	since	since	SCONJ
ejpam-2608	125	9	[	[	X
ejpam-2608	125	10	φ]a	φ]a	NOUN
ejpam-2608	125	11	∈	∈	NOUN
ejpam-2608	125	12	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	125	13	)	)	PUNCT
ejpam-2608	125	14	+	+	CCONJ
ejpam-2608	125	15	im(∂	im(∂	NOUN
ejpam-2608	125	16	)	)	PUNCT
ejpam-2608	125	17	)	)	PUNCT
ejpam-2608	125	18	:	:	PUNCT
ejpam-2608	126	1	hp	hp	PROPN
ejpam-2608	126	2	,	,	PUNCT
ejpam-2608	126	3	q	q	NOUN
ejpam-2608	126	4	∂̄	∂̄	PROPN
ejpam-2608	126	5	→	→	SYM
ejpam-2608	126	6	hp	hp	PROPN
ejpam-2608	126	7	,	,	PUNCT
ejpam-2608	126	8	q	q	NOUN
ejpam-2608	126	9	a	a	NOUN
ejpam-2608	126	10	)	)	PUNCT
ejpam-2608	126	11	.	.	PUNCT
ejpam-2608	127	1	clearly	clearly	ADV
ejpam-2608	127	2	,	,	PUNCT
ejpam-2608	127	3	∂̄([φ]a	∂̄([φ]a	X
ejpam-2608	127	4	)	)	PUNCT
ejpam-2608	127	5	=	=	PUNCT
ejpam-2608	128	1	[	[	X
ejpam-2608	128	2	∂̄φ]bc	∂̄φ]bc	X
ejpam-2608	128	3	=	=	SYM
ejpam-2608	128	4	0	0	NUM
ejpam-2608	128	5	in	in	ADP
ejpam-2608	128	6	hp	hp	PROPN
ejpam-2608	128	7	,	,	PUNCT
ejpam-2608	128	8	q+1	q+1	PROPN
ejpam-2608	128	9	bc	bc	PROPN
ejpam-2608	128	10	.	.	PUNCT
ejpam-2608	129	1	thus	thus	ADV
ejpam-2608	129	2	[	[	X
ejpam-2608	129	3	φ]a	φ]a	NOUN
ejpam-2608	129	4	∈	∈	ADJ
ejpam-2608	129	5	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	129	6	:	:	PUNCT
ejpam-2608	129	7	hp	hp	PROPN
ejpam-2608	129	8	,	,	PUNCT
ejpam-2608	129	9	q	q	PROPN
ejpam-2608	129	10	a	a	DET
ejpam-2608	129	11	→	→	SYM
ejpam-2608	129	12	hp	hp	PROPN
ejpam-2608	129	13	,	,	PUNCT
ejpam-2608	129	14	q+1	q+1	PROPN
ejpam-2608	129	15	bc	bc	PROPN
ejpam-2608	129	16	)	)	PUNCT
ejpam-2608	129	17	and	and	CCONJ
ejpam-2608	129	18	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	129	19	)	)	PUNCT
ejpam-2608	129	20	+	+	NUM
ejpam-2608	129	21	im(∂	im(∂	NOUN
ejpam-2608	129	22	)	)	PUNCT
ejpam-2608	129	23	)	)	PUNCT
ejpam-2608	129	24	:	:	PUNCT
ejpam-2608	129	25	hp	hp	PROPN
ejpam-2608	129	26	,	,	PUNCT
ejpam-2608	129	27	q	q	NOUN
ejpam-2608	129	28	∂̄	∂̄	PROPN
ejpam-2608	129	29	→	→	SYM
ejpam-2608	129	30	hp	hp	PROPN
ejpam-2608	129	31	,	,	PUNCT
ejpam-2608	129	32	q	q	PROPN
ejpam-2608	129	33	a	a	NOUN
ejpam-2608	129	34	)	)	PUNCT
ejpam-2608	129	35	⊆	⊆	NUM
ejpam-2608	129	36	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	129	37	:	:	PUNCT
ejpam-2608	129	38	hp	hp	PROPN
ejpam-2608	129	39	,	,	PUNCT
ejpam-2608	129	40	q	q	PROPN
ejpam-2608	129	41	a	a	DET
ejpam-2608	129	42	→	→	SYM
ejpam-2608	129	43	hp	hp	PROPN
ejpam-2608	129	44	,	,	PUNCT
ejpam-2608	129	45	q+1	q+1	PROPN
ejpam-2608	129	46	bc	bc	PROPN
ejpam-2608	129	47	)	)	PUNCT
ejpam-2608	129	48	.	.	PUNCT
ejpam-2608	130	1	the	the	DET
ejpam-2608	130	2	two	two	NUM
ejpam-2608	130	3	inclusions	inclusion	NOUN
ejpam-2608	130	4	give	give	VERB
ejpam-2608	130	5	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	130	6	)	)	PUNCT
ejpam-2608	130	7	+	+	CCONJ
ejpam-2608	130	8	im(∂	im(∂	NOUN
ejpam-2608	130	9	)	)	PUNCT
ejpam-2608	130	10	)	)	PUNCT
ejpam-2608	130	11	:	:	PUNCT
ejpam-2608	131	1	hp	hp	PROPN
ejpam-2608	131	2	,	,	PUNCT
ejpam-2608	131	3	q	q	NOUN
ejpam-2608	131	4	∂̄	∂̄	PROPN
ejpam-2608	131	5	→	→	SYM
ejpam-2608	131	6	hp	hp	PROPN
ejpam-2608	131	7	,	,	PUNCT
ejpam-2608	131	8	q	q	NOUN
ejpam-2608	131	9	a	a	NOUN
ejpam-2608	131	10	)	)	PUNCT
ejpam-2608	131	11	=	=	SYM
ejpam-2608	131	12	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	131	13	:	:	PUNCT
ejpam-2608	131	14	hp	hp	PROPN
ejpam-2608	131	15	,	,	PUNCT
ejpam-2608	131	16	q	q	PROPN
ejpam-2608	131	17	a	a	DET
ejpam-2608	131	18	→	→	SYM
ejpam-2608	131	19	hp	hp	PROPN
ejpam-2608	131	20	,	,	PUNCT
ejpam-2608	131	21	q+1	q+1	PROPN
ejpam-2608	131	22	bc	bc	PROPN
ejpam-2608	131	23	)	)	PUNCT
ejpam-2608	131	24	.	.	PUNCT
ejpam-2608	132	1	lemma	lemma	PROPN
ejpam-2608	132	2	4	4	X
ejpam-2608	132	3	.	.	PUNCT
ejpam-2608	133	1	the	the	DET
ejpam-2608	133	2	sequence	sequence	NOUN
ejpam-2608	133	3	of	of	ADP
ejpam-2608	133	4	maps	map	NOUN
ejpam-2608	133	5	above	above	ADV
ejpam-2608	133	6	is	be	AUX
ejpam-2608	133	7	exact	exact	ADJ
ejpam-2608	133	8	at	at	ADP
ejpam-2608	133	9	hp	hp	PROPN
ejpam-2608	133	10	,	,	PUNCT
ejpam-2608	133	11	q	q	PROPN
ejpam-2608	133	12	bc	bc	PROPN
ejpam-2608	133	13	.	.	PUNCT
ejpam-2608	134	1	namely	namely	ADV
ejpam-2608	134	2	,	,	PUNCT
ejpam-2608	134	3	ker(/im(∂̄	ker(/im(∂̄	PROPN
ejpam-2608	134	4	)	)	PUNCT
ejpam-2608	134	5	:	:	PUNCT
ejpam-2608	135	1	hp	hp	PROPN
ejpam-2608	135	2	,	,	PUNCT
ejpam-2608	135	3	q	q	PROPN
ejpam-2608	135	4	bc	bc	PROPN
ejpam-2608	135	5	→	→	SYM
ejpam-2608	135	6	hp	hp	PROPN
ejpam-2608	135	7	,	,	PUNCT
ejpam-2608	135	8	q	q	NOUN
ejpam-2608	135	9	∂̄	∂̄	ADJ
ejpam-2608	135	10	)	)	PUNCT
ejpam-2608	135	11	=	=	PUNCT
ejpam-2608	136	1	im(∂̄	im(∂̄	NOUN
ejpam-2608	136	2	:	:	PUNCT
ejpam-2608	136	3	hp	hp	PROPN
ejpam-2608	136	4	,	,	PUNCT
ejpam-2608	136	5	q−1	q−1	PROPN
ejpam-2608	136	6	a	a	DET
ejpam-2608	136	7	→	→	SYM
ejpam-2608	136	8	hp	hp	PROPN
ejpam-2608	136	9	,	,	PUNCT
ejpam-2608	136	10	q+1	q+1	PROPN
ejpam-2608	136	11	bc	bc	PROPN
ejpam-2608	136	12	)	)	PUNCT
ejpam-2608	136	13	.	.	PUNCT
ejpam-2608	137	1	proof	proof	NOUN
ejpam-2608	137	2	.	.	PUNCT
ejpam-2608	138	1	let	let	VERB
ejpam-2608	138	2	[	[	X
ejpam-2608	138	3	γ]bc	γ]bc	NOUN
ejpam-2608	138	4	∈	∈	PROPN
ejpam-2608	138	5	im(∂̄	im(∂̄	NOUN
ejpam-2608	138	6	:	:	PUNCT
ejpam-2608	138	7	hp	hp	PROPN
ejpam-2608	138	8	,	,	PUNCT
ejpam-2608	138	9	q−1	q−1	PROPN
ejpam-2608	138	10	a	a	DET
ejpam-2608	138	11	→	→	SYM
ejpam-2608	138	12	hp	hp	PROPN
ejpam-2608	138	13	,	,	PUNCT
ejpam-2608	138	14	q	q	PROPN
ejpam-2608	138	15	bc	bc	PROPN
ejpam-2608	138	16	)	)	PUNCT
ejpam-2608	138	17	where	where	SCONJ
ejpam-2608	138	18	γ	γ	PROPN
ejpam-2608	138	19	is	be	AUX
ejpam-2608	138	20	some	some	DET
ejpam-2608	138	21	smooth	smooth	ADJ
ejpam-2608	138	22	p	p	NOUN
ejpam-2608	138	23	,	,	PUNCT
ejpam-2608	138	24	q	q	ADJ
ejpam-2608	138	25	-	-	PUNCT
ejpam-2608	138	26	form	form	NOUN
ejpam-2608	138	27	representative	representative	NOUN
ejpam-2608	138	28	of	of	ADP
ejpam-2608	138	29	[	[	X
ejpam-2608	138	30	γ]bc	γ]bc	PROPN
ejpam-2608	138	31	.	.	PUNCT
ejpam-2608	139	1	since	since	SCONJ
ejpam-2608	139	2	[	[	X
ejpam-2608	139	3	γ]bc	γ]bc	PROPN
ejpam-2608	139	4	∈	∈	PROPN
ejpam-2608	139	5	im(∂̄	im(∂̄	NOUN
ejpam-2608	139	6	:	:	PUNCT
ejpam-2608	139	7	hp	hp	PROPN
ejpam-2608	139	8	,	,	PUNCT
ejpam-2608	139	9	q−1	q−1	PROPN
ejpam-2608	139	10	a	a	DET
ejpam-2608	139	11	→	→	SYM
ejpam-2608	139	12	hp	hp	PROPN
ejpam-2608	139	13	,	,	PUNCT
ejpam-2608	139	14	q	q	PROPN
ejpam-2608	139	15	bc	bc	PROPN
ejpam-2608	139	16	)	)	PUNCT
ejpam-2608	139	17	we	we	PRON
ejpam-2608	139	18	may	may	AUX
ejpam-2608	139	19	assume	assume	VERB
ejpam-2608	139	20	γ	γ	X
ejpam-2608	139	21	=	=	SYM
ejpam-2608	139	22	∂̄µ	∂̄µ	PROPN
ejpam-2608	139	23	for	for	ADP
ejpam-2608	139	24	some	some	DET
ejpam-2608	139	25	p	p	NOUN
ejpam-2608	139	26	,	,	PUNCT
ejpam-2608	139	27	q	q	NOUN
ejpam-2608	139	28	−	−	PROPN
ejpam-2608	139	29	1	1	NUM
ejpam-2608	139	30	-	-	PUNCT
ejpam-2608	139	31	form	form	NOUN
ejpam-2608	139	32	µ	µ	NOUN
ejpam-2608	139	33	such	such	ADJ
ejpam-2608	139	34	that	that	DET
ejpam-2608	139	35	∂∂̄µ	∂∂̄µ	NOUN
ejpam-2608	139	36	=	=	NOUN
ejpam-2608	140	1	0	0	X
ejpam-2608	140	2	.	.	PUNCT
ejpam-2608	141	1	clearly	clearly	ADV
ejpam-2608	141	2	,	,	PUNCT
ejpam-2608	141	3	γ	γ	X
ejpam-2608	141	4	/	/	SYM
ejpam-2608	141	5	im(∂̄	im(∂̄	NOUN
ejpam-2608	141	6	)	)	PUNCT
ejpam-2608	141	7	=	=	SYM
ejpam-2608	141	8	∂̄µ/im(∂̄	∂̄µ/im(∂̄	X
ejpam-2608	141	9	)	)	PUNCT
ejpam-2608	141	10	=	=	SYM
ejpam-2608	141	11	0	0	NUM
ejpam-2608	141	12	/	/	SYM
ejpam-2608	141	13	im(∂̄	im(∂̄	NOUN
ejpam-2608	141	14	)	)	PUNCT
ejpam-2608	141	15	and	and	CCONJ
ejpam-2608	141	16	[	[	X
ejpam-2608	141	17	γ	γ	X
ejpam-2608	141	18	]	]	X
ejpam-2608	141	19	∈	∈	PROPN
ejpam-2608	141	20	ker(/im(∂̄	ker(/im(∂̄	X
ejpam-2608	141	21	)	)	PUNCT
ejpam-2608	141	22	:	:	PUNCT
ejpam-2608	142	1	hp	hp	PROPN
ejpam-2608	142	2	,	,	PUNCT
ejpam-2608	142	3	q	q	PROPN
ejpam-2608	142	4	bc	bc	PROPN
ejpam-2608	142	5	→	→	SYM
ejpam-2608	142	6	hp	hp	PROPN
ejpam-2608	142	7	,	,	PUNCT
ejpam-2608	142	8	q	q	NOUN
ejpam-2608	142	9	∂̄	∂̄	ADJ
ejpam-2608	142	10	)	)	PUNCT
ejpam-2608	142	11	.	.	PUNCT
ejpam-2608	143	1	thus	thus	ADV
ejpam-2608	143	2	im(∂̄	im(∂̄	NOUN
ejpam-2608	143	3	:	:	PUNCT
ejpam-2608	143	4	hp	hp	PROPN
ejpam-2608	143	5	,	,	PUNCT
ejpam-2608	143	6	q−1	q−1	PROPN
ejpam-2608	143	7	a	a	DET
ejpam-2608	143	8	→	→	SYM
ejpam-2608	143	9	hp	hp	PROPN
ejpam-2608	143	10	,	,	PUNCT
ejpam-2608	143	11	q	q	PROPN
ejpam-2608	143	12	bc	bc	PROPN
ejpam-2608	143	13	)	)	PUNCT
ejpam-2608	143	14	⊆	⊆	NUM
ejpam-2608	143	15	ker(/im(∂̄	ker(/im(∂̄	NOUN
ejpam-2608	143	16	)	)	PUNCT
ejpam-2608	143	17	:	:	PUNCT
ejpam-2608	144	1	hp	hp	PROPN
ejpam-2608	144	2	,	,	PUNCT
ejpam-2608	144	3	q	q	PROPN
ejpam-2608	144	4	bc	bc	PROPN
ejpam-2608	144	5	→	→	SYM
ejpam-2608	144	6	hp	hp	PROPN
ejpam-2608	144	7	,	,	PUNCT
ejpam-2608	144	8	q	q	NOUN
ejpam-2608	144	9	∂̄	∂̄	ADJ
ejpam-2608	144	10	)	)	PUNCT
ejpam-2608	144	11	.	.	PUNCT
ejpam-2608	145	1	now	now	ADV
ejpam-2608	145	2	let	let	VERB
ejpam-2608	145	3	[	[	X
ejpam-2608	145	4	γ]bc	γ]bc	NOUN
ejpam-2608	145	5	∈	∈	PROPN
ejpam-2608	145	6	ker(/im(∂̄	ker(/im(∂̄	X
ejpam-2608	145	7	)	)	PUNCT
ejpam-2608	145	8	:	:	PUNCT
ejpam-2608	146	1	hp	hp	PROPN
ejpam-2608	146	2	,	,	PUNCT
ejpam-2608	146	3	q	q	PROPN
ejpam-2608	146	4	bc	bc	PROPN
ejpam-2608	146	5	→	→	SYM
ejpam-2608	146	6	hp	hp	PROPN
ejpam-2608	146	7	,	,	PUNCT
ejpam-2608	146	8	q	q	NOUN
ejpam-2608	146	9	∂̄	∂̄	NOUN
ejpam-2608	146	10	)	)	PUNCT
ejpam-2608	146	11	where	where	SCONJ
ejpam-2608	146	12	γ	γ	PROPN
ejpam-2608	146	13	is	be	AUX
ejpam-2608	146	14	some	some	DET
ejpam-2608	146	15	smooth	smooth	ADJ
ejpam-2608	146	16	p	p	NOUN
ejpam-2608	146	17	,	,	PUNCT
ejpam-2608	146	18	q	q	ADJ
ejpam-2608	146	19	-	-	PUNCT
ejpam-2608	146	20	form	form	NOUN
ejpam-2608	146	21	representative	representative	NOUN
ejpam-2608	146	22	of	of	ADP
ejpam-2608	146	23	[	[	X
ejpam-2608	146	24	γ]bc	γ]bc	PROPN
ejpam-2608	146	25	.	.	PUNCT
ejpam-2608	147	1	since	since	SCONJ
ejpam-2608	147	2	[	[	X
ejpam-2608	147	3	γ]bc	γ]bc	PROPN
ejpam-2608	147	4	∈	∈	PROPN
ejpam-2608	147	5	ker(/im(∂̄	ker(/im(∂̄	X
ejpam-2608	147	6	)	)	PUNCT
ejpam-2608	147	7	:	:	PUNCT
ejpam-2608	147	8	hp	hp	PROPN
ejpam-2608	147	9	,	,	PUNCT
ejpam-2608	147	10	q	q	PROPN
ejpam-2608	147	11	bc	bc	PROPN
ejpam-2608	147	12	→	→	SYM
ejpam-2608	147	13	hp	hp	PROPN
ejpam-2608	147	14	,	,	PUNCT
ejpam-2608	147	15	q	q	NOUN
ejpam-2608	147	16	∂̄	∂̄	ADJ
ejpam-2608	147	17	)	)	PUNCT
ejpam-2608	147	18	a.	a.	PROPN
ejpam-2608	147	19	mchugh	mchugh	PROPN
ejpam-2608	147	20	/	/	SYM
ejpam-2608	147	21	eur	eur	PROPN
ejpam-2608	147	22	.	.	PUNCT
ejpam-2608	148	1	j.	j.	PROPN
ejpam-2608	148	2	pure	pure	PROPN
ejpam-2608	148	3	appl	appl	PROPN
ejpam-2608	148	4	.	.	PROPN
ejpam-2608	148	5	math	math	PROPN
ejpam-2608	148	6	,	,	PUNCT
ejpam-2608	148	7	10	10	NUM
ejpam-2608	148	8	(	(	PUNCT
ejpam-2608	148	9	3	3	NUM
ejpam-2608	148	10	)	)	PUNCT
ejpam-2608	148	11	(	(	PUNCT
ejpam-2608	148	12	2017	2017	NUM
ejpam-2608	148	13	)	)	PUNCT
ejpam-2608	148	14	,	,	PUNCT
ejpam-2608	148	15	440	440	NUM
ejpam-2608	148	16	-	-	SYM
ejpam-2608	148	17	454	454	NUM
ejpam-2608	148	18	446	446	NUM
ejpam-2608	148	19	we	we	PRON
ejpam-2608	148	20	have	have	VERB
ejpam-2608	148	21	γ	γ	X
ejpam-2608	148	22	/	/	SYM
ejpam-2608	148	23	im(∂̄	im(∂̄	NOUN
ejpam-2608	148	24	)	)	PUNCT
ejpam-2608	148	25	=	=	SYM
ejpam-2608	148	26	0	0	NUM
ejpam-2608	148	27	/	/	SYM
ejpam-2608	148	28	im(∂̄	im(∂̄	NOUN
ejpam-2608	148	29	)	)	PUNCT
ejpam-2608	148	30	.	.	PUNCT
ejpam-2608	149	1	thus	thus	ADV
ejpam-2608	149	2	γ	γ	X
ejpam-2608	149	3	=	=	SYM
ejpam-2608	149	4	∂̄µ	∂̄µ	PROPN
ejpam-2608	149	5	for	for	ADP
ejpam-2608	149	6	some	some	DET
ejpam-2608	149	7	p	p	NOUN
ejpam-2608	149	8	,	,	PUNCT
ejpam-2608	149	9	q	q	NOUN
ejpam-2608	149	10	−	−	PROPN
ejpam-2608	149	11	1	1	NUM
ejpam-2608	149	12	-	-	PUNCT
ejpam-2608	149	13	form	form	NOUN
ejpam-2608	149	14	µ.	µ.	NOUN
ejpam-2608	149	15	now	now	ADV
ejpam-2608	149	16	,	,	PUNCT
ejpam-2608	149	17	γ	γ	PROPN
ejpam-2608	149	18	is	be	AUX
ejpam-2608	149	19	∂̄-closed	∂̄-close	VERB
ejpam-2608	149	20	and	and	CCONJ
ejpam-2608	149	21	also	also	ADV
ejpam-2608	149	22	∂-closed	∂-close	VERB
ejpam-2608	149	23	.	.	PUNCT
ejpam-2608	150	1	thus	thus	ADV
ejpam-2608	150	2	,	,	PUNCT
ejpam-2608	150	3	∂γ	∂γ	PROPN
ejpam-2608	150	4	=	=	PUNCT
ejpam-2608	150	5	∂∂̄µ	∂∂̄µ	X
ejpam-2608	151	1	=	=	SYM
ejpam-2608	151	2	0	0	NUM
ejpam-2608	151	3	.	.	PUNCT
ejpam-2608	152	1	this	this	PRON
ejpam-2608	152	2	shows	show	VERB
ejpam-2608	152	3	[	[	X
ejpam-2608	152	4	γ]bc	γ]bc	X
ejpam-2608	152	5	=	=	PUNCT
ejpam-2608	152	6	∂̄([µ]a	∂̄([µ]a	X
ejpam-2608	152	7	)	)	PUNCT
ejpam-2608	152	8	and	and	CCONJ
ejpam-2608	152	9	[	[	X
ejpam-2608	152	10	γ]bc	γ]bc	NOUN
ejpam-2608	152	11	∈	∈	PROPN
ejpam-2608	152	12	im(∂̄	im(∂̄	NOUN
ejpam-2608	152	13	:	:	PUNCT
ejpam-2608	152	14	hp	hp	PROPN
ejpam-2608	152	15	,	,	PUNCT
ejpam-2608	152	16	q−1	q−1	PROPN
ejpam-2608	152	17	a	a	DET
ejpam-2608	152	18	→	→	SYM
ejpam-2608	152	19	hp	hp	PROPN
ejpam-2608	152	20	,	,	PUNCT
ejpam-2608	152	21	q	q	NOUN
ejpam-2608	152	22	bc	bc	PROPN
ejpam-2608	152	23	)	)	PUNCT
ejpam-2608	152	24	.	.	PUNCT
ejpam-2608	153	1	hence	hence	ADV
ejpam-2608	153	2	,	,	PUNCT
ejpam-2608	153	3	ker(/im(∂̄	ker(/im(∂̄	PROPN
ejpam-2608	153	4	)	)	PUNCT
ejpam-2608	153	5	:	:	PUNCT
ejpam-2608	154	1	hp	hp	PROPN
ejpam-2608	154	2	,	,	PUNCT
ejpam-2608	154	3	q	q	PROPN
ejpam-2608	154	4	bc	bc	PROPN
ejpam-2608	154	5	→	→	SYM
ejpam-2608	154	6	hp	hp	PROPN
ejpam-2608	154	7	,	,	PUNCT
ejpam-2608	154	8	q	q	NOUN
ejpam-2608	154	9	∂̄	∂̄	NOUN
ejpam-2608	154	10	)	)	PUNCT
ejpam-2608	155	1	⊆	⊆	NUM
ejpam-2608	155	2	im(∂̄	im(∂̄	NUM
ejpam-2608	155	3	:	:	PUNCT
ejpam-2608	155	4	hp	hp	PROPN
ejpam-2608	155	5	,	,	PUNCT
ejpam-2608	155	6	q−1	q−1	PROPN
ejpam-2608	155	7	a	a	DET
ejpam-2608	155	8	→	→	SYM
ejpam-2608	155	9	hp	hp	PROPN
ejpam-2608	155	10	,	,	PUNCT
ejpam-2608	155	11	q	q	NOUN
ejpam-2608	155	12	bc	bc	PROPN
ejpam-2608	155	13	)	)	PUNCT
ejpam-2608	155	14	and	and	CCONJ
ejpam-2608	155	15	the	the	DET
ejpam-2608	155	16	two	two	NUM
ejpam-2608	155	17	inclusions	inclusion	NOUN
ejpam-2608	155	18	give	give	VERB
ejpam-2608	155	19	the	the	DET
ejpam-2608	155	20	equality	equality	NOUN
ejpam-2608	155	21	,	,	PUNCT
ejpam-2608	155	22	ker(/im(∂̄	ker(/im(∂̄	PROPN
ejpam-2608	155	23	)	)	PUNCT
ejpam-2608	155	24	:	:	PUNCT
ejpam-2608	156	1	hp	hp	PROPN
ejpam-2608	156	2	,	,	PUNCT
ejpam-2608	156	3	q	q	PROPN
ejpam-2608	156	4	bc	bc	PROPN
ejpam-2608	156	5	→	→	SYM
ejpam-2608	156	6	hp	hp	PROPN
ejpam-2608	156	7	,	,	PUNCT
ejpam-2608	156	8	q	q	NOUN
ejpam-2608	156	9	∂̄	∂̄	NOUN
ejpam-2608	156	10	)	)	PUNCT
ejpam-2608	157	1	⊆	⊆	NUM
ejpam-2608	157	2	im(∂̄	im(∂̄	NUM
ejpam-2608	157	3	:	:	PUNCT
ejpam-2608	157	4	hp	hp	PROPN
ejpam-2608	157	5	,	,	PUNCT
ejpam-2608	157	6	q−1	q−1	PROPN
ejpam-2608	157	7	a	a	DET
ejpam-2608	157	8	→	→	SYM
ejpam-2608	157	9	hp	hp	PROPN
ejpam-2608	157	10	,	,	PUNCT
ejpam-2608	157	11	q	q	NOUN
ejpam-2608	157	12	bc	bc	PROPN
ejpam-2608	157	13	)	)	PUNCT
ejpam-2608	157	14	.	.	PUNCT
ejpam-2608	158	1	lemma	lemma	PROPN
ejpam-2608	158	2	5	5	NUM
ejpam-2608	158	3	.	.	PUNCT
ejpam-2608	159	1	if	if	SCONJ
ejpam-2608	159	2	the	the	DET
ejpam-2608	159	3	betti	betti	ADJ
ejpam-2608	159	4	number	number	NOUN
ejpam-2608	159	5	,	,	PUNCT
ejpam-2608	159	6	bp+q	bp+q	NOUN
ejpam-2608	159	7	=	=	PUNCT
ejpam-2608	159	8	0	0	NUM
ejpam-2608	159	9	on	on	ADP
ejpam-2608	159	10	our	our	PRON
ejpam-2608	159	11	complex	complex	ADJ
ejpam-2608	159	12	manifold	manifold	NOUN
ejpam-2608	159	13	,	,	PUNCT
ejpam-2608	159	14	x	x	PRON
ejpam-2608	159	15	,	,	PUNCT
ejpam-2608	159	16	then	then	ADV
ejpam-2608	159	17	the	the	DET
ejpam-2608	159	18	sequence	sequence	NOUN
ejpam-2608	159	19	above	above	ADV
ejpam-2608	159	20	is	be	AUX
ejpam-2608	159	21	exact	exact	ADJ
ejpam-2608	159	22	at	at	ADP
ejpam-2608	159	23	hp	hp	PROPN
ejpam-2608	159	24	,	,	PUNCT
ejpam-2608	159	25	q	q	NOUN
ejpam-2608	159	26	∂̄	∂̄	NOUN
ejpam-2608	159	27	.	.	PUNCT
ejpam-2608	160	1	more	more	ADV
ejpam-2608	160	2	specifically	specifically	ADV
ejpam-2608	160	3	,	,	PUNCT
ejpam-2608	160	4	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	160	5	)	)	PUNCT
ejpam-2608	160	6	:	:	PUNCT
ejpam-2608	161	1	hp	hp	PROPN
ejpam-2608	161	2	,	,	PUNCT
ejpam-2608	161	3	q	q	PROPN
ejpam-2608	161	4	bc	bc	PROPN
ejpam-2608	161	5	→	→	SYM
ejpam-2608	161	6	hp	hp	PROPN
ejpam-2608	161	7	,	,	PUNCT
ejpam-2608	161	8	q	q	NOUN
ejpam-2608	161	9	∂̄	∂̄	ADJ
ejpam-2608	161	10	)	)	PUNCT
ejpam-2608	161	11	=	=	SYM
ejpam-2608	161	12	ker(/(im(∂̄	ker(/(im(∂̄	X
ejpam-2608	161	13	)	)	PUNCT
ejpam-2608	161	14	+	+	NUM
ejpam-2608	161	15	im(∂	im(∂	NOUN
ejpam-2608	161	16	)	)	PUNCT
ejpam-2608	161	17	)	)	PUNCT
ejpam-2608	161	18	:	:	PUNCT
ejpam-2608	162	1	hp	hp	PROPN
ejpam-2608	162	2	,	,	PUNCT
ejpam-2608	162	3	q	q	NOUN
ejpam-2608	162	4	∂̄	∂̄	PROPN
ejpam-2608	162	5	→	→	SYM
ejpam-2608	162	6	hp	hp	PROPN
ejpam-2608	162	7	,	,	PUNCT
ejpam-2608	162	8	q	q	NOUN
ejpam-2608	162	9	a	a	NOUN
ejpam-2608	162	10	)	)	PUNCT
ejpam-2608	162	11	.	.	PUNCT
ejpam-2608	163	1	proof	proof	NOUN
ejpam-2608	163	2	.	.	PUNCT
ejpam-2608	164	1	let	let	VERB
ejpam-2608	164	2	[	[	PUNCT
ejpam-2608	164	3	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	164	4	∈	∈	NOUN
ejpam-2608	164	5	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	164	6	)	)	PUNCT
ejpam-2608	164	7	:	:	PUNCT
ejpam-2608	165	1	hp	hp	PROPN
ejpam-2608	165	2	,	,	PUNCT
ejpam-2608	165	3	q	q	PROPN
ejpam-2608	165	4	bc	bc	PROPN
ejpam-2608	165	5	→	→	SYM
ejpam-2608	165	6	hp	hp	PROPN
ejpam-2608	165	7	,	,	PUNCT
ejpam-2608	165	8	q	q	NOUN
ejpam-2608	165	9	∂̄	∂̄	ADJ
ejpam-2608	165	10	)	)	PUNCT
ejpam-2608	165	11	.	.	PUNCT
ejpam-2608	166	1	we	we	PRON
ejpam-2608	166	2	have	have	VERB
ejpam-2608	166	3	dφ	dφ	ADJ
ejpam-2608	166	4	=	=	PUNCT
ejpam-2608	166	5	∂φ+	∂φ+	NOUN
ejpam-2608	166	6	∂̄φ	∂̄φ	PROPN
ejpam-2608	166	7	=	=	SYM
ejpam-2608	166	8	0	0	X
ejpam-2608	166	9	.	.	PUNCT
ejpam-2608	167	1	since	since	SCONJ
ejpam-2608	167	2	bp+q	bp+q	NUM
ejpam-2608	167	3	=	=	SYM
ejpam-2608	167	4	0	0	NUM
ejpam-2608	167	5	,	,	PUNCT
ejpam-2608	167	6	we	we	PRON
ejpam-2608	167	7	have	have	VERB
ejpam-2608	167	8	that	that	DET
ejpam-2608	167	9	φ	φ	PROPN
ejpam-2608	167	10	=	=	SYM
ejpam-2608	167	11	dλ	dλ	NOUN
ejpam-2608	167	12	for	for	ADP
ejpam-2608	167	13	some	some	DET
ejpam-2608	167	14	p+q−1	p+q−1	NOUN
ejpam-2608	167	15	-	-	PUNCT
ejpam-2608	167	16	form	form	NOUN
ejpam-2608	167	17	,	,	PUNCT
ejpam-2608	167	18	λ	λ	PROPN
ejpam-2608	167	19	on	on	ADP
ejpam-2608	167	20	x.	x.	NOUN
ejpam-2608	167	21	thus	thus	ADV
ejpam-2608	167	22	φ	φ	PROPN
ejpam-2608	167	23	=	=	SYM
ejpam-2608	167	24	∂λp−1,q	∂λp−1,q	NOUN
ejpam-2608	167	25	+	+	CCONJ
ejpam-2608	167	26	∂̄λp	∂̄λp	PROPN
ejpam-2608	167	27	,	,	PUNCT
ejpam-2608	167	28	q−1	q−1	PROPN
ejpam-2608	167	29	where	where	SCONJ
ejpam-2608	167	30	∂λp−1,q	∂λp−1,q	NOUN
ejpam-2608	167	31	and	and	CCONJ
ejpam-2608	167	32	∂̄λp	∂̄λp	PROPN
ejpam-2608	167	33	,	,	PUNCT
ejpam-2608	167	34	q−1	q−1	PROPN
ejpam-2608	167	35	are	be	AUX
ejpam-2608	167	36	the	the	DET
ejpam-2608	167	37	projections	projection	NOUN
ejpam-2608	167	38	of	of	ADP
ejpam-2608	167	39	λ	λ	PROPN
ejpam-2608	167	40	to	to	ADP
ejpam-2608	167	41	its	its	PRON
ejpam-2608	167	42	p−	p−	NOUN
ejpam-2608	167	43	1	1	NUM
ejpam-2608	167	44	,	,	PUNCT
ejpam-2608	167	45	q	q	NOUN
ejpam-2608	167	46	and	and	CCONJ
ejpam-2608	167	47	p	p	X
ejpam-2608	167	48	,	,	PUNCT
ejpam-2608	167	49	q	q	NOUN
ejpam-2608	167	50	−	−	PROPN
ejpam-2608	167	51	1	1	NUM
ejpam-2608	167	52	parts	part	NOUN
ejpam-2608	167	53	respectively	respectively	ADV
ejpam-2608	167	54	.	.	PUNCT
ejpam-2608	168	1	thus	thus	ADV
ejpam-2608	168	2	[	[	X
ejpam-2608	168	3	φ]a	φ]a	X
ejpam-2608	168	4	=	=	SYM
ejpam-2608	168	5	0	0	NUM
ejpam-2608	168	6	in	in	ADP
ejpam-2608	168	7	hp	hp	PROPN
ejpam-2608	168	8	,	,	PUNCT
ejpam-2608	168	9	q	q	NOUN
ejpam-2608	168	10	a	a	X
ejpam-2608	168	11	,	,	PUNCT
ejpam-2608	168	12	and	and	CCONJ
ejpam-2608	168	13	[	[	X
ejpam-2608	168	14	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	168	15	∈	∈	NOUN
ejpam-2608	168	16	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	168	17	)	)	PUNCT
ejpam-2608	168	18	+	+	NUM
ejpam-2608	168	19	im(∂	im(∂	NOUN
ejpam-2608	168	20	)	)	PUNCT
ejpam-2608	168	21	)	)	PUNCT
ejpam-2608	168	22	:	:	PUNCT
ejpam-2608	168	23	hp	hp	PROPN
ejpam-2608	168	24	,	,	PUNCT
ejpam-2608	168	25	q	q	NOUN
ejpam-2608	168	26	∂̄	∂̄	PROPN
ejpam-2608	168	27	→	→	SYM
ejpam-2608	168	28	hp	hp	PROPN
ejpam-2608	168	29	,	,	PUNCT
ejpam-2608	168	30	q	q	NOUN
ejpam-2608	168	31	a	a	NOUN
ejpam-2608	168	32	)	)	PUNCT
ejpam-2608	168	33	and	and	CCONJ
ejpam-2608	168	34	we	we	PRON
ejpam-2608	168	35	have	have	AUX
ejpam-2608	168	36	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	168	37	)	)	PUNCT
ejpam-2608	168	38	:	:	PUNCT
ejpam-2608	168	39	hp	hp	PROPN
ejpam-2608	168	40	,	,	PUNCT
ejpam-2608	168	41	q	q	PROPN
ejpam-2608	168	42	bc	bc	PROPN
ejpam-2608	168	43	→	→	SYM
ejpam-2608	168	44	hp	hp	PROPN
ejpam-2608	168	45	,	,	PUNCT
ejpam-2608	168	46	q	q	NOUN
ejpam-2608	168	47	∂̄	∂̄	NOUN
ejpam-2608	168	48	)	)	PUNCT
ejpam-2608	168	49	⊆	⊆	NUM
ejpam-2608	168	50	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	168	51	)	)	PUNCT
ejpam-2608	168	52	+	+	NUM
ejpam-2608	168	53	im(∂	im(∂	NOUN
ejpam-2608	168	54	)	)	PUNCT
ejpam-2608	168	55	)	)	PUNCT
ejpam-2608	168	56	:	:	PUNCT
ejpam-2608	169	1	hp	hp	PROPN
ejpam-2608	169	2	,	,	PUNCT
ejpam-2608	169	3	q	q	NOUN
ejpam-2608	169	4	∂̄	∂̄	PROPN
ejpam-2608	169	5	→	→	SYM
ejpam-2608	169	6	hp	hp	PROPN
ejpam-2608	169	7	,	,	PUNCT
ejpam-2608	169	8	q	q	NOUN
ejpam-2608	169	9	a	a	NOUN
ejpam-2608	169	10	)	)	PUNCT
ejpam-2608	169	11	.	.	PUNCT
ejpam-2608	170	1	now	now	ADV
ejpam-2608	170	2	let	let	VERB
ejpam-2608	170	3	[	[	PUNCT
ejpam-2608	170	4	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	170	5	∈	∈	NOUN
ejpam-2608	170	6	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	170	7	)	)	PUNCT
ejpam-2608	170	8	+	+	NUM
ejpam-2608	170	9	im(∂	im(∂	NOUN
ejpam-2608	170	10	)	)	PUNCT
ejpam-2608	170	11	)	)	PUNCT
ejpam-2608	170	12	:	:	PUNCT
ejpam-2608	171	1	hp	hp	PROPN
ejpam-2608	171	2	,	,	PUNCT
ejpam-2608	171	3	q	q	NOUN
ejpam-2608	171	4	∂̄	∂̄	PROPN
ejpam-2608	171	5	→	→	SYM
ejpam-2608	171	6	hp	hp	PROPN
ejpam-2608	171	7	,	,	PUNCT
ejpam-2608	171	8	q	q	NOUN
ejpam-2608	171	9	a	a	NOUN
ejpam-2608	171	10	)	)	PUNCT
ejpam-2608	171	11	.	.	PUNCT
ejpam-2608	172	1	note	note	VERB
ejpam-2608	172	2	that	that	SCONJ
ejpam-2608	172	3	φ	φ	PROPN
ejpam-2608	172	4	is	be	AUX
ejpam-2608	172	5	∂̄-closed	∂̄-close	VERB
ejpam-2608	172	6	.	.	PUNCT
ejpam-2608	173	1	since	since	SCONJ
ejpam-2608	173	2	[	[	X
ejpam-2608	173	3	φ]a	φ]a	NOUN
ejpam-2608	173	4	=	=	SYM
ejpam-2608	173	5	0	0	NUM
ejpam-2608	173	6	,	,	PUNCT
ejpam-2608	173	7	we	we	PRON
ejpam-2608	173	8	have	have	VERB
ejpam-2608	173	9	φ	φ	NOUN
ejpam-2608	173	10	=	=	SYM
ejpam-2608	173	11	∂µ+	∂µ+	NOUN
ejpam-2608	173	12	∂̄ν	∂̄ν	NOUN
ejpam-2608	173	13	for	for	ADP
ejpam-2608	173	14	some	some	DET
ejpam-2608	173	15	p−	p−	NOUN
ejpam-2608	173	16	1	1	NUM
ejpam-2608	173	17	,	,	PUNCT
ejpam-2608	173	18	q	q	ADJ
ejpam-2608	173	19	-	-	PUNCT
ejpam-2608	173	20	form	form	NOUN
ejpam-2608	173	21	µ	µ	NOUN
ejpam-2608	173	22	and	and	CCONJ
ejpam-2608	173	23	some	some	DET
ejpam-2608	173	24	p	p	NOUN
ejpam-2608	173	25	,	,	PUNCT
ejpam-2608	173	26	q	q	NOUN
ejpam-2608	173	27	−	−	PROPN
ejpam-2608	173	28	1	1	NUM
ejpam-2608	173	29	-	-	PUNCT
ejpam-2608	173	30	form	form	NOUN
ejpam-2608	173	31	,	,	PUNCT
ejpam-2608	173	32	ν	ν	X
ejpam-2608	173	33	.	.	PROPN
ejpam-2608	174	1	since	since	SCONJ
ejpam-2608	174	2	∂̄φ	∂̄φ	PROPN
ejpam-2608	174	3	=	=	SYM
ejpam-2608	174	4	0	0	NUM
ejpam-2608	174	5	we	we	PRON
ejpam-2608	174	6	have	have	VERB
ejpam-2608	174	7	∂̄(∂µ	∂̄(∂µ	PROPN
ejpam-2608	174	8	)	)	PUNCT
ejpam-2608	175	1	=	=	SYM
ejpam-2608	175	2	0	0	NUM
ejpam-2608	176	1	and	and	CCONJ
ejpam-2608	176	2	[	[	X
ejpam-2608	176	3	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	176	4	=	=	PUNCT
ejpam-2608	177	1	[	[	X
ejpam-2608	177	2	∂µ	∂µ	X
ejpam-2608	177	3	]	]	X
ejpam-2608	177	4	in	in	ADP
ejpam-2608	177	5	hp	hp	PROPN
ejpam-2608	177	6	,	,	PUNCT
ejpam-2608	177	7	q	q	NOUN
ejpam-2608	177	8	∂̄	∂̄	NOUN
ejpam-2608	177	9	.	.	PUNCT
ejpam-2608	178	1	we	we	PRON
ejpam-2608	178	2	also	also	ADV
ejpam-2608	178	3	have	have	VERB
ejpam-2608	178	4	obviously	obviously	ADV
ejpam-2608	178	5	that	that	DET
ejpam-2608	178	6	∂(∂µ	∂(∂µ	NOUN
ejpam-2608	178	7	)	)	PUNCT
ejpam-2608	178	8	=	=	SYM
ejpam-2608	178	9	0	0	NUM
ejpam-2608	178	10	and	and	CCONJ
ejpam-2608	178	11	thus	thus	ADV
ejpam-2608	178	12	[	[	X
ejpam-2608	178	13	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	178	14	=	=	SYM
ejpam-2608	178	15	(	(	PUNCT
ejpam-2608	178	16	/im(∂̄))([∂µ]bc	/im(∂̄))([∂µ]bc	PUNCT
ejpam-2608	178	17	)	)	PUNCT
ejpam-2608	178	18	∈	∈	PROPN
ejpam-2608	178	19	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	178	20	)	)	PUNCT
ejpam-2608	178	21	:	:	PUNCT
ejpam-2608	179	1	hp	hp	PROPN
ejpam-2608	179	2	,	,	PUNCT
ejpam-2608	179	3	q	q	PROPN
ejpam-2608	179	4	bc	bc	PROPN
ejpam-2608	179	5	→	→	SYM
ejpam-2608	179	6	hp	hp	PROPN
ejpam-2608	179	7	,	,	PUNCT
ejpam-2608	179	8	q	q	NOUN
ejpam-2608	179	9	∂̄	∂̄	ADJ
ejpam-2608	179	10	)	)	PUNCT
ejpam-2608	179	11	.	.	PUNCT
ejpam-2608	180	1	and	and	CCONJ
ejpam-2608	180	2	hence	hence	ADV
ejpam-2608	180	3	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	180	4	)	)	PUNCT
ejpam-2608	181	1	+	+	NUM
ejpam-2608	181	2	im(∂	im(∂	NOUN
ejpam-2608	181	3	)	)	PUNCT
ejpam-2608	181	4	)	)	PUNCT
ejpam-2608	181	5	:	:	PUNCT
ejpam-2608	182	1	hp	hp	PROPN
ejpam-2608	182	2	,	,	PUNCT
ejpam-2608	182	3	q	q	NOUN
ejpam-2608	182	4	∂̄	∂̄	PROPN
ejpam-2608	182	5	→	→	SYM
ejpam-2608	182	6	hp	hp	PROPN
ejpam-2608	182	7	,	,	PUNCT
ejpam-2608	182	8	q	q	PROPN
ejpam-2608	182	9	a	a	NOUN
ejpam-2608	182	10	)	)	PUNCT
ejpam-2608	182	11	⊆	⊆	NUM
ejpam-2608	182	12	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	182	13	)	)	PUNCT
ejpam-2608	182	14	:	:	PUNCT
ejpam-2608	183	1	hp	hp	PROPN
ejpam-2608	183	2	,	,	PUNCT
ejpam-2608	183	3	q	q	PROPN
ejpam-2608	183	4	bc	bc	PROPN
ejpam-2608	183	5	→	→	SYM
ejpam-2608	183	6	hp	hp	PROPN
ejpam-2608	183	7	,	,	PUNCT
ejpam-2608	183	8	q	q	NOUN
ejpam-2608	183	9	∂̄	∂̄	ADJ
ejpam-2608	183	10	)	)	PUNCT
ejpam-2608	183	11	.	.	PUNCT
ejpam-2608	184	1	a.	a.	PROPN
ejpam-2608	184	2	mchugh	mchugh	PROPN
ejpam-2608	184	3	/	/	SYM
ejpam-2608	184	4	eur	eur	PROPN
ejpam-2608	184	5	.	.	PUNCT
ejpam-2608	185	1	j.	j.	PROPN
ejpam-2608	185	2	pure	pure	PROPN
ejpam-2608	185	3	appl	appl	PROPN
ejpam-2608	185	4	.	.	PROPN
ejpam-2608	185	5	math	math	PROPN
ejpam-2608	185	6	,	,	PUNCT
ejpam-2608	185	7	10	10	NUM
ejpam-2608	185	8	(	(	PUNCT
ejpam-2608	185	9	3	3	NUM
ejpam-2608	185	10	)	)	PUNCT
ejpam-2608	185	11	(	(	PUNCT
ejpam-2608	185	12	2017	2017	NUM
ejpam-2608	185	13	)	)	PUNCT
ejpam-2608	185	14	,	,	PUNCT
ejpam-2608	185	15	440	440	NUM
ejpam-2608	185	16	-	-	SYM
ejpam-2608	185	17	454	454	NUM
ejpam-2608	185	18	447	447	NUM
ejpam-2608	185	19	the	the	DET
ejpam-2608	185	20	two	two	NUM
ejpam-2608	185	21	inclusions	inclusion	NOUN
ejpam-2608	185	22	allow	allow	VERB
ejpam-2608	185	23	us	we	PRON
ejpam-2608	185	24	to	to	PART
ejpam-2608	185	25	conclude	conclude	VERB
ejpam-2608	185	26	that	that	PRON
ejpam-2608	185	27	ker(/(im(∂̄	ker(/(im(∂̄	PROPN
ejpam-2608	185	28	)	)	PUNCT
ejpam-2608	185	29	+	+	NUM
ejpam-2608	185	30	im(∂	im(∂	NOUN
ejpam-2608	185	31	)	)	PUNCT
ejpam-2608	185	32	)	)	PUNCT
ejpam-2608	185	33	:	:	PUNCT
ejpam-2608	186	1	hp	hp	PROPN
ejpam-2608	186	2	,	,	PUNCT
ejpam-2608	186	3	q	q	NOUN
ejpam-2608	186	4	∂̄	∂̄	PROPN
ejpam-2608	186	5	→	→	SYM
ejpam-2608	186	6	hp	hp	PROPN
ejpam-2608	186	7	,	,	PUNCT
ejpam-2608	186	8	q	q	NOUN
ejpam-2608	186	9	a	a	NOUN
ejpam-2608	186	10	)	)	PUNCT
ejpam-2608	186	11	=	=	SYM
ejpam-2608	186	12	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	186	13	)	)	PUNCT
ejpam-2608	186	14	:	:	PUNCT
ejpam-2608	187	1	hp	hp	PROPN
ejpam-2608	187	2	,	,	PUNCT
ejpam-2608	187	3	q	q	PROPN
ejpam-2608	187	4	bc	bc	PROPN
ejpam-2608	187	5	→	→	SYM
ejpam-2608	187	6	hp	hp	PROPN
ejpam-2608	187	7	,	,	PUNCT
ejpam-2608	187	8	q	q	NOUN
ejpam-2608	187	9	∂̄	∂̄	ADJ
ejpam-2608	187	10	)	)	PUNCT
ejpam-2608	187	11	.	.	PUNCT
ejpam-2608	188	1	notice	notice	VERB
ejpam-2608	188	2	above	above	ADV
ejpam-2608	188	3	that	that	SCONJ
ejpam-2608	188	4	we	we	PRON
ejpam-2608	188	5	nowhere	nowhere	ADV
ejpam-2608	188	6	used	use	VERB
ejpam-2608	188	7	that	that	SCONJ
ejpam-2608	188	8	bp+q	bp+q	PRON
ejpam-2608	188	9	=	=	SYM
ejpam-2608	188	10	0	0	NUM
ejpam-2608	188	11	in	in	ADP
ejpam-2608	188	12	proving	prove	VERB
ejpam-2608	188	13	the	the	DET
ejpam-2608	188	14	inclusion	inclusion	NOUN
ejpam-2608	188	15	,	,	PUNCT
ejpam-2608	188	16	[	[	X
ejpam-2608	188	17	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	188	18	∈	∈	NOUN
ejpam-2608	188	19	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	188	20	)	)	PUNCT
ejpam-2608	188	21	+	+	NUM
ejpam-2608	188	22	im(∂	im(∂	NOUN
ejpam-2608	188	23	)	)	PUNCT
ejpam-2608	188	24	)	)	PUNCT
ejpam-2608	188	25	:	:	PUNCT
ejpam-2608	189	1	hp	hp	PROPN
ejpam-2608	189	2	,	,	PUNCT
ejpam-2608	189	3	q	q	NOUN
ejpam-2608	189	4	∂̄	∂̄	PROPN
ejpam-2608	189	5	→	→	SYM
ejpam-2608	189	6	hp	hp	PROPN
ejpam-2608	189	7	,	,	PUNCT
ejpam-2608	189	8	q	q	PROPN
ejpam-2608	189	9	a	a	NOUN
ejpam-2608	189	10	)	)	PUNCT
ejpam-2608	189	11	⊆	⊆	NUM
ejpam-2608	189	12	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	189	13	)	)	PUNCT
ejpam-2608	189	14	:	:	PUNCT
ejpam-2608	190	1	hp	hp	PROPN
ejpam-2608	190	2	,	,	PUNCT
ejpam-2608	190	3	q	q	PROPN
ejpam-2608	190	4	bc	bc	PROPN
ejpam-2608	190	5	→	→	SYM
ejpam-2608	190	6	hp	hp	PROPN
ejpam-2608	190	7	,	,	PUNCT
ejpam-2608	190	8	q	q	NOUN
ejpam-2608	190	9	∂̄	∂̄	ADJ
ejpam-2608	190	10	)	)	PUNCT
ejpam-2608	190	11	.	.	PUNCT
ejpam-2608	191	1	this	this	PRON
ejpam-2608	191	2	suggests	suggest	VERB
ejpam-2608	191	3	that	that	SCONJ
ejpam-2608	191	4	we	we	PRON
ejpam-2608	191	5	define	define	VERB
ejpam-2608	191	6	what	what	PRON
ejpam-2608	191	7	we	we	PRON
ejpam-2608	191	8	shall	shall	AUX
ejpam-2608	191	9	call	call	VERB
ejpam-2608	191	10	bca	bca	NOUN
ejpam-2608	191	11	-	-	PUNCT
ejpam-2608	191	12	cohomology	cohomology	NOUN
ejpam-2608	191	13	:	:	PUNCT
ejpam-2608	191	14	ep	ep	PROPN
ejpam-2608	191	15	,	,	PUNCT
ejpam-2608	191	16	q	q	PROPN
ejpam-2608	191	17	bca	bca	PROPN
ejpam-2608	191	18	=	=	SYM
ejpam-2608	191	19	ker(∂	ker(∂	PROPN
ejpam-2608	191	20	)	)	PUNCT
ejpam-2608	191	21	∩	∩	NOUN
ejpam-2608	191	22	ker(∂̄	ker(∂̄	X
ejpam-2608	191	23	)	)	PUNCT
ejpam-2608	191	24	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	191	25	)	)	PUNCT
ejpam-2608	191	26	∩	∩	ADJ
ejpam-2608	191	27	im(∂	im(∂	NOUN
ejpam-2608	191	28	)	)	PUNCT
ejpam-2608	191	29	+	+	CCONJ
ejpam-2608	191	30	ker(∂	ker(∂	PROPN
ejpam-2608	191	31	)	)	PUNCT
ejpam-2608	191	32	∩	∩	NOUN
ejpam-2608	191	33	im(∂̄	im(∂̄	NOUN
ejpam-2608	191	34	)	)	PUNCT
ejpam-2608	191	35	.	.	PUNCT
ejpam-2608	192	1	this	this	DET
ejpam-2608	192	2	definition	definition	NOUN
ejpam-2608	192	3	is	be	AUX
ejpam-2608	192	4	along	along	ADP
ejpam-2608	192	5	the	the	DET
ejpam-2608	192	6	lines	line	NOUN
ejpam-2608	192	7	of	of	ADP
ejpam-2608	192	8	varouchas[12	varouchas[12	PROPN
ejpam-2608	192	9	]	]	PUNCT
ejpam-2608	192	10	who	who	PRON
ejpam-2608	192	11	defines	define	VERB
ejpam-2608	192	12	similar	similar	ADJ
ejpam-2608	192	13	in	in	ADP
ejpam-2608	192	14	spirit	spirit	PROPN
ejpam-2608	192	15	vector	vector	NOUN
ejpam-2608	192	16	spaces	space	NOUN
ejpam-2608	192	17	to	to	PART
ejpam-2608	192	18	create	create	VERB
ejpam-2608	192	19	long	long	ADJ
ejpam-2608	192	20	exact	exact	ADJ
ejpam-2608	192	21	sequences	sequence	NOUN
ejpam-2608	192	22	involving	involve	VERB
ejpam-2608	192	23	bott	bott	PROPN
ejpam-2608	192	24	-	-	PUNCT
ejpam-2608	192	25	chern	chern	PROPN
ejpam-2608	192	26	,	,	PUNCT
ejpam-2608	192	27	dolbeault	dolbeault	NOUN
ejpam-2608	192	28	,	,	PUNCT
ejpam-2608	192	29	and	and	CCONJ
ejpam-2608	192	30	aeppli	aeppli	VERB
ejpam-2608	192	31	cohomology	cohomology	NOUN
ejpam-2608	192	32	.	.	PUNCT
ejpam-2608	193	1	we	we	PRON
ejpam-2608	193	2	refer	refer	VERB
ejpam-2608	193	3	the	the	DET
ejpam-2608	193	4	reader	reader	NOUN
ejpam-2608	193	5	also	also	ADV
ejpam-2608	193	6	to	to	ADP
ejpam-2608	193	7	angella[1	angella[1	VERB
ejpam-2608	193	8	]	]	PUNCT
ejpam-2608	193	9	for	for	ADP
ejpam-2608	193	10	more	more	ADJ
ejpam-2608	193	11	details	detail	NOUN
ejpam-2608	193	12	.	.	PUNCT
ejpam-2608	194	1	it	it	PRON
ejpam-2608	194	2	is	be	AUX
ejpam-2608	194	3	easy	easy	ADJ
ejpam-2608	194	4	to	to	PART
ejpam-2608	194	5	show	show	VERB
ejpam-2608	194	6	that	that	SCONJ
ejpam-2608	194	7	if	if	SCONJ
ejpam-2608	194	8	bp+q	bp+q	ADJ
ejpam-2608	194	9	=	=	NOUN
ejpam-2608	194	10	0	0	NUM
ejpam-2608	194	11	then	then	ADV
ejpam-2608	194	12	ep	ep	PROPN
ejpam-2608	194	13	,	,	PUNCT
ejpam-2608	194	14	q	q	PROPN
ejpam-2608	194	15	bca	bca	PROPN
ejpam-2608	194	16	=	=	PUNCT
ejpam-2608	194	17	{	{	PUNCT
ejpam-2608	194	18	0	0	NUM
ejpam-2608	194	19	}	}	PUNCT
ejpam-2608	194	20	.	.	PUNCT
ejpam-2608	195	1	we	we	PRON
ejpam-2608	195	2	have	have	VERB
ejpam-2608	195	3	the	the	DET
ejpam-2608	195	4	following	follow	VERB
ejpam-2608	195	5	claim	claim	NOUN
ejpam-2608	195	6	:	:	PUNCT
ejpam-2608	195	7	lemma	lemma	PROPN
ejpam-2608	195	8	6	6	NUM
ejpam-2608	195	9	.	.	PUNCT
ejpam-2608	196	1	for	for	ADP
ejpam-2608	196	2	a	a	DET
ejpam-2608	196	3	compact	compact	ADJ
ejpam-2608	196	4	complex	complex	ADJ
ejpam-2608	196	5	manifold	manifold	NOUN
ejpam-2608	196	6	,	,	PUNCT
ejpam-2608	196	7	x	x	PRON
ejpam-2608	196	8	,	,	PUNCT
ejpam-2608	196	9	the	the	DET
ejpam-2608	196	10	sequence	sequence	NOUN
ejpam-2608	196	11	above	above	ADV
ejpam-2608	196	12	is	be	AUX
ejpam-2608	196	13	exact	exact	ADJ
ejpam-2608	196	14	at	at	ADP
ejpam-2608	196	15	hp	hp	PROPN
ejpam-2608	196	16	,	,	PUNCT
ejpam-2608	196	17	q	q	X
ejpam-2608	196	18	∂̄	∂̄	ADV
ejpam-2608	196	19	if	if	SCONJ
ejpam-2608	197	1	and	and	CCONJ
ejpam-2608	197	2	only	only	ADV
ejpam-2608	197	3	if	if	SCONJ
ejpam-2608	197	4	ep	ep	PROPN
ejpam-2608	197	5	,	,	PUNCT
ejpam-2608	197	6	q	q	PROPN
ejpam-2608	197	7	bca	bca	PROPN
ejpam-2608	197	8	=	=	PUNCT
ejpam-2608	197	9	{	{	PUNCT
ejpam-2608	197	10	0	0	NUM
ejpam-2608	197	11	}	}	PUNCT
ejpam-2608	197	12	.	.	PUNCT
ejpam-2608	198	1	proof	proof	NOUN
ejpam-2608	198	2	.	.	PUNCT
ejpam-2608	199	1	let	let	VERB
ejpam-2608	199	2	us	we	PRON
ejpam-2608	199	3	first	first	ADV
ejpam-2608	199	4	assume	assume	VERB
ejpam-2608	199	5	that	that	SCONJ
ejpam-2608	199	6	ep	ep	PROPN
ejpam-2608	199	7	,	,	PUNCT
ejpam-2608	199	8	q	q	PROPN
ejpam-2608	199	9	bca	bca	PROPN
ejpam-2608	199	10	=	=	PUNCT
ejpam-2608	199	11	{	{	PUNCT
ejpam-2608	199	12	0	0	NUM
ejpam-2608	199	13	}	}	PUNCT
ejpam-2608	199	14	.	.	PUNCT
ejpam-2608	200	1	we	we	PRON
ejpam-2608	200	2	need	need	VERB
ejpam-2608	200	3	to	to	PART
ejpam-2608	200	4	only	only	ADV
ejpam-2608	200	5	to	to	PART
ejpam-2608	200	6	show	show	VERB
ejpam-2608	200	7	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	200	8	)	)	PUNCT
ejpam-2608	200	9	:	:	PUNCT
ejpam-2608	201	1	hp	hp	PROPN
ejpam-2608	201	2	,	,	PUNCT
ejpam-2608	201	3	q	q	PROPN
ejpam-2608	201	4	bc	bc	PROPN
ejpam-2608	201	5	→	→	SYM
ejpam-2608	201	6	hp	hp	PROPN
ejpam-2608	201	7	,	,	PUNCT
ejpam-2608	201	8	q	q	NOUN
ejpam-2608	201	9	∂̄	∂̄	NOUN
ejpam-2608	201	10	)	)	PUNCT
ejpam-2608	201	11	⊆	⊆	NUM
ejpam-2608	201	12	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	201	13	)	)	PUNCT
ejpam-2608	201	14	+	+	NUM
ejpam-2608	201	15	im(∂	im(∂	NOUN
ejpam-2608	201	16	)	)	PUNCT
ejpam-2608	201	17	)	)	PUNCT
ejpam-2608	201	18	:	:	PUNCT
ejpam-2608	202	1	hp	hp	PROPN
ejpam-2608	202	2	,	,	PUNCT
ejpam-2608	202	3	q	q	NOUN
ejpam-2608	202	4	∂̄	∂̄	PROPN
ejpam-2608	202	5	→	→	SYM
ejpam-2608	202	6	hp	hp	PROPN
ejpam-2608	202	7	,	,	PUNCT
ejpam-2608	202	8	q	q	NOUN
ejpam-2608	202	9	a	a	NOUN
ejpam-2608	202	10	)	)	PUNCT
ejpam-2608	202	11	since	since	SCONJ
ejpam-2608	202	12	the	the	DET
ejpam-2608	202	13	reverse	reverse	ADJ
ejpam-2608	202	14	inclusion	inclusion	NOUN
ejpam-2608	202	15	has	have	AUX
ejpam-2608	202	16	already	already	ADV
ejpam-2608	202	17	been	be	AUX
ejpam-2608	202	18	shown	show	VERB
ejpam-2608	202	19	true	true	ADJ
ejpam-2608	202	20	in	in	ADP
ejpam-2608	202	21	general	general	ADJ
ejpam-2608	202	22	.	.	PUNCT
ejpam-2608	203	1	let	let	VERB
ejpam-2608	203	2	[	[	PUNCT
ejpam-2608	203	3	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	203	4	∈	∈	NOUN
ejpam-2608	203	5	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	203	6	)	)	PUNCT
ejpam-2608	203	7	:	:	PUNCT
ejpam-2608	204	1	hp	hp	PROPN
ejpam-2608	204	2	,	,	PUNCT
ejpam-2608	204	3	q	q	PROPN
ejpam-2608	204	4	bc	bc	PROPN
ejpam-2608	204	5	→	→	SYM
ejpam-2608	204	6	hp	hp	PROPN
ejpam-2608	204	7	,	,	PUNCT
ejpam-2608	204	8	q	q	NOUN
ejpam-2608	204	9	∂̄	∂̄	ADJ
ejpam-2608	204	10	)	)	PUNCT
ejpam-2608	204	11	.	.	PUNCT
ejpam-2608	205	1	we	we	PRON
ejpam-2608	205	2	may	may	AUX
ejpam-2608	205	3	assume	assume	VERB
ejpam-2608	205	4	φ	φ	PROPN
ejpam-2608	205	5	∈	∈	PROPN
ejpam-2608	205	6	ker(∂	ker(∂	PROPN
ejpam-2608	205	7	)	)	PUNCT
ejpam-2608	205	8	∩	∩	NOUN
ejpam-2608	205	9	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	205	10	)	)	PUNCT
ejpam-2608	205	11	.	.	PUNCT
ejpam-2608	206	1	since	since	SCONJ
ejpam-2608	206	2	ep	ep	PROPN
ejpam-2608	206	3	,	,	PUNCT
ejpam-2608	206	4	q	q	PROPN
ejpam-2608	206	5	bca	bca	PROPN
ejpam-2608	206	6	=	=	PUNCT
ejpam-2608	206	7	{	{	PUNCT
ejpam-2608	206	8	0	0	NUM
ejpam-2608	206	9	}	}	PUNCT
ejpam-2608	206	10	,	,	PUNCT
ejpam-2608	206	11	we	we	PRON
ejpam-2608	206	12	have	have	VERB
ejpam-2608	206	13	φ	φ	PROPN
ejpam-2608	206	14	∈	∈	PROPN
ejpam-2608	206	15	(	(	PUNCT
ejpam-2608	206	16	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	206	17	)	)	PUNCT
ejpam-2608	206	18	∩	∩	ADJ
ejpam-2608	206	19	im(∂	im(∂	NOUN
ejpam-2608	206	20	)	)	PUNCT
ejpam-2608	207	1	+	+	CCONJ
ejpam-2608	207	2	ker(∂	ker(∂	PROPN
ejpam-2608	207	3	)	)	PUNCT
ejpam-2608	207	4	∩	∩	NOUN
ejpam-2608	207	5	im(∂̄	im(∂̄	NOUN
ejpam-2608	207	6	)	)	PUNCT
ejpam-2608	207	7	)	)	PUNCT
ejpam-2608	208	1	⊆	⊆	NUM
ejpam-2608	208	2	(	(	PUNCT
ejpam-2608	208	3	im(∂	im(∂	NOUN
ejpam-2608	208	4	)	)	PUNCT
ejpam-2608	208	5	+	+	SYM
ejpam-2608	208	6	im(∂̄	im(∂̄	NOUN
ejpam-2608	208	7	)	)	PUNCT
ejpam-2608	208	8	)	)	PUNCT
ejpam-2608	208	9	.	.	PUNCT
ejpam-2608	209	1	hence	hence	ADV
ejpam-2608	209	2	[	[	X
ejpam-2608	209	3	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	209	4	∈	∈	NOUN
ejpam-2608	209	5	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	209	6	)	)	PUNCT
ejpam-2608	209	7	+	+	NUM
ejpam-2608	209	8	im(∂	im(∂	NOUN
ejpam-2608	209	9	)	)	PUNCT
ejpam-2608	209	10	)	)	PUNCT
ejpam-2608	209	11	:	:	PUNCT
ejpam-2608	210	1	hp	hp	PROPN
ejpam-2608	210	2	,	,	PUNCT
ejpam-2608	210	3	q	q	NOUN
ejpam-2608	210	4	∂̄	∂̄	PROPN
ejpam-2608	210	5	→	→	SYM
ejpam-2608	210	6	hp	hp	PROPN
ejpam-2608	210	7	,	,	PUNCT
ejpam-2608	210	8	q	q	NOUN
ejpam-2608	210	9	a	a	NOUN
ejpam-2608	210	10	)	)	PUNCT
ejpam-2608	210	11	and	and	CCONJ
ejpam-2608	210	12	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	210	13	)	)	PUNCT
ejpam-2608	210	14	:	:	PUNCT
ejpam-2608	211	1	hp	hp	PROPN
ejpam-2608	211	2	,	,	PUNCT
ejpam-2608	211	3	q	q	PROPN
ejpam-2608	211	4	bc	bc	PROPN
ejpam-2608	211	5	→	→	SYM
ejpam-2608	211	6	hp	hp	PROPN
ejpam-2608	211	7	,	,	PUNCT
ejpam-2608	211	8	q	q	NOUN
ejpam-2608	211	9	∂̄	∂̄	NOUN
ejpam-2608	211	10	)	)	PUNCT
ejpam-2608	211	11	⊆	⊆	NUM
ejpam-2608	211	12	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	211	13	)	)	PUNCT
ejpam-2608	211	14	+	+	NUM
ejpam-2608	211	15	im(∂	im(∂	NOUN
ejpam-2608	211	16	)	)	PUNCT
ejpam-2608	211	17	)	)	PUNCT
ejpam-2608	211	18	:	:	PUNCT
ejpam-2608	212	1	hp	hp	PROPN
ejpam-2608	212	2	,	,	PUNCT
ejpam-2608	212	3	q	q	NOUN
ejpam-2608	212	4	∂̄	∂̄	PROPN
ejpam-2608	212	5	→	→	SYM
ejpam-2608	212	6	hp	hp	PROPN
ejpam-2608	212	7	,	,	PUNCT
ejpam-2608	212	8	q	q	NOUN
ejpam-2608	212	9	a	a	NOUN
ejpam-2608	212	10	)	)	PUNCT
ejpam-2608	212	11	.	.	PUNCT
ejpam-2608	213	1	thus	thus	ADV
ejpam-2608	213	2	im(/im(∂̄	im(/im(∂̄	VERB
ejpam-2608	213	3	)	)	PUNCT
ejpam-2608	213	4	:	:	PUNCT
ejpam-2608	214	1	hp	hp	PROPN
ejpam-2608	214	2	,	,	PUNCT
ejpam-2608	214	3	q	q	PROPN
ejpam-2608	214	4	bc	bc	PROPN
ejpam-2608	214	5	→	→	SYM
ejpam-2608	214	6	hp	hp	PROPN
ejpam-2608	214	7	,	,	PUNCT
ejpam-2608	214	8	q	q	NOUN
ejpam-2608	214	9	∂̄	∂̄	ADJ
ejpam-2608	214	10	)	)	PUNCT
ejpam-2608	214	11	=	=	SYM
ejpam-2608	214	12	ker(/(im(∂̄	ker(/(im(∂̄	X
ejpam-2608	214	13	)	)	PUNCT
ejpam-2608	214	14	+	+	NUM
ejpam-2608	214	15	im(∂	im(∂	NOUN
ejpam-2608	214	16	)	)	PUNCT
ejpam-2608	214	17	)	)	PUNCT
ejpam-2608	214	18	:	:	PUNCT
ejpam-2608	215	1	hp	hp	PROPN
ejpam-2608	215	2	,	,	PUNCT
ejpam-2608	215	3	q	q	NOUN
ejpam-2608	215	4	∂̄	∂̄	PROPN
ejpam-2608	215	5	→	→	SYM
ejpam-2608	215	6	hp	hp	PROPN
ejpam-2608	215	7	,	,	PUNCT
ejpam-2608	215	8	q	q	NOUN
ejpam-2608	215	9	a	a	NOUN
ejpam-2608	215	10	)	)	PUNCT
ejpam-2608	215	11	.	.	PUNCT
ejpam-2608	216	1	and	and	CCONJ
ejpam-2608	216	2	the	the	DET
ejpam-2608	216	3	sequence	sequence	NOUN
ejpam-2608	216	4	above	above	ADV
ejpam-2608	216	5	is	be	AUX
ejpam-2608	216	6	exact	exact	ADJ
ejpam-2608	216	7	at	at	ADP
ejpam-2608	216	8	hp	hp	PROPN
ejpam-2608	216	9	,	,	PUNCT
ejpam-2608	216	10	q	q	NOUN
ejpam-2608	216	11	∂̄	∂̄	NOUN
ejpam-2608	216	12	.	.	PUNCT
ejpam-2608	217	1	in	in	ADP
ejpam-2608	217	2	the	the	DET
ejpam-2608	217	3	other	other	ADJ
ejpam-2608	217	4	direction	direction	NOUN
ejpam-2608	217	5	we	we	PRON
ejpam-2608	217	6	assume	assume	VERB
ejpam-2608	217	7	the	the	DET
ejpam-2608	217	8	sequence	sequence	NOUN
ejpam-2608	217	9	above	above	ADV
ejpam-2608	217	10	is	be	AUX
ejpam-2608	217	11	exact	exact	ADJ
ejpam-2608	217	12	at	at	ADP
ejpam-2608	217	13	hp	hp	PROPN
ejpam-2608	217	14	,	,	PUNCT
ejpam-2608	217	15	q	q	NOUN
ejpam-2608	217	16	∂̄	∂̄	NOUN
ejpam-2608	217	17	and	and	CCONJ
ejpam-2608	217	18	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	217	19	)	)	PUNCT
ejpam-2608	217	20	:	:	PUNCT
ejpam-2608	218	1	hp	hp	PROPN
ejpam-2608	218	2	,	,	PUNCT
ejpam-2608	218	3	q	q	PROPN
ejpam-2608	218	4	bc	bc	PROPN
ejpam-2608	218	5	→	→	SYM
ejpam-2608	218	6	hp	hp	PROPN
ejpam-2608	218	7	,	,	PUNCT
ejpam-2608	218	8	q	q	NOUN
ejpam-2608	218	9	∂̄	∂̄	ADJ
ejpam-2608	218	10	)	)	PUNCT
ejpam-2608	218	11	=	=	SYM
ejpam-2608	218	12	ker(/(im(∂̄	ker(/(im(∂̄	X
ejpam-2608	218	13	)	)	PUNCT
ejpam-2608	218	14	+	+	NUM
ejpam-2608	218	15	im(∂	im(∂	NOUN
ejpam-2608	218	16	)	)	PUNCT
ejpam-2608	218	17	)	)	PUNCT
ejpam-2608	218	18	:	:	PUNCT
ejpam-2608	219	1	hp	hp	PROPN
ejpam-2608	219	2	,	,	PUNCT
ejpam-2608	219	3	q	q	NOUN
ejpam-2608	219	4	∂̄	∂̄	PROPN
ejpam-2608	219	5	→	→	SYM
ejpam-2608	219	6	hp	hp	PROPN
ejpam-2608	219	7	,	,	PUNCT
ejpam-2608	219	8	q	q	NOUN
ejpam-2608	219	9	a	a	NOUN
ejpam-2608	219	10	)	)	PUNCT
ejpam-2608	219	11	.	.	PUNCT
ejpam-2608	220	1	let	let	VERB
ejpam-2608	220	2	φ	φ	PROPN
ejpam-2608	220	3	∈	∈	PROPN
ejpam-2608	220	4	ker(∂	ker(∂	PROPN
ejpam-2608	220	5	)	)	PUNCT
ejpam-2608	220	6	∩	∩	NOUN
ejpam-2608	220	7	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	220	8	)	)	PUNCT
ejpam-2608	220	9	.	.	PUNCT
ejpam-2608	221	1	then	then	ADV
ejpam-2608	221	2	[	[	X
ejpam-2608	221	3	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	221	4	∈	∈	NOUN
ejpam-2608	221	5	im(/im(∂̄	im(/im(∂̄	NOUN
ejpam-2608	221	6	)	)	PUNCT
ejpam-2608	221	7	:	:	PUNCT
ejpam-2608	222	1	hp	hp	PROPN
ejpam-2608	222	2	,	,	PUNCT
ejpam-2608	222	3	q	q	PROPN
ejpam-2608	222	4	bc	bc	PROPN
ejpam-2608	222	5	→	→	SYM
ejpam-2608	222	6	hp	hp	PROPN
ejpam-2608	222	7	,	,	PUNCT
ejpam-2608	222	8	q	q	NOUN
ejpam-2608	222	9	∂̄	∂̄	ADJ
ejpam-2608	222	10	)	)	PUNCT
ejpam-2608	222	11	a.	a.	PROPN
ejpam-2608	222	12	mchugh	mchugh	PROPN
ejpam-2608	222	13	/	/	SYM
ejpam-2608	222	14	eur	eur	PROPN
ejpam-2608	222	15	.	.	PUNCT
ejpam-2608	223	1	j.	j.	PROPN
ejpam-2608	223	2	pure	pure	PROPN
ejpam-2608	223	3	appl	appl	PROPN
ejpam-2608	223	4	.	.	PROPN
ejpam-2608	223	5	math	math	PROPN
ejpam-2608	223	6	,	,	PUNCT
ejpam-2608	223	7	10	10	NUM
ejpam-2608	223	8	(	(	PUNCT
ejpam-2608	223	9	3	3	NUM
ejpam-2608	223	10	)	)	PUNCT
ejpam-2608	223	11	(	(	PUNCT
ejpam-2608	223	12	2017	2017	NUM
ejpam-2608	223	13	)	)	PUNCT
ejpam-2608	223	14	,	,	PUNCT
ejpam-2608	223	15	440	440	NUM
ejpam-2608	223	16	-	-	SYM
ejpam-2608	223	17	454	454	NUM
ejpam-2608	223	18	448	448	NUM
ejpam-2608	223	19	and	and	CCONJ
ejpam-2608	223	20	thus	thus	ADV
ejpam-2608	223	21	[	[	X
ejpam-2608	223	22	φ]∂̄	φ]∂̄	NOUN
ejpam-2608	223	23	∈	∈	NOUN
ejpam-2608	223	24	ker(/(im(∂̄	ker(/(im(∂̄	NOUN
ejpam-2608	223	25	)	)	PUNCT
ejpam-2608	223	26	+	+	NUM
ejpam-2608	223	27	im(∂	im(∂	NOUN
ejpam-2608	223	28	)	)	PUNCT
ejpam-2608	223	29	)	)	PUNCT
ejpam-2608	223	30	:	:	PUNCT
ejpam-2608	224	1	hp	hp	PROPN
ejpam-2608	224	2	,	,	PUNCT
ejpam-2608	224	3	q	q	NOUN
ejpam-2608	224	4	∂̄	∂̄	PROPN
ejpam-2608	224	5	→	→	SYM
ejpam-2608	224	6	hp	hp	PROPN
ejpam-2608	224	7	,	,	PUNCT
ejpam-2608	224	8	q	q	NOUN
ejpam-2608	224	9	a	a	NOUN
ejpam-2608	224	10	)	)	PUNCT
ejpam-2608	224	11	.	.	PUNCT
ejpam-2608	225	1	specifically	specifically	ADV
ejpam-2608	225	2	,	,	PUNCT
ejpam-2608	225	3	[	[	X
ejpam-2608	225	4	φ]a	φ]a	NOUN
ejpam-2608	225	5	=	=	SYM
ejpam-2608	225	6	0	0	X
ejpam-2608	225	7	.	.	PUNCT
ejpam-2608	226	1	hence	hence	ADV
ejpam-2608	226	2	φ	φ	PROPN
ejpam-2608	226	3	=	=	SYM
ejpam-2608	226	4	∂µ+	∂µ+	NOUN
ejpam-2608	226	5	∂̄ν	∂̄ν	NOUN
ejpam-2608	226	6	for	for	ADP
ejpam-2608	226	7	some	some	DET
ejpam-2608	226	8	p	p	NOUN
ejpam-2608	226	9	−	−	PROPN
ejpam-2608	226	10	1	1	NUM
ejpam-2608	226	11	,	,	PUNCT
ejpam-2608	226	12	q	q	ADJ
ejpam-2608	226	13	-	-	PUNCT
ejpam-2608	226	14	form	form	NOUN
ejpam-2608	226	15	,	,	PUNCT
ejpam-2608	226	16	µ	µ	NOUN
ejpam-2608	226	17	and	and	CCONJ
ejpam-2608	226	18	p	p	X
ejpam-2608	226	19	,	,	PUNCT
ejpam-2608	226	20	q	q	NOUN
ejpam-2608	226	21	−	−	PROPN
ejpam-2608	226	22	1	1	NUM
ejpam-2608	226	23	-	-	PUNCT
ejpam-2608	226	24	form	form	NOUN
ejpam-2608	226	25	ν	ν	NOUN
ejpam-2608	226	26	.	.	PUNCT
ejpam-2608	227	1	since	since	SCONJ
ejpam-2608	227	2	∂̄φ	∂̄φ	PROPN
ejpam-2608	227	3	=	=	SYM
ejpam-2608	227	4	0	0	NUM
ejpam-2608	227	5	we	we	PRON
ejpam-2608	227	6	have	have	VERB
ejpam-2608	227	7	∂̄(∂µ	∂̄(∂µ	PROPN
ejpam-2608	227	8	)	)	PUNCT
ejpam-2608	227	9	=	=	SYM
ejpam-2608	227	10	0	0	NUM
ejpam-2608	227	11	and	and	CCONJ
ejpam-2608	227	12	∂µ	∂µ	PROPN
ejpam-2608	227	13	∈	∈	PROPN
ejpam-2608	227	14	ker(∂̄)∩im(∂	ker(∂̄)∩im(∂	PROPN
ejpam-2608	227	15	)	)	PUNCT
ejpam-2608	227	16	.	.	PUNCT
ejpam-2608	228	1	similiarly	similiarly	ADV
ejpam-2608	228	2	,	,	PUNCT
ejpam-2608	228	3	since	since	SCONJ
ejpam-2608	228	4	∂φ	∂φ	PROPN
ejpam-2608	228	5	=	=	SYM
ejpam-2608	228	6	0	0	NUM
ejpam-2608	228	7	we	we	PRON
ejpam-2608	228	8	have	have	VERB
ejpam-2608	228	9	∂(∂̄ν	∂(∂̄ν	PROPN
ejpam-2608	228	10	)	)	PUNCT
ejpam-2608	229	1	=	=	SYM
ejpam-2608	229	2	0	0	NUM
ejpam-2608	229	3	and	and	CCONJ
ejpam-2608	229	4	∂̄ν	∂̄ν	VERB
ejpam-2608	229	5	∈	∈	PROPN
ejpam-2608	229	6	ker(∂)∩im(∂̄	ker(∂)∩im(∂̄	PROPN
ejpam-2608	229	7	)	)	PUNCT
ejpam-2608	229	8	.	.	PUNCT
ejpam-2608	230	1	thus	thus	ADV
ejpam-2608	230	2	φ	φ	PROPN
ejpam-2608	230	3	∈	∈	PROPN
ejpam-2608	230	4	(	(	PUNCT
ejpam-2608	230	5	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	230	6	)	)	PUNCT
ejpam-2608	230	7	∩	∩	ADJ
ejpam-2608	230	8	im(∂	im(∂	NOUN
ejpam-2608	230	9	)	)	PUNCT
ejpam-2608	231	1	+	+	CCONJ
ejpam-2608	231	2	ker(∂	ker(∂	PROPN
ejpam-2608	231	3	)	)	PUNCT
ejpam-2608	231	4	∩	∩	NOUN
ejpam-2608	231	5	im(∂̄	im(∂̄	NOUN
ejpam-2608	231	6	)	)	PUNCT
ejpam-2608	231	7	)	)	PUNCT
ejpam-2608	231	8	and	and	CCONJ
ejpam-2608	231	9	ep	ep	PROPN
ejpam-2608	231	10	,	,	PUNCT
ejpam-2608	231	11	q	q	PROPN
ejpam-2608	231	12	bca	bca	PROPN
ejpam-2608	231	13	=	=	PUNCT
ejpam-2608	231	14	{	{	PUNCT
ejpam-2608	231	15	0	0	NUM
ejpam-2608	231	16	}	}	PUNCT
ejpam-2608	231	17	.	.	PUNCT
ejpam-2608	232	1	lemma	lemma	PROPN
ejpam-2608	232	2	7	7	X
ejpam-2608	232	3	.	.	PUNCT
ejpam-2608	233	1	let	let	VERB
ejpam-2608	233	2	x	x	PRON
ejpam-2608	233	3	be	be	AUX
ejpam-2608	233	4	a	a	DET
ejpam-2608	233	5	compact	compact	ADJ
ejpam-2608	233	6	complex	complex	ADJ
ejpam-2608	233	7	manifold	manifold	NOUN
ejpam-2608	233	8	of	of	ADP
ejpam-2608	233	9	complex	complex	ADJ
ejpam-2608	233	10	dimension	dimension	NOUN
ejpam-2608	233	11	n.	n.	NOUN
ejpam-2608	233	12	if	if	SCONJ
ejpam-2608	233	13	we	we	PRON
ejpam-2608	233	14	have	have	VERB
ejpam-2608	233	15	the	the	DET
ejpam-2608	233	16	first	first	ADJ
ejpam-2608	233	17	betti	betti	ADJ
ejpam-2608	233	18	number	number	NOUN
ejpam-2608	233	19	is	be	AUX
ejpam-2608	233	20	zero	zero	NUM
ejpam-2608	233	21	(	(	PUNCT
ejpam-2608	233	22	b1	b1	NOUN
ejpam-2608	233	23	=	=	SYM
ejpam-2608	233	24	0	0	NUM
ejpam-2608	233	25	)	)	PUNCT
ejpam-2608	233	26	,	,	PUNCT
ejpam-2608	233	27	then	then	ADV
ejpam-2608	233	28	h1,0	h1,0	PROPN
ejpam-2608	233	29	bc	bc	PROPN
ejpam-2608	233	30	=	=	SYM
ejpam-2608	233	31	h0,1	h0,1	PROPN
ejpam-2608	233	32	bc	bc	PROPN
ejpam-2608	233	33	=	=	SYM
ejpam-2608	233	34	hn	hn	PROPN
ejpam-2608	233	35	,	,	PUNCT
ejpam-2608	233	36	n−1	n−1	PROPN
ejpam-2608	233	37	a	a	PRON
ejpam-2608	233	38	=	=	X
ejpam-2608	233	39	hn−1,n	hn−1,n	X
ejpam-2608	233	40	a	a	PRON
ejpam-2608	233	41	=	=	NOUN
ejpam-2608	233	42	0	0	NUM
ejpam-2608	233	43	.	.	PUNCT
ejpam-2608	234	1	proof	proof	NOUN
ejpam-2608	234	2	.	.	PUNCT
ejpam-2608	235	1	consider	consider	VERB
ejpam-2608	235	2	a	a	DET
ejpam-2608	235	3	1	1	NUM
ejpam-2608	235	4	,	,	PUNCT
ejpam-2608	235	5	0	0	NUM
ejpam-2608	235	6	-	-	PUNCT
ejpam-2608	235	7	form	form	NOUN
ejpam-2608	235	8	,	,	PUNCT
ejpam-2608	235	9	µ	µ	NOUN
ejpam-2608	235	10	such	such	ADJ
ejpam-2608	235	11	that	that	SCONJ
ejpam-2608	235	12	µ	µ	PROPN
ejpam-2608	235	13	∈	∈	PROPN
ejpam-2608	235	14	ker(∂	ker(∂	PROPN
ejpam-2608	235	15	)	)	PUNCT
ejpam-2608	235	16	∩	∩	NOUN
ejpam-2608	235	17	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	235	18	)	)	PUNCT
ejpam-2608	235	19	.	.	PUNCT
ejpam-2608	236	1	we	we	PRON
ejpam-2608	236	2	have	have	VERB
ejpam-2608	236	3	then	then	ADV
ejpam-2608	236	4	dµ	dµ	VERB
ejpam-2608	236	5	=	=	SYM
ejpam-2608	236	6	0	0	X
ejpam-2608	236	7	.	.	PUNCT
ejpam-2608	237	1	since	since	SCONJ
ejpam-2608	237	2	b1	b1	NOUN
ejpam-2608	237	3	=	=	SYM
ejpam-2608	237	4	0	0	NUM
ejpam-2608	237	5	,	,	PUNCT
ejpam-2608	237	6	we	we	PRON
ejpam-2608	237	7	have	have	VERB
ejpam-2608	237	8	µ	µ	NOUN
ejpam-2608	237	9	=	=	SYM
ejpam-2608	237	10	df	df	NOUN
ejpam-2608	237	11	form	form	VERB
ejpam-2608	237	12	some	some	DET
ejpam-2608	237	13	function	function	NOUN
ejpam-2608	237	14	f	f	X
ejpam-2608	237	15	.	.	PUNCT
ejpam-2608	238	1	thus	thus	ADV
ejpam-2608	238	2	µ	µ	X
ejpam-2608	238	3	=	=	SYM
ejpam-2608	238	4	∂f	∂f	PROPN
ejpam-2608	238	5	+	+	CCONJ
ejpam-2608	238	6	∂̄f	∂̄f	PROPN
ejpam-2608	238	7	.	.	PUNCT
ejpam-2608	239	1	we	we	PRON
ejpam-2608	239	2	must	must	AUX
ejpam-2608	239	3	have	have	VERB
ejpam-2608	239	4	∂̄f	∂̄f	PROPN
ejpam-2608	239	5	=	=	SYM
ejpam-2608	239	6	0	0	PUNCT
ejpam-2608	239	7	since	since	SCONJ
ejpam-2608	239	8	µ	µ	NOUN
ejpam-2608	239	9	is	be	AUX
ejpam-2608	239	10	a	a	DET
ejpam-2608	239	11	1	1	NUM
ejpam-2608	239	12	,	,	PUNCT
ejpam-2608	239	13	0	0	NUM
ejpam-2608	239	14	-	-	PUNCT
ejpam-2608	239	15	form	form	NOUN
ejpam-2608	239	16	.	.	PUNCT
ejpam-2608	240	1	hence	hence	ADV
ejpam-2608	240	2	f	f	PROPN
ejpam-2608	240	3	is	be	AUX
ejpam-2608	240	4	a	a	DET
ejpam-2608	240	5	holomorphic	holomorphic	ADJ
ejpam-2608	240	6	function	function	NOUN
ejpam-2608	240	7	on	on	ADP
ejpam-2608	240	8	a	a	DET
ejpam-2608	240	9	compact	compact	ADJ
ejpam-2608	240	10	complex	complex	NOUN
ejpam-2608	240	11	manifold	manifold	NOUN
ejpam-2608	240	12	and	and	CCONJ
ejpam-2608	240	13	thus	thus	ADV
ejpam-2608	240	14	must	must	AUX
ejpam-2608	240	15	be	be	AUX
ejpam-2608	240	16	a	a	DET
ejpam-2608	240	17	constant	constant	ADJ
ejpam-2608	240	18	function	function	NOUN
ejpam-2608	240	19	.	.	PUNCT
ejpam-2608	241	1	finally	finally	ADV
ejpam-2608	241	2	,	,	PUNCT
ejpam-2608	241	3	we	we	PRON
ejpam-2608	241	4	have	have	VERB
ejpam-2608	241	5	µ	µ	NOUN
ejpam-2608	241	6	=	=	SYM
ejpam-2608	241	7	∂f	∂f	PROPN
ejpam-2608	241	8	=	=	SYM
ejpam-2608	241	9	0	0	PROPN
ejpam-2608	241	10	since	since	SCONJ
ejpam-2608	241	11	f	f	PROPN
ejpam-2608	241	12	is	be	AUX
ejpam-2608	241	13	constant	constant	ADJ
ejpam-2608	241	14	.	.	PUNCT
ejpam-2608	242	1	thus	thus	ADV
ejpam-2608	242	2	ker(∂	ker(∂	NOUN
ejpam-2608	242	3	)	)	PUNCT
ejpam-2608	242	4	∩	∩	NOUN
ejpam-2608	242	5	ker(∂̄	ker(∂̄	NOUN
ejpam-2608	242	6	)	)	PUNCT
ejpam-2608	242	7	=	=	PRON
ejpam-2608	242	8	{	{	PUNCT
ejpam-2608	242	9	0	0	NUM
ejpam-2608	242	10	}	}	PUNCT
ejpam-2608	242	11	for	for	ADP
ejpam-2608	242	12	1	1	NUM
ejpam-2608	242	13	,	,	PUNCT
ejpam-2608	242	14	0	0	NUM
ejpam-2608	242	15	-	-	NOUN
ejpam-2608	242	16	forms	form	NOUN
ejpam-2608	242	17	and	and	CCONJ
ejpam-2608	242	18	h1,0	h1,0	PROPN
ejpam-2608	242	19	bc	bc	PROPN
ejpam-2608	242	20	=	=	SYM
ejpam-2608	242	21	0	0	PROPN
ejpam-2608	242	22	.	.	PUNCT
ejpam-2608	243	1	the	the	DET
ejpam-2608	243	2	other	other	ADJ
ejpam-2608	243	3	equalities	equality	NOUN
ejpam-2608	243	4	follow	follow	VERB
ejpam-2608	243	5	from	from	ADP
ejpam-2608	243	6	”	"	PUNCT
ejpam-2608	243	7	complex	complex	ADJ
ejpam-2608	243	8	conjugation	conjugation	NOUN
ejpam-2608	243	9	”	"	PUNCT
ejpam-2608	243	10	and	and	CCONJ
ejpam-2608	243	11	serre	serre	VERB
ejpam-2608	243	12	duality	duality	NOUN
ejpam-2608	243	13	mentioned	mention	VERB
ejpam-2608	243	14	above	above	ADV
ejpam-2608	243	15	.	.	PUNCT
ejpam-2608	244	1	lemma	lemma	PROPN
ejpam-2608	244	2	8	8	NUM
ejpam-2608	244	3	.	.	PUNCT
ejpam-2608	245	1	the	the	DET
ejpam-2608	245	2	map	map	NOUN
ejpam-2608	245	3	of	of	ADP
ejpam-2608	245	4	vector	vector	NOUN
ejpam-2608	245	5	spaces	space	NOUN
ejpam-2608	245	6	,	,	PUNCT
ejpam-2608	245	7	hp,0	hp,0	PROPN
ejpam-2608	245	8	bc	bc	PROPN
ejpam-2608	245	9	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	245	10	hp,0	hp,0	PROPN
ejpam-2608	245	11	∂̄	∂̄	PROPN
ejpam-2608	245	12	,	,	PUNCT
ejpam-2608	245	13	is	be	AUX
ejpam-2608	245	14	injective	injective	ADJ
ejpam-2608	245	15	.	.	PUNCT
ejpam-2608	246	1	proof	proof	NOUN
ejpam-2608	246	2	.	.	PUNCT
ejpam-2608	247	1	a	a	DET
ejpam-2608	247	2	p	p	X
ejpam-2608	247	3	,	,	PUNCT
ejpam-2608	247	4	0	0	NUM
ejpam-2608	247	5	-	-	PUNCT
ejpam-2608	247	6	form	form	NOUN
ejpam-2608	247	7	can	can	AUX
ejpam-2608	247	8	not	not	PART
ejpam-2608	247	9	be	be	AUX
ejpam-2608	247	10	in	in	ADP
ejpam-2608	247	11	the	the	DET
ejpam-2608	247	12	image	image	NOUN
ejpam-2608	247	13	of	of	ADP
ejpam-2608	247	14	∂̄∂	∂̄∂	NUM
ejpam-2608	247	15	or	or	CCONJ
ejpam-2608	247	16	∂̄.	∂̄.	NOUN
ejpam-2608	247	17	thus	thus	ADV
ejpam-2608	247	18	,	,	PUNCT
ejpam-2608	247	19	(	(	PUNCT
ejpam-2608	247	20	/im(∂̄	/im(∂̄	NUM
ejpam-2608	247	21	)	)	PUNCT
ejpam-2608	247	22	)	)	PUNCT
ejpam-2608	248	1	(	(	PUNCT
ejpam-2608	248	2	[	[	X
ejpam-2608	248	3	µ]bc	µ]bc	PROPN
ejpam-2608	248	4	)	)	PUNCT
ejpam-2608	248	5	=	=	PUNCT
ejpam-2608	249	1	[	[	X
ejpam-2608	249	2	0]∂̄	0]∂̄	NOUN
ejpam-2608	249	3	if	if	SCONJ
ejpam-2608	249	4	and	and	CCONJ
ejpam-2608	249	5	only	only	ADV
ejpam-2608	249	6	if	if	SCONJ
ejpam-2608	249	7	µ	µ	X
ejpam-2608	249	8	=	=	SYM
ejpam-2608	249	9	0	0	X
ejpam-2608	249	10	.	.	PUNCT
ejpam-2608	250	1	we	we	PRON
ejpam-2608	250	2	also	also	ADV
ejpam-2608	250	3	note	note	VERB
ejpam-2608	250	4	on	on	ADP
ejpam-2608	250	5	the	the	DET
ejpam-2608	250	6	end	end	NOUN
ejpam-2608	250	7	of	of	ADP
ejpam-2608	250	8	the	the	DET
ejpam-2608	250	9	sequence	sequence	NOUN
ejpam-2608	250	10	we	we	PRON
ejpam-2608	250	11	have	have	VERB
ejpam-2608	250	12	hp	hp	VERB
ejpam-2608	250	13	,	,	PUNCT
ejpam-2608	250	14	n	n	PRON
ejpam-2608	250	15	a	a	DET
ejpam-2608	250	16	∂̄→	∂̄→	PROPN
ejpam-2608	250	17	hp	hp	PROPN
ejpam-2608	250	18	,	,	PUNCT
ejpam-2608	250	19	n+1	n+1	PROPN
ejpam-2608	250	20	bc	bc	X
ejpam-2608	250	21	=	=	PUNCT
ejpam-2608	250	22	{	{	PUNCT
ejpam-2608	250	23	0	0	NUM
ejpam-2608	250	24	}	}	PUNCT
ejpam-2608	250	25	.	.	PUNCT
ejpam-2608	251	1	now	now	ADV
ejpam-2608	251	2	we	we	PRON
ejpam-2608	251	3	focus	focus	VERB
ejpam-2608	251	4	again	again	ADV
ejpam-2608	251	5	on	on	ADP
ejpam-2608	251	6	our	our	PRON
ejpam-2608	251	7	compact	compact	ADJ
ejpam-2608	251	8	complex	complex	ADJ
ejpam-2608	251	9	manifold	manifold	NOUN
ejpam-2608	251	10	,	,	PUNCT
ejpam-2608	251	11	x	x	PRON
ejpam-2608	251	12	,	,	PUNCT
ejpam-2608	251	13	being	be	AUX
ejpam-2608	251	14	topologically	topologically	ADV
ejpam-2608	251	15	equivalent	equivalent	ADJ
ejpam-2608	251	16	to	to	ADP
ejpam-2608	251	17	s6	s6	PROPN
ejpam-2608	251	18	.	.	PUNCT
ejpam-2608	252	1	noting	note	VERB
ejpam-2608	252	2	,	,	PUNCT
ejpam-2608	252	3	that	that	SCONJ
ejpam-2608	252	4	b0	b0	NOUN
ejpam-2608	252	5	=	=	SYM
ejpam-2608	252	6	b6	b6	NOUN
ejpam-2608	252	7	=	=	SYM
ejpam-2608	252	8	1,and	1,and	NUM
ejpam-2608	252	9	bj	bj	VERB
ejpam-2608	252	10	=	=	SYM
ejpam-2608	252	11	0	0	NUM
ejpam-2608	252	12	for	for	ADP
ejpam-2608	252	13	1	1	NUM
ejpam-2608	252	14	≤	≤	NUM
ejpam-2608	252	15	j	j	PROPN
ejpam-2608	252	16	≤	≤	ADV
ejpam-2608	252	17	5	5	NUM
ejpam-2608	252	18	,	,	PUNCT
ejpam-2608	252	19	we	we	PRON
ejpam-2608	252	20	have	have	AUX
ejpam-2608	252	21	,	,	PUNCT
ejpam-2608	252	22	using	use	VERB
ejpam-2608	252	23	the	the	DET
ejpam-2608	252	24	above	above	ADJ
ejpam-2608	252	25	lemmas	lemma	NOUN
ejpam-2608	252	26	,	,	PUNCT
ejpam-2608	252	27	the	the	DET
ejpam-2608	252	28	following	following	NOUN
ejpam-2608	252	29	:	:	PUNCT
ejpam-2608	252	30	theorem	theorem	NOUN
ejpam-2608	252	31	3	3	NUM
ejpam-2608	252	32	.	.	X
ejpam-2608	252	33	for	for	ADP
ejpam-2608	252	34	a	a	DET
ejpam-2608	252	35	complex	complex	ADJ
ejpam-2608	252	36	structure	structure	NOUN
ejpam-2608	252	37	on	on	ADP
ejpam-2608	252	38	a	a	DET
ejpam-2608	252	39	manifold	manifold	ADJ
ejpam-2608	252	40	x	x	SYM
ejpam-2608	252	41	topologically	topologically	ADV
ejpam-2608	252	42	equivalent	equivalent	ADJ
ejpam-2608	252	43	to	to	ADP
ejpam-2608	252	44	s6	s6	PROPN
ejpam-2608	252	45	,	,	PUNCT
ejpam-2608	252	46	we	we	PRON
ejpam-2608	252	47	have	have	VERB
ejpam-2608	252	48	the	the	DET
ejpam-2608	252	49	following	follow	VERB
ejpam-2608	252	50	long	long	ADJ
ejpam-2608	252	51	exact	exact	ADJ
ejpam-2608	252	52	sequences	sequence	NOUN
ejpam-2608	252	53	of	of	ADP
ejpam-2608	252	54	vector	vector	NOUN
ejpam-2608	252	55	spaces	space	NOUN
ejpam-2608	252	56	:	:	PUNCT
ejpam-2608	253	1	0	0	X
ejpam-2608	253	2	.	.	PUNCT
ejpam-2608	254	1	(	(	PUNCT
ejpam-2608	254	2	p	p	X
ejpam-2608	254	3	=	=	NOUN
ejpam-2608	254	4	0	0	NUM
ejpam-2608	254	5	)	)	PUNCT
ejpam-2608	254	6	0	0	NUM
ejpam-2608	255	1	→	→	SYM
ejpam-2608	255	2	h0,1	h0,1	NOUN
ejpam-2608	255	3	∂̄	∂̄	NOUN
ejpam-2608	255	4	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	256	1	h0,1	h0,1	INTJ
ejpam-2608	256	2	a	a	DET
ejpam-2608	256	3	∂̄→	∂̄→	PROPN
ejpam-2608	256	4	h0,2	h0,2	NOUN
ejpam-2608	256	5	bc	bc	PROPN
ejpam-2608	256	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	256	7	h0,2	h0,2	PROPN
ejpam-2608	256	8	∂̄	∂̄	ADV
ejpam-2608	256	9	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	257	1	h0,2	h0,2	PROPN
ejpam-2608	257	2	a	a	DET
ejpam-2608	257	3	∂̄→	∂̄→	PROPN
ejpam-2608	257	4	h0,3	h0,3	PROPN
ejpam-2608	257	5	bc	bc	PROPN
ejpam-2608	257	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	258	1	h0,3	h0,3	PROPN
ejpam-2608	258	2	∂̄	∂̄	ADV
ejpam-2608	258	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	259	1	h0,3	h0,3	ADP
ejpam-2608	259	2	a	a	DET
ejpam-2608	259	3	∂̄→	∂̄→	PROPN
ejpam-2608	259	4	0	0	NUM
ejpam-2608	259	5	a.	a.	PROPN
ejpam-2608	259	6	mchugh	mchugh	PROPN
ejpam-2608	259	7	/	/	SYM
ejpam-2608	259	8	eur	eur	PROPN
ejpam-2608	259	9	.	.	PUNCT
ejpam-2608	260	1	j.	j.	PROPN
ejpam-2608	260	2	pure	pure	PROPN
ejpam-2608	260	3	appl	appl	PROPN
ejpam-2608	260	4	.	.	PROPN
ejpam-2608	260	5	math	math	PROPN
ejpam-2608	260	6	,	,	PUNCT
ejpam-2608	260	7	10	10	NUM
ejpam-2608	260	8	(	(	PUNCT
ejpam-2608	260	9	3	3	NUM
ejpam-2608	260	10	)	)	PUNCT
ejpam-2608	260	11	(	(	PUNCT
ejpam-2608	260	12	2017	2017	NUM
ejpam-2608	260	13	)	)	PUNCT
ejpam-2608	260	14	,	,	PUNCT
ejpam-2608	260	15	440	440	NUM
ejpam-2608	260	16	-	-	SYM
ejpam-2608	260	17	454	454	NUM
ejpam-2608	260	18	449	449	NUM
ejpam-2608	260	19	1	1	NUM
ejpam-2608	260	20	.	.	PUNCT
ejpam-2608	261	1	(	(	PUNCT
ejpam-2608	261	2	p	p	NOUN
ejpam-2608	261	3	=	=	NOUN
ejpam-2608	261	4	1	1	NUM
ejpam-2608	261	5	)	)	PUNCT
ejpam-2608	261	6	0	0	NUM
ejpam-2608	262	1	→	→	SYM
ejpam-2608	262	2	h1,0	h1,0	VERB
ejpam-2608	262	3	∂̄	∂̄	NOUN
ejpam-2608	262	4	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	263	1	h1,0	h1,0	VERB
ejpam-2608	263	2	a	a	DET
ejpam-2608	263	3	∂̄→	∂̄→	PROPN
ejpam-2608	263	4	h1,1	h1,1	NOUN
ejpam-2608	263	5	bc	bc	PROPN
ejpam-2608	263	6	/im(∂̄)−→	/im(∂̄)−→	X
ejpam-2608	263	7	h1,1	h1,1	PROPN
ejpam-2608	263	8	∂̄	∂̄	PROPN
ejpam-2608	263	9	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	264	1	h1,1	h1,1	INTJ
ejpam-2608	264	2	a	a	DET
ejpam-2608	264	3	∂̄→	∂̄→	PROPN
ejpam-2608	264	4	h1,2	h1,2	ADJ
ejpam-2608	264	5	bc	bc	PROPN
ejpam-2608	264	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	265	1	h1,2	h1,2	ADJ
ejpam-2608	265	2	∂̄	∂̄	NOUN
ejpam-2608	265	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	266	1	h1,2	h1,2	ADV
ejpam-2608	266	2	a	a	DET
ejpam-2608	266	3	∂̄→	∂̄→	PROPN
ejpam-2608	266	4	h1,3	h1,3	NOUN
ejpam-2608	266	5	bc	bc	PROPN
ejpam-2608	266	6	/im(∂̄)−→	/im(∂̄)−→	X
ejpam-2608	266	7	h1,3	h1,3	PROPN
ejpam-2608	266	8	∂̄	∂̄	ADV
ejpam-2608	266	9	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	267	1	h1,3	h1,3	PROPN
ejpam-2608	267	2	a	a	DET
ejpam-2608	267	3	∂̄→	∂̄→	PROPN
ejpam-2608	267	4	0	0	NUM
ejpam-2608	267	5	2	2	NUM
ejpam-2608	267	6	.	.	PUNCT
ejpam-2608	268	1	(	(	PUNCT
ejpam-2608	268	2	p	p	NOUN
ejpam-2608	268	3	=	=	NOUN
ejpam-2608	268	4	2	2	NUM
ejpam-2608	268	5	)	)	PUNCT
ejpam-2608	268	6	0	0	NUM
ejpam-2608	269	1	→	→	SYM
ejpam-2608	269	2	h2,0	h2,0	PROPN
ejpam-2608	269	3	bc	bc	PROPN
ejpam-2608	269	4	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	270	1	h2,0	h2,0	NOUN
ejpam-2608	270	2	∂̄	∂̄	VERB
ejpam-2608	270	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	271	1	h2,0	h2,0	PROPN
ejpam-2608	271	2	a	a	DET
ejpam-2608	271	3	∂̄→	∂̄→	PROPN
ejpam-2608	271	4	h2,1	h2,1	PROPN
ejpam-2608	271	5	bc	bc	PROPN
ejpam-2608	271	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	272	1	h2,1	h2,1	PROPN
ejpam-2608	272	2	∂̄	∂̄	NOUN
ejpam-2608	272	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	273	1	h2,1	h2,1	PROPN
ejpam-2608	274	1	a	a	DET
ejpam-2608	274	2	∂̄→	∂̄→	PROPN
ejpam-2608	274	3	h2,2	h2,2	PROPN
ejpam-2608	274	4	bc	bc	X
ejpam-2608	274	5	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	275	1	h2,2	h2,2	PROPN
ejpam-2608	275	2	∂̄	∂̄	ADV
ejpam-2608	275	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	276	1	h2,2	h2,2	PROPN
ejpam-2608	276	2	a	a	DET
ejpam-2608	276	3	∂̄→	∂̄→	PROPN
ejpam-2608	276	4	h2,3	h2,3	NOUN
ejpam-2608	276	5	bc	bc	PROPN
ejpam-2608	276	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	277	1	h2,3	h2,3	ADJ
ejpam-2608	277	2	∂̄	∂̄	NOUN
ejpam-2608	277	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	278	1	h2,3	h2,3	ADV
ejpam-2608	278	2	a	a	DET
ejpam-2608	278	3	∂̄→	∂̄→	PROPN
ejpam-2608	278	4	0	0	NUM
ejpam-2608	278	5	3	3	NUM
ejpam-2608	278	6	.	.	PUNCT
ejpam-2608	279	1	(	(	PUNCT
ejpam-2608	279	2	p	p	NOUN
ejpam-2608	279	3	=	=	NOUN
ejpam-2608	279	4	3	3	NUM
ejpam-2608	279	5	)	)	PUNCT
ejpam-2608	279	6	0	0	NUM
ejpam-2608	280	1	→	→	SYM
ejpam-2608	280	2	h3,0	h3,0	PROPN
ejpam-2608	280	3	bc	bc	X
ejpam-2608	280	4	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	281	1	h3,0	h3,0	INTJ
ejpam-2608	281	2	∂̄	∂̄	ADV
ejpam-2608	281	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	282	1	h3,0	h3,0	INTJ
ejpam-2608	282	2	a	a	DET
ejpam-2608	282	3	∂̄→	∂̄→	PROPN
ejpam-2608	282	4	h3,1	h3,1	PROPN
ejpam-2608	282	5	bc	bc	PROPN
ejpam-2608	282	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	283	1	h3,1	h3,1	VERB
ejpam-2608	283	2	∂̄	∂̄	NOUN
ejpam-2608	283	3	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	284	1	h3,1	h3,1	VERB
ejpam-2608	284	2	a	a	DET
ejpam-2608	284	3	∂̄→	∂̄→	PROPN
ejpam-2608	284	4	h3,2	h3,2	NOUN
ejpam-2608	284	5	bc	bc	PROPN
ejpam-2608	284	6	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	284	7	h3,2	h3,2	NOUN
ejpam-2608	284	8	∂̄	∂̄	VERB
ejpam-2608	284	9	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	284	10	0	0	NUM
ejpam-2608	285	1	one	one	NUM
ejpam-2608	285	2	of	of	ADP
ejpam-2608	285	3	our	our	PRON
ejpam-2608	285	4	goals	goal	NOUN
ejpam-2608	285	5	is	be	AUX
ejpam-2608	285	6	to	to	PART
ejpam-2608	285	7	complete	complete	VERB
ejpam-2608	285	8	as	as	ADV
ejpam-2608	285	9	much	much	ADJ
ejpam-2608	285	10	as	as	ADP
ejpam-2608	285	11	possible	possible	ADJ
ejpam-2608	285	12	a	a	DET
ejpam-2608	285	13	table	table	NOUN
ejpam-2608	285	14	of	of	ADP
ejpam-2608	285	15	hodge	hodge	PROPN
ejpam-2608	285	16	numbers	number	NOUN
ejpam-2608	285	17	for	for	ADP
ejpam-2608	285	18	bottchern	bottchern	NOUN
ejpam-2608	285	19	cohomology	cohomology	NOUN
ejpam-2608	285	20	on	on	ADP
ejpam-2608	285	21	a	a	DET
ejpam-2608	285	22	complex	complex	ADJ
ejpam-2608	285	23	s6	s6	PROPN
ejpam-2608	285	24	.	.	PUNCT
ejpam-2608	286	1	the	the	DET
ejpam-2608	286	2	table	table	NOUN
ejpam-2608	286	3	of	of	ADP
ejpam-2608	286	4	hodge	hodge	PROPN
ejpam-2608	286	5	numbers	number	NOUN
ejpam-2608	286	6	for	for	ADP
ejpam-2608	286	7	aeppli	aeppli	ADJ
ejpam-2608	286	8	cohomology	cohomology	NOUN
ejpam-2608	286	9	is	be	AUX
ejpam-2608	286	10	,	,	PUNCT
ejpam-2608	286	11	of	of	ADP
ejpam-2608	286	12	course	course	NOUN
ejpam-2608	286	13	,	,	PUNCT
ejpam-2608	286	14	given	give	VERB
ejpam-2608	286	15	by	by	ADP
ejpam-2608	286	16	the	the	DET
ejpam-2608	286	17	serre	serre	PROPN
ejpam-2608	286	18	duality	duality	NOUN
ejpam-2608	286	19	with	with	ADP
ejpam-2608	286	20	bott	bott	PROPN
ejpam-2608	286	21	-	-	PUNCT
ejpam-2608	286	22	chern	chern	PROPN
ejpam-2608	286	23	cohomology	cohomology	NOUN
ejpam-2608	286	24	.	.	PUNCT
ejpam-2608	287	1	since	since	SCONJ
ejpam-2608	287	2	hp	hp	PROPN
ejpam-2608	287	3	,	,	PUNCT
ejpam-2608	287	4	qbc	qbc	NOUN
ejpam-2608	287	5	=	=	SYM
ejpam-2608	287	6	hq	hq	PROPN
ejpam-2608	287	7	,	,	PUNCT
ejpam-2608	287	8	pbc	pbc	PROPN
ejpam-2608	287	9	,	,	PUNCT
ejpam-2608	287	10	we	we	PRON
ejpam-2608	287	11	may	may	AUX
ejpam-2608	287	12	concern	concern	VERB
ejpam-2608	287	13	ourselves	ourselves	PRON
ejpam-2608	287	14	with	with	ADP
ejpam-2608	287	15	just	just	ADV
ejpam-2608	287	16	the	the	DET
ejpam-2608	287	17	bottom	bottom	ADJ
ejpam-2608	287	18	triangle	triangle	NOUN
ejpam-2608	287	19	of	of	ADP
ejpam-2608	287	20	the	the	DET
ejpam-2608	287	21	table	table	NOUN
ejpam-2608	287	22	.	.	PUNCT
ejpam-2608	288	1	using	use	VERB
ejpam-2608	288	2	h3,0	h3,0	PRON
ejpam-2608	288	3	∂̄	∂̄	NOUN
ejpam-2608	288	4	=	=	SYM
ejpam-2608	288	5	0	0	NUM
ejpam-2608	288	6	,	,	PUNCT
ejpam-2608	288	7	we	we	PRON
ejpam-2608	288	8	can	can	AUX
ejpam-2608	288	9	see	see	VERB
ejpam-2608	288	10	straight	straight	ADV
ejpam-2608	288	11	away	away	ADV
ejpam-2608	288	12	from	from	ADP
ejpam-2608	288	13	the	the	DET
ejpam-2608	288	14	long	long	ADJ
ejpam-2608	288	15	exact	exact	ADJ
ejpam-2608	288	16	sequence	sequence	NOUN
ejpam-2608	288	17	for	for	ADP
ejpam-2608	288	18	p	p	NOUN
ejpam-2608	288	19	=	=	NOUN
ejpam-2608	288	20	3	3	NUM
ejpam-2608	288	21	that	that	PRON
ejpam-2608	288	22	h3,0	h3,0	PROPN
ejpam-2608	288	23	bc	bc	X
ejpam-2608	288	24	=	=	SYM
ejpam-2608	288	25	0	0	PROPN
ejpam-2608	288	26	.	.	PUNCT
ejpam-2608	289	1	we	we	PRON
ejpam-2608	289	2	also	also	ADV
ejpam-2608	289	3	see	see	VERB
ejpam-2608	289	4	that	that	SCONJ
ejpam-2608	289	5	h2,3	h2,3	ADJ
ejpam-2608	289	6	bc	bc	PROPN
ejpam-2608	289	7	=	=	PROPN
ejpam-2608	289	8	h3,2	h3,2	PROPN
ejpam-2608	289	9	bc	bc	PROPN
ejpam-2608	289	10	≥	≥	PROPN
ejpam-2608	289	11	h	h	PROPN
ejpam-2608	289	12	3,2	3,2	NUM
ejpam-2608	289	13	∂̄	∂̄	ADJ
ejpam-2608	289	14	=	=	PUNCT
ejpam-2608	289	15	h0,1	h0,1	PROPN
ejpam-2608	289	16	∂̄	∂̄	X
ejpam-2608	289	17	≥	≥	NOUN
ejpam-2608	289	18	1	1	NUM
ejpam-2608	289	19	.	.	PUNCT
ejpam-2608	290	1	we	we	PRON
ejpam-2608	290	2	also	also	ADV
ejpam-2608	290	3	show	show	VERB
ejpam-2608	290	4	the	the	DET
ejpam-2608	290	5	following	following	NOUN
ejpam-2608	290	6	:	:	PUNCT
ejpam-2608	290	7	lemma	lemma	PROPN
ejpam-2608	290	8	9	9	X
ejpam-2608	290	9	.	.	PUNCT
ejpam-2608	291	1	h2,0	h2,0	PROPN
ejpam-2608	291	2	bc	bc	PROPN
ejpam-2608	292	1	=	=	PUNCT
ejpam-2608	292	2	h2,0	h2,0	PROPN
ejpam-2608	292	3	∂̄	∂̄	ADV
ejpam-2608	292	4	and	and	CCONJ
ejpam-2608	292	5	h3,1	h3,1	PROPN
ejpam-2608	292	6	bc	bc	PROPN
ejpam-2608	292	7	=	=	SYM
ejpam-2608	292	8	h3,1	h3,1	PROPN
ejpam-2608	292	9	∂̄	∂̄	ADV
ejpam-2608	292	10	=	=	SYM
ejpam-2608	292	11	c	c	NOUN
ejpam-2608	292	12	.	.	PUNCT
ejpam-2608	293	1	proof	proof	NOUN
ejpam-2608	293	2	.	.	PUNCT
ejpam-2608	294	1	we	we	PRON
ejpam-2608	294	2	know	know	VERB
ejpam-2608	294	3	that	that	SCONJ
ejpam-2608	294	4	if	if	SCONJ
ejpam-2608	294	5	φ	φ	PROPN
ejpam-2608	294	6	is	be	AUX
ejpam-2608	294	7	a	a	DET
ejpam-2608	294	8	∂̄-closed	∂̄-close	VERB
ejpam-2608	294	9	2,0	2,0	NOUN
ejpam-2608	294	10	-	-	PUNCT
ejpam-2608	294	11	form	form	NOUN
ejpam-2608	294	12	,	,	PUNCT
ejpam-2608	294	13	then	then	ADV
ejpam-2608	294	14	∂φ	∂φ	PROPN
ejpam-2608	294	15	=	=	SYM
ejpam-2608	295	1	0	0	X
ejpam-2608	295	2	.	.	PUNCT
ejpam-2608	295	3	thus	thus	ADV
ejpam-2608	295	4	dφ	dφ	ADP
ejpam-2608	295	5	=	=	SYM
ejpam-2608	295	6	∂φ+	∂φ+	X
ejpam-2608	295	7	∂̄φ	∂̄φ	PROPN
ejpam-2608	295	8	=	=	SYM
ejpam-2608	295	9	0	0	PROPN
ejpam-2608	295	10	.	.	PUNCT
ejpam-2608	296	1	since	since	SCONJ
ejpam-2608	296	2	b1	b1	NOUN
ejpam-2608	296	3	=	=	SYM
ejpam-2608	296	4	0	0	NUM
ejpam-2608	296	5	,	,	PUNCT
ejpam-2608	296	6	we	we	PRON
ejpam-2608	296	7	have	have	VERB
ejpam-2608	296	8	φ	φ	NOUN
ejpam-2608	296	9	=	=	SYM
ejpam-2608	296	10	dη	dη	PROPN
ejpam-2608	296	11	=	=	SYM
ejpam-2608	296	12	∂η	∂η	PROPN
ejpam-2608	297	1	+	+	CCONJ
ejpam-2608	297	2	∂̄η	∂̄η	NOUN
ejpam-2608	297	3	for	for	ADP
ejpam-2608	297	4	some	some	DET
ejpam-2608	297	5	1	1	NUM
ejpam-2608	297	6	-	-	PUNCT
ejpam-2608	297	7	form	form	NOUN
ejpam-2608	297	8	,	,	PUNCT
ejpam-2608	297	9	η	η	PROPN
ejpam-2608	297	10	.	.	PROPN
ejpam-2608	297	11	thus	thus	ADV
ejpam-2608	297	12	the	the	DET
ejpam-2608	297	13	image	image	NOUN
ejpam-2608	297	14	of	of	ADP
ejpam-2608	297	15	the	the	DET
ejpam-2608	297	16	map	map	NOUN
ejpam-2608	297	17	,	,	PUNCT
ejpam-2608	297	18	h2,0	h2,0	NOUN
ejpam-2608	297	19	∂̄	∂̄	NOUN
ejpam-2608	297	20	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	298	1	h2,0	h2,0	PROPN
ejpam-2608	298	2	a	a	DET
ejpam-2608	298	3	a.	a.	NOUN
ejpam-2608	298	4	mchugh	mchugh	PROPN
ejpam-2608	298	5	/	/	SYM
ejpam-2608	298	6	eur	eur	PROPN
ejpam-2608	298	7	.	.	PUNCT
ejpam-2608	299	1	j.	j.	PROPN
ejpam-2608	299	2	pure	pure	PROPN
ejpam-2608	299	3	appl	appl	PROPN
ejpam-2608	299	4	.	.	PROPN
ejpam-2608	299	5	math	math	PROPN
ejpam-2608	299	6	,	,	PUNCT
ejpam-2608	299	7	10	10	NUM
ejpam-2608	299	8	(	(	PUNCT
ejpam-2608	299	9	3	3	NUM
ejpam-2608	299	10	)	)	PUNCT
ejpam-2608	299	11	(	(	PUNCT
ejpam-2608	299	12	2017	2017	NUM
ejpam-2608	299	13	)	)	PUNCT
ejpam-2608	299	14	,	,	PUNCT
ejpam-2608	299	15	440	440	NUM
ejpam-2608	299	16	-	-	SYM
ejpam-2608	299	17	454	454	NUM
ejpam-2608	299	18	450	450	NUM
ejpam-2608	299	19	is	be	AUX
ejpam-2608	299	20	{	{	PUNCT
ejpam-2608	299	21	0	0	NUM
ejpam-2608	299	22	}	}	PUNCT
ejpam-2608	299	23	.	.	PUNCT
ejpam-2608	300	1	hence	hence	ADV
ejpam-2608	300	2	,	,	PUNCT
ejpam-2608	300	3	since	since	SCONJ
ejpam-2608	300	4	the	the	DET
ejpam-2608	300	5	p	p	X
ejpam-2608	300	6	=	=	SYM
ejpam-2608	300	7	2	2	NUM
ejpam-2608	300	8	sequence	sequence	NOUN
ejpam-2608	300	9	is	be	AUX
ejpam-2608	300	10	exact	exact	ADJ
ejpam-2608	300	11	,	,	PUNCT
ejpam-2608	300	12	the	the	DET
ejpam-2608	300	13	map	map	NOUN
ejpam-2608	300	14	,	,	PUNCT
ejpam-2608	300	15	h2,0	h2,0	PROPN
ejpam-2608	300	16	bc	bc	PROPN
ejpam-2608	300	17	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	301	1	h2,0	h2,0	PROPN
ejpam-2608	301	2	∂̄	∂̄	PROPN
ejpam-2608	301	3	is	be	AUX
ejpam-2608	301	4	an	an	DET
ejpam-2608	301	5	isomorphism	isomorphism	NOUN
ejpam-2608	301	6	and	and	CCONJ
ejpam-2608	301	7	we	we	PRON
ejpam-2608	301	8	have	have	VERB
ejpam-2608	301	9	h2,0	h2,0	PROPN
ejpam-2608	301	10	bc	bc	PROPN
ejpam-2608	301	11	=	=	PROPN
ejpam-2608	301	12	h2,0	h2,0	PROPN
ejpam-2608	301	13	∂̄	∂̄	PROPN
ejpam-2608	301	14	.	.	PUNCT
ejpam-2608	302	1	notice	notice	VERB
ejpam-2608	302	2	in	in	ADP
ejpam-2608	302	3	the	the	DET
ejpam-2608	302	4	above	above	ADJ
ejpam-2608	302	5	argument	argument	NOUN
ejpam-2608	302	6	we	we	PRON
ejpam-2608	302	7	could	could	AUX
ejpam-2608	302	8	also	also	ADV
ejpam-2608	302	9	have	have	AUX
ejpam-2608	302	10	concluded	conclude	VERB
ejpam-2608	302	11	more	more	ADV
ejpam-2608	302	12	specifically	specifically	ADV
ejpam-2608	302	13	for	for	ADP
ejpam-2608	302	14	our	our	PRON
ejpam-2608	302	15	∂̄-closed	∂̄-close	VERB
ejpam-2608	302	16	2,0	2,0	NOUN
ejpam-2608	302	17	-	-	PUNCT
ejpam-2608	302	18	form	form	NOUN
ejpam-2608	302	19	,	,	PUNCT
ejpam-2608	302	20	φ	φ	NOUN
ejpam-2608	302	21	,	,	PUNCT
ejpam-2608	302	22	that	that	SCONJ
ejpam-2608	302	23	φ	φ	PROPN
ejpam-2608	302	24	=	=	SYM
ejpam-2608	302	25	∂η	∂η	PROPN
ejpam-2608	302	26	for	for	ADP
ejpam-2608	302	27	some	some	DET
ejpam-2608	302	28	1,0	1,0	NUM
ejpam-2608	302	29	-	-	PUNCT
ejpam-2608	302	30	form	form	NOUN
ejpam-2608	302	31	,	,	PUNCT
ejpam-2608	302	32	η	η	PROPN
ejpam-2608	302	33	.	.	PROPN
ejpam-2608	302	34	in	in	ADP
ejpam-2608	302	35	a	a	DET
ejpam-2608	302	36	similar	similar	ADJ
ejpam-2608	302	37	manner	manner	NOUN
ejpam-2608	302	38	,	,	PUNCT
ejpam-2608	302	39	we	we	PRON
ejpam-2608	302	40	take	take	VERB
ejpam-2608	302	41	µ	µ	PRON
ejpam-2608	302	42	to	to	PART
ejpam-2608	302	43	be	be	AUX
ejpam-2608	302	44	a	a	DET
ejpam-2608	302	45	0,2	0,2	NUM
ejpam-2608	302	46	-	-	PUNCT
ejpam-2608	302	47	form	form	NOUN
ejpam-2608	302	48	representative	representative	NOUN
ejpam-2608	302	49	of	of	ADP
ejpam-2608	302	50	an	an	DET
ejpam-2608	302	51	element	element	NOUN
ejpam-2608	302	52	in	in	ADP
ejpam-2608	302	53	h0,2	h0,2	PROPN
ejpam-2608	302	54	bc	bc	PROPN
ejpam-2608	302	55	.	.	PUNCT
ejpam-2608	303	1	since	since	SCONJ
ejpam-2608	303	2	dµ	dµ	PROPN
ejpam-2608	303	3	=	=	SYM
ejpam-2608	303	4	0	0	NUM
ejpam-2608	303	5	,	,	PUNCT
ejpam-2608	303	6	we	we	PRON
ejpam-2608	303	7	may	may	AUX
ejpam-2608	303	8	conclude	conclude	VERB
ejpam-2608	303	9	that	that	SCONJ
ejpam-2608	303	10	µ	µ	NOUN
ejpam-2608	303	11	=	=	SYM
ejpam-2608	303	12	∂̄χ	∂̄χ	NOUN
ejpam-2608	303	13	for	for	ADP
ejpam-2608	303	14	some	some	DET
ejpam-2608	303	15	0,1	0,1	NUM
ejpam-2608	303	16	-	-	PUNCT
ejpam-2608	303	17	form	form	NOUN
ejpam-2608	303	18	,	,	PUNCT
ejpam-2608	303	19	χ	χ	X
ejpam-2608	303	20	.	.	PUNCT
ejpam-2608	304	1	thus	thus	ADV
ejpam-2608	304	2	the	the	DET
ejpam-2608	304	3	image	image	NOUN
ejpam-2608	304	4	of	of	ADP
ejpam-2608	304	5	the	the	DET
ejpam-2608	304	6	map	map	NOUN
ejpam-2608	304	7	,	,	PUNCT
ejpam-2608	304	8	h0,2	h0,2	PROPN
ejpam-2608	304	9	bc	bc	VERB
ejpam-2608	304	10	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	305	1	h0,2	h0,2	PROPN
ejpam-2608	305	2	∂̄	∂̄	ADV
ejpam-2608	305	3	is	be	AUX
ejpam-2608	305	4	{	{	PUNCT
ejpam-2608	305	5	0	0	NUM
ejpam-2608	305	6	}	}	PUNCT
ejpam-2608	305	7	and	and	CCONJ
ejpam-2608	305	8	hence	hence	ADV
ejpam-2608	305	9	,	,	PUNCT
ejpam-2608	305	10	using	use	VERB
ejpam-2608	305	11	the	the	DET
ejpam-2608	305	12	fact	fact	NOUN
ejpam-2608	305	13	h0,3	h0,3	PROPN
ejpam-2608	305	14	bc	bc	PROPN
ejpam-2608	305	15	=	=	PROPN
ejpam-2608	306	1	h3,0	h3,0	PROPN
ejpam-2608	306	2	bc	bc	X
ejpam-2608	306	3	=	=	SYM
ejpam-2608	306	4	0	0	PROPN
ejpam-2608	306	5	,	,	PUNCT
ejpam-2608	306	6	the	the	DET
ejpam-2608	306	7	map	map	NOUN
ejpam-2608	306	8	,	,	PUNCT
ejpam-2608	306	9	h0,2	h0,2	PROPN
ejpam-2608	306	10	∂̄	∂̄	ADV
ejpam-2608	306	11	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	307	1	h0,2	h0,2	PROPN
ejpam-2608	307	2	a	a	PRON
ejpam-2608	307	3	is	be	AUX
ejpam-2608	307	4	an	an	DET
ejpam-2608	307	5	isomorphism	isomorphism	NOUN
ejpam-2608	307	6	.	.	PUNCT
ejpam-2608	308	1	we	we	PRON
ejpam-2608	308	2	have	have	VERB
ejpam-2608	308	3	then	then	ADV
ejpam-2608	308	4	h3,1	h3,1	PROPN
ejpam-2608	308	5	bc	bc	PROPN
ejpam-2608	309	1	=	=	SYM
ejpam-2608	310	1	h0,2	h0,2	PROPN
ejpam-2608	310	2	a	a	DET
ejpam-2608	310	3	=	=	X
ejpam-2608	310	4	c	c	NOUN
ejpam-2608	310	5	.	.	PUNCT
ejpam-2608	311	1	the	the	DET
ejpam-2608	311	2	fact	fact	NOUN
ejpam-2608	311	3	that	that	SCONJ
ejpam-2608	311	4	the	the	DET
ejpam-2608	311	5	image	image	NOUN
ejpam-2608	311	6	of	of	ADP
ejpam-2608	311	7	the	the	DET
ejpam-2608	311	8	map	map	NOUN
ejpam-2608	311	9	,	,	PUNCT
ejpam-2608	311	10	h0,2	h0,2	PROPN
ejpam-2608	311	11	bc	bc	VERB
ejpam-2608	311	12	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	312	1	h0,2	h0,2	PROPN
ejpam-2608	312	2	∂̄	∂̄	ADV
ejpam-2608	312	3	is	be	AUX
ejpam-2608	312	4	{	{	PUNCT
ejpam-2608	312	5	0	0	NUM
ejpam-2608	312	6	}	}	PUNCT
ejpam-2608	312	7	also	also	ADV
ejpam-2608	312	8	shows	show	VERB
ejpam-2608	312	9	from	from	ADP
ejpam-2608	312	10	the	the	DET
ejpam-2608	312	11	p=2	p=2	PROPN
ejpam-2608	312	12	sequence	sequence	NOUN
ejpam-2608	312	13	that	that	PRON
ejpam-2608	312	14	we	we	PRON
ejpam-2608	312	15	have	have	VERB
ejpam-2608	312	16	the	the	DET
ejpam-2608	312	17	short	short	ADJ
ejpam-2608	312	18	exact	exact	ADJ
ejpam-2608	312	19	sequence	sequence	NOUN
ejpam-2608	312	20	0→	0→	PROPN
ejpam-2608	312	21	h0,1	h0,1	NOUN
ejpam-2608	312	22	∂̄	∂̄	VERB
ejpam-2608	312	23	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	313	1	h0,1	h0,1	INTJ
ejpam-2608	313	2	a	a	DET
ejpam-2608	313	3	∂̄→	∂̄→	PROPN
ejpam-2608	313	4	h0,2	h0,2	PROPN
ejpam-2608	313	5	bc	bc	PROPN
ejpam-2608	313	6	/im(∂̄)−→	/im(∂̄)−→	X
ejpam-2608	313	7	0	0	PUNCT
ejpam-2608	314	1	and	and	CCONJ
ejpam-2608	314	2	thus	thus	ADV
ejpam-2608	314	3	that	that	SCONJ
ejpam-2608	314	4	h3,2	h3,2	NOUN
ejpam-2608	314	5	bc	bc	PROPN
ejpam-2608	314	6	=	=	PROPN
ejpam-2608	315	1	h0,1	h0,1	PROPN
ejpam-2608	315	2	a	a	DET
ejpam-2608	315	3	=	=	X
ejpam-2608	315	4	h0,1	h0,1	NOUN
ejpam-2608	315	5	∂̄	∂̄	NOUN
ejpam-2608	315	6	+	+	CCONJ
ejpam-2608	315	7	h2,0	h2,0	NOUN
ejpam-2608	315	8	∂̄	∂̄	ADV
ejpam-2608	315	9	=	=	PUNCT
ejpam-2608	315	10	c+	c+	VERB
ejpam-2608	315	11	1	1	NUM
ejpam-2608	315	12	+	+	NUM
ejpam-2608	315	13	h2,0	h2,0	NOUN
ejpam-2608	315	14	∂̄	∂̄	NOUN
ejpam-2608	315	15	.	.	PUNCT
ejpam-2608	316	1	please	please	INTJ
ejpam-2608	316	2	recall	recall	VERB
ejpam-2608	316	3	that	that	SCONJ
ejpam-2608	316	4	a	a	DET
ejpam-2608	316	5	=	=	X
ejpam-2608	316	6	h2,0	h2,0	PROPN
ejpam-2608	316	7	∂̄	∂̄	ADP
ejpam-2608	316	8	−	−	PROPN
ejpam-2608	316	9	h1,0	h1,0	PROPN
ejpam-2608	316	10	∂̄	∂̄	NOUN
ejpam-2608	316	11	.	.	PUNCT
ejpam-2608	317	1	in	in	ADP
ejpam-2608	317	2	trying	try	VERB
ejpam-2608	317	3	to	to	PART
ejpam-2608	317	4	be	be	AUX
ejpam-2608	317	5	as	as	ADV
ejpam-2608	317	6	complete	complete	ADJ
ejpam-2608	317	7	as	as	ADP
ejpam-2608	317	8	possible	possible	ADJ
ejpam-2608	317	9	,	,	PUNCT
ejpam-2608	317	10	we	we	PRON
ejpam-2608	317	11	also	also	ADV
ejpam-2608	317	12	show	show	VERB
ejpam-2608	317	13	:	:	PUNCT
ejpam-2608	317	14	theorem	theorem	NOUN
ejpam-2608	317	15	4	4	NUM
ejpam-2608	317	16	.	.	PUNCT
ejpam-2608	318	1	if	if	SCONJ
ejpam-2608	318	2	x	x	PRON
ejpam-2608	318	3	is	be	AUX
ejpam-2608	318	4	a	a	DET
ejpam-2608	318	5	compact	compact	ADJ
ejpam-2608	318	6	complex	complex	ADJ
ejpam-2608	318	7	manifold	manifold	NOUN
ejpam-2608	318	8	then	then	ADV
ejpam-2608	318	9	h0,0	h0,0	NOUN
ejpam-2608	318	10	bc	bc	PROPN
ejpam-2608	318	11	=	=	SYM
ejpam-2608	318	12	1	1	X
ejpam-2608	318	13	.	.	PUNCT
ejpam-2608	319	1	furthermore	furthermore	ADV
ejpam-2608	319	2	,	,	PUNCT
ejpam-2608	319	3	if	if	SCONJ
ejpam-2608	319	4	b1	b1	NOUN
ejpam-2608	319	5	=	=	NOUN
ejpam-2608	319	6	0	0	PUNCT
ejpam-2608	320	1	then	then	ADV
ejpam-2608	320	2	h3,3	h3,3	PROPN
ejpam-2608	320	3	bc	bc	PROPN
ejpam-2608	320	4	=	=	SYM
ejpam-2608	320	5	1	1	X
ejpam-2608	320	6	.	.	PUNCT
ejpam-2608	320	7	a.	a.	PROPN
ejpam-2608	320	8	mchugh	mchugh	PROPN
ejpam-2608	320	9	/	/	SYM
ejpam-2608	320	10	eur	eur	PROPN
ejpam-2608	320	11	.	.	PUNCT
ejpam-2608	321	1	j.	j.	PROPN
ejpam-2608	321	2	pure	pure	PROPN
ejpam-2608	321	3	appl	appl	PROPN
ejpam-2608	321	4	.	.	PROPN
ejpam-2608	321	5	math	math	PROPN
ejpam-2608	321	6	,	,	PUNCT
ejpam-2608	321	7	10	10	NUM
ejpam-2608	321	8	(	(	PUNCT
ejpam-2608	321	9	3	3	NUM
ejpam-2608	321	10	)	)	PUNCT
ejpam-2608	321	11	(	(	PUNCT
ejpam-2608	321	12	2017	2017	NUM
ejpam-2608	321	13	)	)	PUNCT
ejpam-2608	321	14	,	,	PUNCT
ejpam-2608	321	15	440	440	NUM
ejpam-2608	321	16	-	-	SYM
ejpam-2608	321	17	454	454	NUM
ejpam-2608	321	18	451	451	NUM
ejpam-2608	321	19	proof	proof	NOUN
ejpam-2608	321	20	.	.	PUNCT
ejpam-2608	322	1	a	a	DET
ejpam-2608	322	2	0,0	0,0	NUM
ejpam-2608	322	3	-	-	PUNCT
ejpam-2608	322	4	form	form	NOUN
ejpam-2608	322	5	or	or	CCONJ
ejpam-2608	322	6	function	function	NOUN
ejpam-2608	322	7	,	,	PUNCT
ejpam-2608	322	8	f	f	X
ejpam-2608	322	9	,	,	PUNCT
ejpam-2608	322	10	on	on	ADP
ejpam-2608	322	11	a	a	DET
ejpam-2608	322	12	compact	compact	ADJ
ejpam-2608	322	13	complex	complex	ADJ
ejpam-2608	322	14	manifold	manifold	ADJ
ejpam-2608	322	15	,	,	PUNCT
ejpam-2608	322	16	x	x	PRON
ejpam-2608	322	17	,	,	PUNCT
ejpam-2608	322	18	such	such	ADJ
ejpam-2608	322	19	that	that	DET
ejpam-2608	322	20	df	df	NOUN
ejpam-2608	322	21	=	=	SYM
ejpam-2608	322	22	0	0	NUM
ejpam-2608	322	23	is	be	AUX
ejpam-2608	322	24	a	a	DET
ejpam-2608	322	25	constant	constant	ADJ
ejpam-2608	322	26	.	.	PUNCT
ejpam-2608	323	1	thus	thus	ADV
ejpam-2608	323	2	,	,	PUNCT
ejpam-2608	323	3	h0,0	h0,0	PROPN
ejpam-2608	323	4	bc	bc	PROPN
ejpam-2608	323	5	=	=	SYM
ejpam-2608	323	6	c	c	PROPN
ejpam-2608	323	7	and	and	CCONJ
ejpam-2608	323	8	h0,0	h0,0	NOUN
ejpam-2608	323	9	bc	bc	X
ejpam-2608	323	10	=	=	SYM
ejpam-2608	323	11	1	1	X
ejpam-2608	323	12	.	.	PUNCT
ejpam-2608	323	13	we	we	PRON
ejpam-2608	323	14	consider	consider	VERB
ejpam-2608	323	15	now	now	ADV
ejpam-2608	323	16	h0,0	h0,0	NOUN
ejpam-2608	323	17	a	a	PRON
ejpam-2608	323	18	.	.	PUNCT
ejpam-2608	324	1	we	we	PRON
ejpam-2608	324	2	know	know	VERB
ejpam-2608	324	3	that	that	SCONJ
ejpam-2608	324	4	h0,0	h0,0	NOUN
ejpam-2608	324	5	∂̄	∂̄	PROPN
ejpam-2608	324	6	consists	consist	VERB
ejpam-2608	324	7	of	of	ADP
ejpam-2608	324	8	the	the	DET
ejpam-2608	324	9	constant	constant	ADJ
ejpam-2608	324	10	functions	function	NOUN
ejpam-2608	324	11	.	.	PUNCT
ejpam-2608	325	1	the	the	DET
ejpam-2608	325	2	sequence	sequence	NOUN
ejpam-2608	325	3	,	,	PUNCT
ejpam-2608	325	4	0→	0→	PROPN
ejpam-2608	325	5	h0,0	h0,0	NUM
ejpam-2608	325	6	bc	bc	PROPN
ejpam-2608	325	7	/im(∂̄)−→	/im(∂̄)−→	PUNCT
ejpam-2608	325	8	h0,0	h0,0	NOUN
ejpam-2608	325	9	∂̄	∂̄	NOUN
ejpam-2608	325	10	/(im(∂̄)+im(∂))−→	/(im(∂̄)+im(∂))−→	PUNCT
ejpam-2608	325	11	h0,0	h0,0	NOUN
ejpam-2608	325	12	a	a	DET
ejpam-2608	325	13	∂̄→	∂̄→	PROPN
ejpam-2608	325	14	h0,1	h0,1	PROPN
ejpam-2608	325	15	bc	bc	PROPN
ejpam-2608	325	16	is	be	AUX
ejpam-2608	325	17	not	not	PART
ejpam-2608	325	18	exact	exact	ADJ
ejpam-2608	325	19	at	at	ADP
ejpam-2608	325	20	h0,0	h0,0	NOUN
ejpam-2608	325	21	∂̄	∂̄	NOUN
ejpam-2608	325	22	but	but	CCONJ
ejpam-2608	325	23	it	it	PRON
ejpam-2608	325	24	is	be	AUX
ejpam-2608	325	25	exact	exact	ADJ
ejpam-2608	325	26	at	at	ADP
ejpam-2608	325	27	h0,0	h0,0	NOUN
ejpam-2608	325	28	a	a	NOUN
ejpam-2608	325	29	.	.	PUNCT
ejpam-2608	326	1	thus	thus	ADV
ejpam-2608	326	2	,	,	PUNCT
ejpam-2608	326	3	since	since	SCONJ
ejpam-2608	326	4	h0,1	h0,1	PROPN
ejpam-2608	326	5	bc	bc	PROPN
ejpam-2608	326	6	=	=	SYM
ejpam-2608	326	7	0	0	PROPN
ejpam-2608	326	8	,	,	PUNCT
ejpam-2608	326	9	we	we	PRON
ejpam-2608	326	10	know	know	VERB
ejpam-2608	326	11	that	that	SCONJ
ejpam-2608	326	12	h0,0	h0,0	NOUN
ejpam-2608	326	13	a	a	DET
ejpam-2608	326	14	=	=	SYM
ejpam-2608	326	15	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	326	16	)	)	PUNCT
ejpam-2608	326	17	+	+	CCONJ
ejpam-2608	326	18	im(∂	im(∂	NOUN
ejpam-2608	326	19	)	)	PUNCT
ejpam-2608	326	20	)	)	PUNCT
ejpam-2608	326	21	:	:	PUNCT
ejpam-2608	326	22	h0,0	h0,0	NOUN
ejpam-2608	326	23	∂̄	∂̄	ADV
ejpam-2608	326	24	→	→	SYM
ejpam-2608	326	25	h0,0	h0,0	NOUN
ejpam-2608	326	26	a	a	PRON
ejpam-2608	326	27	)	)	PUNCT
ejpam-2608	326	28	.	.	PUNCT
ejpam-2608	327	1	now	now	ADV
ejpam-2608	327	2	if	if	SCONJ
ejpam-2608	327	3	f	f	PROPN
ejpam-2608	327	4	is	be	AUX
ejpam-2608	327	5	a	a	DET
ejpam-2608	327	6	constant	constant	ADJ
ejpam-2608	327	7	function	function	NOUN
ejpam-2608	327	8	,	,	PUNCT
ejpam-2608	327	9	then	then	ADV
ejpam-2608	327	10	f	f	X
ejpam-2608	327	11	/∈	/∈	PUNCT
ejpam-2608	327	12	(	(	PUNCT
ejpam-2608	327	13	im(∂̄	im(∂̄	ADJ
ejpam-2608	327	14	)	)	PUNCT
ejpam-2608	327	15	+	+	NUM
ejpam-2608	327	16	im(∂	im(∂	NOUN
ejpam-2608	327	17	)	)	PUNCT
ejpam-2608	327	18	)	)	PUNCT
ejpam-2608	327	19	so	so	ADV
ejpam-2608	327	20	im(/(im(∂̄	im(/(im(∂̄	NOUN
ejpam-2608	327	21	)	)	PUNCT
ejpam-2608	327	22	+	+	NUM
ejpam-2608	327	23	im(∂	im(∂	NOUN
ejpam-2608	327	24	)	)	PUNCT
ejpam-2608	327	25	)	)	PUNCT
ejpam-2608	327	26	:	:	PUNCT
ejpam-2608	327	27	h0,0	h0,0	NOUN
ejpam-2608	327	28	∂̄	∂̄	ADV
ejpam-2608	327	29	→	→	SYM
ejpam-2608	327	30	h0,0	h0,0	NOUN
ejpam-2608	327	31	a	a	NOUN
ejpam-2608	327	32	)	)	PUNCT
ejpam-2608	327	33	=	=	SYM
ejpam-2608	327	34	c	c	NOUN
ejpam-2608	327	35	and	and	CCONJ
ejpam-2608	327	36	h0,0	h0,0	NOUN
ejpam-2608	327	37	a	a	DET
ejpam-2608	327	38	=	=	X
ejpam-2608	327	39	c.	c.	NOUN
ejpam-2608	327	40	by	by	ADP
ejpam-2608	327	41	the	the	DET
ejpam-2608	327	42	serre	serre	PROPN
ejpam-2608	327	43	duality	duality	NOUN
ejpam-2608	327	44	,	,	PUNCT
ejpam-2608	327	45	we	we	PRON
ejpam-2608	327	46	have	have	VERB
ejpam-2608	327	47	h3,3	h3,3	PROPN
ejpam-2608	327	48	bc	bc	PROPN
ejpam-2608	327	49	=	=	SYM
ejpam-2608	327	50	1	1	X
ejpam-2608	327	51	.	.	X
ejpam-2608	327	52	recall	recall	VERB
ejpam-2608	327	53	that	that	DET
ejpam-2608	327	54	hp	hp	PROPN
ejpam-2608	327	55	,	,	PUNCT
ejpam-2608	327	56	qbc	qbc	NOUN
ejpam-2608	327	57	=	=	SYM
ejpam-2608	328	1	hq	hq	PROPN
ejpam-2608	328	2	,	,	PUNCT
ejpam-2608	328	3	pbc	pbc	PROPN
ejpam-2608	328	4	.	.	PUNCT
ejpam-2608	329	1	we	we	PRON
ejpam-2608	329	2	thus	thus	ADV
ejpam-2608	329	3	have	have	VERB
ejpam-2608	329	4	so	so	ADV
ejpam-2608	329	5	far	far	ADV
ejpam-2608	329	6	,	,	PUNCT
ejpam-2608	329	7	for	for	ADP
ejpam-2608	329	8	our	our	PRON
ejpam-2608	329	9	essential	essential	ADJ
ejpam-2608	329	10	lower	low	ADJ
ejpam-2608	329	11	triangle	triangle	NOUN
ejpam-2608	329	12	for	for	ADP
ejpam-2608	329	13	bott	bott	NOUN
ejpam-2608	329	14	-	-	PUNCT
ejpam-2608	329	15	chern	chern	PROPN
ejpam-2608	329	16	cohomology	cohomology	NOUN
ejpam-2608	329	17	1	1	NUM
ejpam-2608	329	18	h2,2	h2,2	NOUN
ejpam-2608	329	19	bc	bc	X
ejpam-2608	329	20	c+	c+	VERB
ejpam-2608	329	21	1	1	NUM
ejpam-2608	329	22	+	+	NUM
ejpam-2608	329	23	h2,0	h2,0	PROPN
ejpam-2608	329	24	∂̄	∂̄	PROPN
ejpam-2608	329	25	h1,1	h1,1	NOUN
ejpam-2608	329	26	bc	bc	PROPN
ejpam-2608	329	27	h2,1	h2,1	PROPN
ejpam-2608	329	28	bc	bc	PROPN
ejpam-2608	329	29	c	c	PROPN
ejpam-2608	329	30	1	1	NUM
ejpam-2608	329	31	0	0	NUM
ejpam-2608	329	32	h2,0	h2,0	NOUN
ejpam-2608	329	33	∂̄	∂̄	ADJ
ejpam-2608	329	34	0	0	PUNCT
ejpam-2608	330	1	we	we	PRON
ejpam-2608	330	2	still	still	ADV
ejpam-2608	330	3	have	have	AUX
ejpam-2608	330	4	not	not	PART
ejpam-2608	330	5	computed	compute	VERB
ejpam-2608	330	6	h1,1	h1,1	PROPN
ejpam-2608	330	7	bc	bc	PROPN
ejpam-2608	330	8	,	,	PUNCT
ejpam-2608	330	9	h	h	PROPN
ejpam-2608	330	10	2,2	2,2	NUM
ejpam-2608	330	11	bc	bc	PROPN
ejpam-2608	330	12	and	and	CCONJ
ejpam-2608	330	13	h2,1	h2,1	PROPN
ejpam-2608	330	14	bc	bc	PROPN
ejpam-2608	330	15	.	.	PUNCT
ejpam-2608	331	1	we	we	PRON
ejpam-2608	331	2	can	can	AUX
ejpam-2608	331	3	determine	determine	VERB
ejpam-2608	331	4	h2,1	h2,1	PROPN
ejpam-2608	331	5	bc	bc	PROPN
ejpam-2608	331	6	in	in	ADP
ejpam-2608	331	7	terms	term	NOUN
ejpam-2608	331	8	of	of	ADP
ejpam-2608	331	9	the	the	DET
ejpam-2608	331	10	others	other	NOUN
ejpam-2608	331	11	by	by	ADP
ejpam-2608	331	12	plugging	plug	VERB
ejpam-2608	331	13	our	our	PRON
ejpam-2608	331	14	results	result	NOUN
ejpam-2608	331	15	so	so	ADV
ejpam-2608	331	16	far	far	ADV
ejpam-2608	331	17	into	into	ADP
ejpam-2608	331	18	the	the	DET
ejpam-2608	331	19	following	follow	VERB
ejpam-2608	331	20	well	well	ADV
ejpam-2608	331	21	known	know	VERB
ejpam-2608	331	22	result	result	NOUN
ejpam-2608	331	23	for	for	ADP
ejpam-2608	331	24	long	long	ADJ
ejpam-2608	331	25	exact	exact	ADJ
ejpam-2608	331	26	sequences	sequence	NOUN
ejpam-2608	331	27	of	of	ADP
ejpam-2608	331	28	vector	vector	NOUN
ejpam-2608	331	29	spaces	space	NOUN
ejpam-2608	331	30	:	:	PUNCT
ejpam-2608	331	31	theorem	theorem	NOUN
ejpam-2608	331	32	5	5	NUM
ejpam-2608	331	33	.	.	PUNCT
ejpam-2608	332	1	if	if	SCONJ
ejpam-2608	332	2	0→	0→	PROPN
ejpam-2608	332	3	a1	a1	NOUN
ejpam-2608	332	4	→	→	SYM
ejpam-2608	332	5	a2	a2	PROPN
ejpam-2608	332	6	→	→	PUNCT
ejpam-2608	332	7	.	.	PUNCT
ejpam-2608	332	8	.	.	PUNCT
ejpam-2608	333	1	.→	.→	PUNCT
ejpam-2608	333	2	an	an	DET
ejpam-2608	333	3	→	→	SYM
ejpam-2608	333	4	0	0	NUM
ejpam-2608	333	5	is	be	AUX
ejpam-2608	333	6	a	a	DET
ejpam-2608	333	7	long	long	ADJ
ejpam-2608	333	8	exact	exact	ADJ
ejpam-2608	333	9	sequence	sequence	NOUN
ejpam-2608	333	10	of	of	ADP
ejpam-2608	333	11	vector	vector	NOUN
ejpam-2608	333	12	spaces	space	NOUN
ejpam-2608	333	13	with	with	ADP
ejpam-2608	333	14	aj	aj	PROPN
ejpam-2608	333	15	=	=	SYM
ejpam-2608	333	16	dim(aj	dim(aj	PROPN
ejpam-2608	333	17	)	)	PUNCT
ejpam-2608	333	18	then	then	ADV
ejpam-2608	333	19	n∑	n∑	ADV
ejpam-2608	333	20	j=1	j=1	NOUN
ejpam-2608	333	21	(	(	PUNCT
ejpam-2608	333	22	−1)j+1aj	−1)j+1aj	PRON
ejpam-2608	333	23	=	=	SYM
ejpam-2608	333	24	0	0	NUM
ejpam-2608	333	25	.	.	PUNCT
ejpam-2608	334	1	we	we	PRON
ejpam-2608	334	2	apply	apply	VERB
ejpam-2608	334	3	this	this	PRON
ejpam-2608	334	4	to	to	ADP
ejpam-2608	334	5	the	the	DET
ejpam-2608	334	6	long	long	ADJ
ejpam-2608	334	7	exact	exact	ADJ
ejpam-2608	334	8	sequence	sequence	NOUN
ejpam-2608	334	9	for	for	ADP
ejpam-2608	334	10	p	p	NOUN
ejpam-2608	334	11	=	=	NOUN
ejpam-2608	334	12	1	1	NUM
ejpam-2608	334	13	:	:	PUNCT
ejpam-2608	334	14	h1,0	h1,0	PROPN
ejpam-2608	334	15	−	−	PROPN
ejpam-2608	334	16	(	(	PUNCT
ejpam-2608	334	17	c+	c+	VERB
ejpam-2608	334	18	1	1	NUM
ejpam-2608	334	19	+	+	NUM
ejpam-2608	334	20	h2,0	h2,0	NOUN
ejpam-2608	334	21	)	)	PUNCT
ejpam-2608	335	1	+	+	CCONJ
ejpam-2608	335	2	h1,1	h1,1	NOUN
ejpam-2608	335	3	bc	bc	PROPN
ejpam-2608	335	4	−	−	PROPN
ejpam-2608	335	5	(	(	PUNCT
ejpam-2608	335	6	d−	d−	PROPN
ejpam-2608	335	7	a+	a+	PUNCT
ejpam-2608	335	8	1	1	NUM
ejpam-2608	335	9	)	)	PUNCT
ejpam-2608	335	10	+	+	CCONJ
ejpam-2608	335	11	h2,2	h2,2	PROPN
ejpam-2608	335	12	bc	bc	VERB
ejpam-2608	335	13	−	−	PROPN
ejpam-2608	335	14	h	h	PROPN
ejpam-2608	335	15	2,1	2,1	NUM
ejpam-2608	335	16	bc	bc	PROPN
ejpam-2608	335	17	+	+	CCONJ
ejpam-2608	335	18	d−	d−	PROPN
ejpam-2608	335	19	h2,1	h2,1	PROPN
ejpam-2608	335	20	bc	bc	PROPN
ejpam-2608	335	21	+	+	CCONJ
ejpam-2608	335	22	c−	c−	PROPN
ejpam-2608	335	23	h2,0	h2,0	PROPN
ejpam-2608	335	24	+	+	CCONJ
ejpam-2608	335	25	h2,0	h2,0	X
ejpam-2608	335	26	=	=	SYM
ejpam-2608	335	27	0	0	PROPN
ejpam-2608	335	28	.	.	PUNCT
ejpam-2608	336	1	a.	a.	PROPN
ejpam-2608	336	2	mchugh	mchugh	PROPN
ejpam-2608	336	3	/	/	SYM
ejpam-2608	336	4	eur	eur	PROPN
ejpam-2608	336	5	.	.	PUNCT
ejpam-2608	337	1	j.	j.	PROPN
ejpam-2608	337	2	pure	pure	PROPN
ejpam-2608	337	3	appl	appl	PROPN
ejpam-2608	337	4	.	.	PROPN
ejpam-2608	337	5	math	math	PROPN
ejpam-2608	337	6	,	,	PUNCT
ejpam-2608	337	7	10	10	NUM
ejpam-2608	337	8	(	(	PUNCT
ejpam-2608	337	9	3	3	NUM
ejpam-2608	337	10	)	)	PUNCT
ejpam-2608	337	11	(	(	PUNCT
ejpam-2608	337	12	2017	2017	NUM
ejpam-2608	337	13	)	)	PUNCT
ejpam-2608	337	14	,	,	PUNCT
ejpam-2608	337	15	440	440	NUM
ejpam-2608	337	16	-	-	SYM
ejpam-2608	337	17	454	454	NUM
ejpam-2608	337	18	452	452	NUM
ejpam-2608	337	19	this	this	PRON
ejpam-2608	337	20	reduces	reduce	VERB
ejpam-2608	337	21	to	to	ADP
ejpam-2608	337	22	h1,1	h1,1	PROPN
ejpam-2608	337	23	bc	bc	PROPN
ejpam-2608	337	24	+	+	CCONJ
ejpam-2608	337	25	h2,2	h2,2	PROPN
ejpam-2608	337	26	bc	bc	X
ejpam-2608	337	27	=	=	SYM
ejpam-2608	337	28	2h2,1	2h2,1	NUM
ejpam-2608	337	29	bc	bc	PROPN
ejpam-2608	338	1	+	+	X
ejpam-2608	338	2	2	2	NUM
ejpam-2608	338	3	.	.	PUNCT
ejpam-2608	339	1	thus	thus	ADV
ejpam-2608	339	2	our	our	PRON
ejpam-2608	339	3	essential	essential	ADJ
ejpam-2608	339	4	lower	low	ADJ
ejpam-2608	339	5	triangle	triangle	NOUN
ejpam-2608	339	6	for	for	ADP
ejpam-2608	339	7	bott	bott	PROPN
ejpam-2608	339	8	-	-	PUNCT
ejpam-2608	339	9	chern	chern	PROPN
ejpam-2608	339	10	cohomology	cohomology	NOUN
ejpam-2608	339	11	is	be	AUX
ejpam-2608	339	12	1	1	NUM
ejpam-2608	339	13	h2,2	h2,2	PROPN
ejpam-2608	339	14	bc	bc	X
ejpam-2608	339	15	c+	c+	VERB
ejpam-2608	339	16	1	1	NUM
ejpam-2608	340	1	+	+	NUM
ejpam-2608	340	2	h2,0	h2,0	PROPN
ejpam-2608	340	3	∂̄	∂̄	PROPN
ejpam-2608	340	4	h1,1	h1,1	NOUN
ejpam-2608	340	5	bc	bc	PROPN
ejpam-2608	340	6	h1,1	h1,1	PROPN
ejpam-2608	340	7	bc+h2,2	bc+h2,2	PROPN
ejpam-2608	340	8	bc	bc	PROPN
ejpam-2608	340	9	2	2	NUM
ejpam-2608	340	10	−	−	PROPN
ejpam-2608	340	11	1	1	NUM
ejpam-2608	340	12	c	c	NOUN
ejpam-2608	340	13	1	1	NUM
ejpam-2608	340	14	0	0	NUM
ejpam-2608	340	15	h2,0	h2,0	NOUN
ejpam-2608	340	16	∂̄	∂̄	ADP
ejpam-2608	340	17	0	0	NUM
ejpam-2608	340	18	3.2	3.2	NUM
ejpam-2608	340	19	.	.	PUNCT
ejpam-2608	341	1	the	the	DET
ejpam-2608	341	2	bott	bott	PROPN
ejpam-2608	341	3	-	-	PUNCT
ejpam-2608	341	4	chern	chern	PROPN
ejpam-2608	341	5	and	and	CCONJ
ejpam-2608	341	6	aeppli	aeppli	VERB
ejpam-2608	341	7	cohomology	cohomology	NOUN
ejpam-2608	341	8	for	for	ADP
ejpam-2608	341	9	a	a	DET
ejpam-2608	341	10	hypothetical	hypothetical	ADJ
ejpam-2608	341	11	possibility	possibility	NOUN
ejpam-2608	341	12	of	of	ADP
ejpam-2608	341	13	the	the	DET
ejpam-2608	341	14	dolbeault	dolbeault	NOUN
ejpam-2608	341	15	cohomology	cohomology	NOUN
ejpam-2608	341	16	on	on	ADP
ejpam-2608	341	17	complex	complex	ADJ
ejpam-2608	341	18	s6	s6	PROPN
ejpam-2608	341	19	we	we	PRON
ejpam-2608	341	20	consider	consider	VERB
ejpam-2608	341	21	a	a	DET
ejpam-2608	341	22	specific	specific	ADJ
ejpam-2608	341	23	possible	possible	ADJ
ejpam-2608	341	24	scenario	scenario	NOUN
ejpam-2608	341	25	of	of	ADP
ejpam-2608	341	26	the	the	DET
ejpam-2608	341	27	dolbeault	dolbeault	NOUN
ejpam-2608	341	28	cohomology	cohomology	NOUN
ejpam-2608	341	29	on	on	ADP
ejpam-2608	341	30	complex	complex	ADJ
ejpam-2608	341	31	s6	s6	PROPN
ejpam-2608	341	32	.	.	PUNCT
ejpam-2608	342	1	namely	namely	ADV
ejpam-2608	342	2	,	,	PUNCT
ejpam-2608	342	3	h2,0	h2,0	PROPN
ejpam-2608	342	4	=	=	PUNCT
ejpam-2608	343	1	a	a	PRON
ejpam-2608	343	2	=	=	PUNCT
ejpam-2608	343	3	c	c	NOUN
ejpam-2608	343	4	=	=	SYM
ejpam-2608	343	5	d	d	NOUN
ejpam-2608	343	6	=	=	SYM
ejpam-2608	343	7	0	0	PROPN
ejpam-2608	343	8	.	.	PUNCT
ejpam-2608	344	1	in	in	ADP
ejpam-2608	344	2	terms	term	NOUN
ejpam-2608	344	3	of	of	ADP
ejpam-2608	344	4	hodge	hodge	PROPN
ejpam-2608	344	5	numbers	number	NOUN
ejpam-2608	344	6	,	,	PUNCT
ejpam-2608	344	7	this	this	PRON
ejpam-2608	344	8	is	be	AUX
ejpam-2608	344	9	h1,0	h1,0	PROPN
ejpam-2608	344	10	=	=	SYM
ejpam-2608	344	11	h2,0	h2,0	NOUN
ejpam-2608	344	12	=	=	PUNCT
ejpam-2608	344	13	h0,2	h0,2	PROPN
ejpam-2608	345	1	=	=	PUNCT
ejpam-2608	345	2	h1,2	h1,2	NOUN
ejpam-2608	345	3	=	=	SYM
ejpam-2608	345	4	0	0	NUM
ejpam-2608	345	5	and	and	CCONJ
ejpam-2608	345	6	h0,1	h0,1	PROPN
ejpam-2608	345	7	=	=	ADJ
ejpam-2608	345	8	h1,1	h1,1	NOUN
ejpam-2608	345	9	=	=	NOUN
ejpam-2608	345	10	1	1	NUM
ejpam-2608	345	11	.	.	PUNCT
ejpam-2608	346	1	this	this	PRON
ejpam-2608	346	2	is	be	AUX
ejpam-2608	346	3	one	one	NUM
ejpam-2608	346	4	of	of	ADP
ejpam-2608	346	5	the	the	DET
ejpam-2608	346	6	dolbeault	dolbeault	NOUN
ejpam-2608	346	7	cohomology	cohomology	NOUN
ejpam-2608	346	8	scenarios	scenario	NOUN
ejpam-2608	346	9	suggested	suggest	VERB
ejpam-2608	346	10	at	at	ADP
ejpam-2608	346	11	the	the	DET
ejpam-2608	346	12	end	end	NOUN
ejpam-2608	346	13	of	of	ADP
ejpam-2608	346	14	etesi[4	etesi[4	X
ejpam-2608	346	15	]	]	PUNCT
ejpam-2608	346	16	.	.	PUNCT
ejpam-2608	347	1	in	in	ADP
ejpam-2608	347	2	fact	fact	NOUN
ejpam-2608	347	3	,	,	PUNCT
ejpam-2608	347	4	the	the	DET
ejpam-2608	347	5	other	other	ADJ
ejpam-2608	347	6	cohomology	cohomology	NOUN
ejpam-2608	347	7	scenario	scenario	NOUN
ejpam-2608	347	8	,	,	PUNCT
ejpam-2608	347	9	with	with	ADP
ejpam-2608	347	10	h1,1	h1,1	NOUN
ejpam-2608	348	1	=	=	PUNCT
ejpam-2608	348	2	h2,1	h2,1	PROPN
ejpam-2608	348	3	=	=	SYM
ejpam-2608	348	4	1	1	NUM
ejpam-2608	348	5	and	and	CCONJ
ejpam-2608	348	6	h1,0	h1,0	PROPN
ejpam-2608	348	7	=	=	SYM
ejpam-2608	348	8	h2,0	h2,0	PROPN
ejpam-2608	348	9	=	=	PUNCT
ejpam-2608	349	1	a	a	DET
ejpam-2608	349	2	=	=	SYM
ejpam-2608	349	3	0	0	NUM
ejpam-2608	349	4	is	be	AUX
ejpam-2608	349	5	not	not	PART
ejpam-2608	349	6	possible	possible	ADJ
ejpam-2608	349	7	on	on	ADP
ejpam-2608	349	8	complex	complex	ADJ
ejpam-2608	349	9	s6	s6	PROPN
ejpam-2608	349	10	according	accord	VERB
ejpam-2608	349	11	to	to	ADP
ejpam-2608	349	12	our	our	PRON
ejpam-2608	349	13	table	table	NOUN
ejpam-2608	349	14	for	for	ADP
ejpam-2608	349	15	dolbeault	dolbeault	NOUN
ejpam-2608	349	16	cohomology	cohomology	NOUN
ejpam-2608	349	17	above	above	ADP
ejpam-2608	349	18	since	since	SCONJ
ejpam-2608	349	19	h1,1	h1,1	NOUN
ejpam-2608	349	20	=	=	X
ejpam-2608	350	1	h1,2	h1,2	PROPN
ejpam-2608	350	2	+	+	NUM
ejpam-2608	350	3	1−	1−	NUM
ejpam-2608	350	4	a	a	PRON
ejpam-2608	350	5	.	.	PUNCT
ejpam-2608	351	1	etesi	etesi	PROPN
ejpam-2608	351	2	does	do	AUX
ejpam-2608	351	3	actually	actually	ADV
ejpam-2608	351	4	in	in	ADP
ejpam-2608	351	5	fact	fact	NOUN
ejpam-2608	351	6	also	also	ADV
ejpam-2608	351	7	show	show	VERB
ejpam-2608	351	8	the	the	DET
ejpam-2608	351	9	incompatibility	incompatibility	NOUN
ejpam-2608	351	10	of	of	ADP
ejpam-2608	351	11	this	this	DET
ejpam-2608	351	12	other	other	ADJ
ejpam-2608	351	13	cohomology	cohomology	NOUN
ejpam-2608	351	14	scenario	scenario	NOUN
ejpam-2608	351	15	.	.	PUNCT
ejpam-2608	352	1	we	we	PRON
ejpam-2608	352	2	look	look	VERB
ejpam-2608	352	3	at	at	ADP
ejpam-2608	352	4	the	the	DET
ejpam-2608	352	5	following	follow	VERB
ejpam-2608	352	6	portion	portion	NOUN
ejpam-2608	352	7	of	of	ADP
ejpam-2608	352	8	the	the	DET
ejpam-2608	352	9	p	p	NOUN
ejpam-2608	352	10	=	=	ADJ
ejpam-2608	352	11	2	2	NUM
ejpam-2608	352	12	-	-	PUNCT
ejpam-2608	352	13	long	long	ADJ
ejpam-2608	352	14	exact	exact	ADJ
ejpam-2608	352	15	sequence	sequence	NOUN
ejpam-2608	352	16	:	:	PUNCT
ejpam-2608	352	17	h2,0	h2,0	PROPN
ejpam-2608	352	18	a	a	DET
ejpam-2608	352	19	→	→	SYM
ejpam-2608	352	20	h2,1	h2,1	PROPN
ejpam-2608	352	21	bc	bc	PROPN
ejpam-2608	352	22	→	→	SYM
ejpam-2608	352	23	h2,1	h2,1	PROPN
ejpam-2608	352	24	∂̄	∂̄	PROPN
ejpam-2608	352	25	→	→	PUNCT
ejpam-2608	352	26	h2,1	h2,1	PROPN
ejpam-2608	352	27	a	a	DET
ejpam-2608	352	28	→	→	SYM
ejpam-2608	352	29	h2,2	h2,2	PROPN
ejpam-2608	352	30	bc	bc	PROPN
ejpam-2608	352	31	→	→	SYM
ejpam-2608	352	32	h2,2	h2,2	PROPN
ejpam-2608	352	33	∂̄	∂̄	NOUN
ejpam-2608	352	34	→	→	PUNCT
ejpam-2608	352	35	h2,2	h2,2	PROPN
ejpam-2608	352	36	a	a	DET
ejpam-2608	352	37	→	→	SYM
ejpam-2608	352	38	h2,3	h2,3	ADJ
ejpam-2608	352	39	bc	bc	PROPN
ejpam-2608	352	40	→	→	SYM
ejpam-2608	352	41	h2,3	h2,3	ADJ
ejpam-2608	352	42	∂̄	∂̄	ADJ
ejpam-2608	352	43	references	reference	VERB
ejpam-2608	352	44	453	453	NUM
ejpam-2608	352	45	using	use	VERB
ejpam-2608	352	46	a	a	DET
ejpam-2608	352	47	total	total	ADJ
ejpam-2608	352	48	abuse	abuse	NOUN
ejpam-2608	352	49	of	of	ADP
ejpam-2608	352	50	notation	notation	NOUN
ejpam-2608	352	51	where	where	SCONJ
ejpam-2608	352	52	we	we	PRON
ejpam-2608	352	53	write	write	VERB
ejpam-2608	352	54	just	just	ADV
ejpam-2608	352	55	the	the	DET
ejpam-2608	352	56	dimensions	dimension	NOUN
ejpam-2608	352	57	of	of	ADP
ejpam-2608	352	58	the	the	DET
ejpam-2608	352	59	vector	vector	NOUN
ejpam-2608	352	60	spaces	space	NOUN
ejpam-2608	352	61	,	,	PUNCT
ejpam-2608	352	62	this	this	PRON
ejpam-2608	352	63	is	be	AUX
ejpam-2608	352	64	:	:	PUNCT
ejpam-2608	352	65	0→	0→	PROPN
ejpam-2608	352	66	h2,1	h2,1	PROPN
ejpam-2608	352	67	bc	bc	PROPN
ejpam-2608	352	68	→	→	SYM
ejpam-2608	352	69	0→	0→	PROPN
ejpam-2608	352	70	h2,1	h2,1	PROPN
ejpam-2608	352	71	a	a	PRON
ejpam-2608	352	72	→	→	PUNCT
ejpam-2608	352	73	h2,2	h2,2	PROPN
ejpam-2608	352	74	bc	bc	PROPN
ejpam-2608	352	75	→	→	SYM
ejpam-2608	352	76	1→	1→	NUM
ejpam-2608	352	77	h2,2	h2,2	PROPN
ejpam-2608	352	78	a	a	DET
ejpam-2608	352	79	→	→	SYM
ejpam-2608	352	80	1→	1→	NUM
ejpam-2608	352	81	0	0	NUM
ejpam-2608	352	82	since	since	SCONJ
ejpam-2608	352	83	the	the	DET
ejpam-2608	352	84	sequence	sequence	NOUN
ejpam-2608	352	85	is	be	AUX
ejpam-2608	352	86	exact	exact	ADJ
ejpam-2608	352	87	,	,	PUNCT
ejpam-2608	352	88	we	we	PRON
ejpam-2608	352	89	have	have	VERB
ejpam-2608	352	90	right	right	ADV
ejpam-2608	352	91	away	away	ADV
ejpam-2608	352	92	,	,	PUNCT
ejpam-2608	352	93	h2,1	h2,1	PROPN
ejpam-2608	352	94	bc	bc	PROPN
ejpam-2608	353	1	=	=	SYM
ejpam-2608	353	2	0	0	PUNCT
ejpam-2608	353	3	and	and	CCONJ
ejpam-2608	353	4	thus	thus	ADV
ejpam-2608	353	5	h2,1	h2,1	VERB
ejpam-2608	354	1	a	a	DET
ejpam-2608	354	2	=	=	NOUN
ejpam-2608	354	3	0	0	NUM
ejpam-2608	354	4	by	by	ADP
ejpam-2608	354	5	the	the	DET
ejpam-2608	354	6	serre	serre	PROPN
ejpam-2608	354	7	duality	duality	NOUN
ejpam-2608	354	8	.	.	PUNCT
ejpam-2608	355	1	by	by	ADP
ejpam-2608	355	2	the	the	DET
ejpam-2608	355	3	frohlicher	frohlicher	PROPN
ejpam-2608	355	4	sequence	sequence	NOUN
ejpam-2608	355	5	,	,	PUNCT
ejpam-2608	355	6	we	we	PRON
ejpam-2608	355	7	know	know	VERB
ejpam-2608	355	8	that	that	PRON
ejpam-2608	355	9	∂	∂	NOUN
ejpam-2608	355	10	:	:	PUNCT
ejpam-2608	355	11	h2,2	h2,2	PROPN
ejpam-2608	355	12	∂̄	∂̄	ADJ
ejpam-2608	355	13	→	→	SYM
ejpam-2608	355	14	h3,2	h3,2	NOUN
ejpam-2608	355	15	∂̄	∂̄	NOUN
ejpam-2608	355	16	is	be	AUX
ejpam-2608	355	17	an	an	DET
ejpam-2608	355	18	isomorphism	isomorphism	NOUN
ejpam-2608	355	19	.	.	PUNCT
ejpam-2608	356	1	in	in	ADP
ejpam-2608	356	2	particular	particular	ADJ
ejpam-2608	356	3	,	,	PUNCT
ejpam-2608	356	4	we	we	PRON
ejpam-2608	356	5	can	can	AUX
ejpam-2608	356	6	not	not	PART
ejpam-2608	356	7	have	have	VERB
ejpam-2608	356	8	a	a	DET
ejpam-2608	356	9	non	non	ADJ
ejpam-2608	356	10	zero	zero	NUM
ejpam-2608	356	11	∂̄-harmonic	∂̄-harmonic	ADJ
ejpam-2608	356	12	2,2	2,2	NUM
ejpam-2608	356	13	-	-	NOUN
ejpam-2608	356	14	form	form	NOUN
ejpam-2608	356	15	being	be	AUX
ejpam-2608	356	16	d	d	NOUN
ejpam-2608	356	17	-	-	PUNCT
ejpam-2608	356	18	closed	closed	ADJ
ejpam-2608	356	19	.	.	PUNCT
ejpam-2608	357	1	thus	thus	ADV
ejpam-2608	357	2	we	we	PRON
ejpam-2608	357	3	can	can	AUX
ejpam-2608	357	4	not	not	PART
ejpam-2608	357	5	have	have	VERB
ejpam-2608	357	6	h2,2	h2,2	PROPN
ejpam-2608	357	7	bc	bc	NOUN
ejpam-2608	357	8	being	be	AUX
ejpam-2608	357	9	isomorphic	isomorphic	ADJ
ejpam-2608	357	10	to	to	ADP
ejpam-2608	357	11	h2,2	h2,2	PROPN
ejpam-2608	357	12	∂̄	∂̄	ADV
ejpam-2608	357	13	.	.	PUNCT
ejpam-2608	358	1	thus	thus	ADV
ejpam-2608	358	2	h2,2	h2,2	NUM
ejpam-2608	358	3	bc	bc	X
ejpam-2608	358	4	=	=	SYM
ejpam-2608	358	5	0	0	PUNCT
ejpam-2608	359	1	and	and	CCONJ
ejpam-2608	359	2	h2,2	h2,2	PRON
ejpam-2608	359	3	a	a	DET
ejpam-2608	359	4	=	=	X
ejpam-2608	359	5	h1,1	h1,1	NOUN
ejpam-2608	359	6	bc	bc	PROPN
ejpam-2608	359	7	=	=	SYM
ejpam-2608	359	8	2	2	X
ejpam-2608	359	9	.	.	PUNCT
ejpam-2608	360	1	this	this	PRON
ejpam-2608	360	2	completes	complete	VERB
ejpam-2608	360	3	the	the	DET
ejpam-2608	360	4	bott	bott	PROPN
ejpam-2608	360	5	-	-	PUNCT
ejpam-2608	360	6	chern	chern	PROPN
ejpam-2608	360	7	and	and	CCONJ
ejpam-2608	360	8	aeppli	aeppli	VERB
ejpam-2608	360	9	cohomology	cohomology	NOUN
ejpam-2608	360	10	for	for	ADP
ejpam-2608	360	11	this	this	DET
ejpam-2608	360	12	possible	possible	ADJ
ejpam-2608	360	13	dolbeault	dolbeault	NOUN
ejpam-2608	360	14	cohomology	cohomology	NOUN
ejpam-2608	360	15	.	.	PUNCT
ejpam-2608	361	1	acknowledgements	acknowledgement	NOUN
ejpam-2608	361	2	i	i	PRON
ejpam-2608	361	3	would	would	AUX
ejpam-2608	361	4	like	like	VERB
ejpam-2608	361	5	to	to	PART
ejpam-2608	361	6	acknowledge	acknowledge	VERB
ejpam-2608	361	7	the	the	DET
ejpam-2608	361	8	hospitality	hospitality	NOUN
ejpam-2608	361	9	and	and	CCONJ
ejpam-2608	361	10	support	support	NOUN
ejpam-2608	361	11	of	of	ADP
ejpam-2608	361	12	the	the	DET
ejpam-2608	361	13	simons	simon	NOUN
ejpam-2608	361	14	workshop	workshop	NOUN
ejpam-2608	361	15	in	in	ADP
ejpam-2608	361	16	mathematics	mathematic	NOUN
ejpam-2608	361	17	and	and	CCONJ
ejpam-2608	361	18	physics	physics	PROPN
ejpam-2608	361	19	,	,	PUNCT
ejpam-2608	361	20	its	its	PRON
ejpam-2608	361	21	participants	participant	NOUN
ejpam-2608	361	22	and	and	CCONJ
ejpam-2608	361	23	its	its	PRON
ejpam-2608	361	24	hosts	host	NOUN
ejpam-2608	361	25	,	,	PUNCT
ejpam-2608	361	26	martin	martin	PROPN
ejpam-2608	361	27	rocek	rocek	PROPN
ejpam-2608	361	28	and	and	CCONJ
ejpam-2608	361	29	cumrun	cumrun	PROPN
ejpam-2608	361	30	vafa	vafa	PROPN
ejpam-2608	361	31	.	.	PUNCT
ejpam-2608	362	1	references	reference	NOUN
ejpam-2608	362	2	[	[	X
ejpam-2608	362	3	1	1	NUM
ejpam-2608	362	4	]	]	PUNCT
ejpam-2608	362	5	d.	d.	NOUN
ejpam-2608	362	6	angella	angella	NOUN
ejpam-2608	362	7	.	.	PUNCT
ejpam-2608	363	1	cohomological	cohomological	ADJ
ejpam-2608	363	2	aspects	aspect	NOUN
ejpam-2608	363	3	in	in	ADP
ejpam-2608	363	4	complex	complex	ADJ
ejpam-2608	363	5	non	non	ADJ
ejpam-2608	363	6	-	-	ADJ
ejpam-2608	363	7	kahler	kahler	ADJ
ejpam-2608	363	8	geometry	geometry	NOUN
ejpam-2608	363	9	.	.	PUNCT
ejpam-2608	364	1	springer	springer	NOUN
ejpam-2608	364	2	,	,	PUNCT
ejpam-2608	364	3	2014	2014	NUM
ejpam-2608	364	4	.	.	PUNCT
ejpam-2608	365	1	[	[	X
ejpam-2608	365	2	2	2	NUM
ejpam-2608	365	3	]	]	X
ejpam-2608	365	4	j.r	j.r	PROPN
ejpam-2608	365	5	.	.	PROPN
ejpam-2608	365	6	brown	brown	PROPN
ejpam-2608	365	7	.	.	PUNCT
ejpam-2608	366	1	properties	property	NOUN
ejpam-2608	366	2	of	of	ADP
ejpam-2608	366	3	exotic	exotic	ADJ
ejpam-2608	366	4	complex	complex	ADJ
ejpam-2608	366	5	structures	structure	NOUN
ejpam-2608	366	6	on	on	ADP
ejpam-2608	366	7	cp3	cp3	PROPN
ejpam-2608	366	8	.	.	PUNCT
ejpam-2608	367	1	mathematica	mathematica	PROPN
ejpam-2608	367	2	bohemica	bohemica	PROPN
ejpam-2608	367	3	,	,	PUNCT
ejpam-2608	367	4	132(1):59–74	132(1):59–74	NUM
ejpam-2608	367	5	,	,	PUNCT
ejpam-2608	367	6	2007	2007	NUM
ejpam-2608	367	7	.	.	PUNCT
ejpam-2608	368	1	[	[	X
ejpam-2608	368	2	3	3	NUM
ejpam-2608	368	3	]	]	X
ejpam-2608	368	4	f.	f.	PROPN
ejpam-2608	368	5	campana	campana	PROPN
ejpam-2608	368	6	,	,	PUNCT
ejpam-2608	368	7	j.p	j.p	PROPN
ejpam-2608	368	8	.	.	PROPN
ejpam-2608	368	9	demailly	demailly	ADV
ejpam-2608	368	10	,	,	PUNCT
ejpam-2608	368	11	and	and	CCONJ
ejpam-2608	368	12	t.	t.	PROPN
ejpam-2608	368	13	peternell	peternell	PROPN
ejpam-2608	368	14	.	.	PUNCT
ejpam-2608	369	1	the	the	DET
ejpam-2608	369	2	algebraic	algebraic	ADJ
ejpam-2608	369	3	dimension	dimension	NOUN
ejpam-2608	369	4	of	of	ADP
ejpam-2608	369	5	compact	compact	ADJ
ejpam-2608	369	6	complex	complex	ADJ
ejpam-2608	369	7	threefolds	threefold	NOUN
ejpam-2608	369	8	with	with	ADP
ejpam-2608	369	9	vanishing	vanish	VERB
ejpam-2608	369	10	second	second	ADJ
ejpam-2608	369	11	betti	betti	ADJ
ejpam-2608	369	12	number	number	NOUN
ejpam-2608	369	13	.	.	PUNCT
ejpam-2608	370	1	compos	compos	PROPN
ejpam-2608	370	2	.	.	PUNCT
ejpam-2608	371	1	math	math	NOUN
ejpam-2608	371	2	.	.	PUNCT
ejpam-2608	371	3	,	,	PUNCT
ejpam-2608	372	1	112:77–91	112:77–91	NUM
ejpam-2608	372	2	,	,	PUNCT
ejpam-2608	372	3	1998	1998	NUM
ejpam-2608	372	4	.	.	PUNCT
ejpam-2608	373	1	[	[	X
ejpam-2608	373	2	4	4	X
ejpam-2608	373	3	]	]	X
ejpam-2608	373	4	g.	g.	PROPN
ejpam-2608	373	5	etesi	etesi	PROPN
ejpam-2608	373	6	.	.	PUNCT
ejpam-2608	374	1	complex	complex	ADJ
ejpam-2608	374	2	structure	structure	NOUN
ejpam-2608	374	3	on	on	ADP
ejpam-2608	374	4	the	the	DET
ejpam-2608	374	5	six	six	NUM
ejpam-2608	374	6	dimensional	dimensional	ADJ
ejpam-2608	374	7	sphere	sphere	NOUN
ejpam-2608	374	8	from	from	ADP
ejpam-2608	374	9	a	a	DET
ejpam-2608	374	10	spontaneous	spontaneous	ADJ
ejpam-2608	374	11	symmetry	symmetry	NOUN
ejpam-2608	374	12	breaking	breaking	NOUN
ejpam-2608	374	13	.	.	PUNCT
ejpam-2608	375	1	journal	journal	PROPN
ejpam-2608	375	2	of	of	ADP
ejpam-2608	375	3	mathematical	mathematical	ADJ
ejpam-2608	375	4	physics	physics	NOUN
ejpam-2608	375	5	,	,	PUNCT
ejpam-2608	375	6	56(4	56(4	NOUN
ejpam-2608	375	7	)	)	PUNCT
ejpam-2608	375	8	,	,	PUNCT
ejpam-2608	375	9	april	april	PROPN
ejpam-2608	375	10	2015	2015	NUM
ejpam-2608	375	11	.	.	PUNCT
ejpam-2608	376	1	[	[	X
ejpam-2608	376	2	5	5	NUM
ejpam-2608	376	3	]	]	PUNCT
ejpam-2608	376	4	a.	a.	NOUN
ejpam-2608	376	5	gray	gray	NOUN
ejpam-2608	376	6	.	.	PUNCT
ejpam-2608	377	1	a	a	DET
ejpam-2608	377	2	property	property	NOUN
ejpam-2608	377	3	of	of	ADP
ejpam-2608	377	4	a	a	DET
ejpam-2608	377	5	hypothetical	hypothetical	ADJ
ejpam-2608	377	6	complex	complex	ADJ
ejpam-2608	377	7	structure	structure	NOUN
ejpam-2608	377	8	on	on	ADP
ejpam-2608	377	9	the	the	DET
ejpam-2608	377	10	six	six	NUM
ejpam-2608	377	11	sphere	sphere	NOUN
ejpam-2608	377	12	.	.	PUNCT
ejpam-2608	378	1	bol	bol	PROPN
ejpam-2608	378	2	.	.	PUNCT
ejpam-2608	379	1	un	un	PROPN
ejpam-2608	379	2	.	.	PROPN
ejpam-2608	379	3	mat	mat	PROPN
ejpam-2608	379	4	.	.	PUNCT
ejpam-2608	379	5	ital	ital	PROPN
ejpam-2608	379	6	.	.	PUNCT
ejpam-2608	380	1	suppl	suppl	PROPN
ejpam-2608	380	2	.	.	PUNCT
ejpam-2608	381	1	fasc	fasc	PROPN
ejpam-2608	381	2	.	.	PROPN
ejpam-2608	381	3	,	,	PUNCT
ejpam-2608	381	4	2:251–255	2:251–255	NUM
ejpam-2608	381	5	,	,	PUNCT
ejpam-2608	381	6	1997	1997	NUM
ejpam-2608	381	7	.	.	PUNCT
ejpam-2608	382	1	[	[	X
ejpam-2608	382	2	6	6	NUM
ejpam-2608	382	3	]	]	PUNCT
ejpam-2608	382	4	f.	f.	PROPN
ejpam-2608	382	5	hirzebruch	hirzebruch	PROPN
ejpam-2608	382	6	.	.	PUNCT
ejpam-2608	383	1	some	some	DET
ejpam-2608	383	2	problems	problem	NOUN
ejpam-2608	383	3	on	on	ADP
ejpam-2608	383	4	differentiable	differentiable	ADJ
ejpam-2608	383	5	and	and	CCONJ
ejpam-2608	383	6	complex	complex	ADJ
ejpam-2608	383	7	manifolds	manifold	NOUN
ejpam-2608	383	8	.	.	PUNCT
ejpam-2608	384	1	ann	ann	PROPN
ejpam-2608	384	2	.	.	PROPN
ejpam-2608	384	3	of	of	ADP
ejpam-2608	384	4	math	math	NOUN
ejpam-2608	384	5	.	.	PUNCT
ejpam-2608	384	6	,	,	PUNCT
ejpam-2608	385	1	60(2):213–236	60(2):213–236	PROPN
ejpam-2608	385	2	,	,	PUNCT
ejpam-2608	385	3	1954	1954	NUM
ejpam-2608	385	4	.	.	PUNCT
ejpam-2608	386	1	[	[	X
ejpam-2608	386	2	7	7	X
ejpam-2608	386	3	]	]	X
ejpam-2608	386	4	a.t	a.t	PROPN
ejpam-2608	386	5	.	.	PROPN
ejpam-2608	386	6	huckleberry	huckleberry	PROPN
ejpam-2608	386	7	,	,	PUNCT
ejpam-2608	386	8	s.	s.	PROPN
ejpam-2608	386	9	kebekus	kebekus	PROPN
ejpam-2608	386	10	,	,	PUNCT
ejpam-2608	386	11	and	and	CCONJ
ejpam-2608	386	12	t.	t.	PROPN
ejpam-2608	386	13	peternell	peternell	PROPN
ejpam-2608	386	14	.	.	PUNCT
ejpam-2608	387	1	group	group	NOUN
ejpam-2608	387	2	actions	action	NOUN
ejpam-2608	387	3	on	on	ADP
ejpam-2608	387	4	s6	s6	PROPN
ejpam-2608	387	5	and	and	CCONJ
ejpam-2608	387	6	complex	complex	ADJ
ejpam-2608	387	7	structures	structure	NOUN
ejpam-2608	387	8	on	on	ADP
ejpam-2608	387	9	p3	p3	PROPN
ejpam-2608	387	10	.	.	PUNCT
ejpam-2608	388	1	duke	duke	PROPN
ejpam-2608	388	2	math	math	PROPN
ejpam-2608	388	3	.	.	PUNCT
ejpam-2608	389	1	j.	j.	PROPN
ejpam-2608	389	2	,	,	PUNCT
ejpam-2608	389	3	102(1):101–124	102(1):101–124	NUM
ejpam-2608	389	4	,	,	PUNCT
ejpam-2608	389	5	2000	2000	NUM
ejpam-2608	389	6	.	.	PUNCT
ejpam-2608	390	1	[	[	X
ejpam-2608	390	2	8	8	NUM
ejpam-2608	390	3	]	]	X
ejpam-2608	390	4	c.	c.	PROPN
ejpam-2608	390	5	lebrun	lebrun	PROPN
ejpam-2608	390	6	.	.	PUNCT
ejpam-2608	391	1	orthogonal	orthogonal	ADJ
ejpam-2608	391	2	complex	complex	ADJ
ejpam-2608	391	3	structures	structure	NOUN
ejpam-2608	391	4	on	on	ADP
ejpam-2608	391	5	s6	s6	PROPN
ejpam-2608	391	6	.	.	PUNCT
ejpam-2608	392	1	proc	proc	PROPN
ejpam-2608	392	2	.	.	PUNCT
ejpam-2608	393	1	amer	amer	PROPN
ejpam-2608	393	2	.	.	PUNCT
ejpam-2608	393	3	math	math	PROPN
ejpam-2608	393	4	.	.	PUNCT
ejpam-2608	394	1	soc	soc	PROPN
ejpam-2608	394	2	.	.	PUNCT
ejpam-2608	394	3	,	,	PUNCT
ejpam-2608	394	4	101:136	101:136	NOUN
ejpam-2608	394	5	–	–	PUNCT
ejpam-2608	394	6	138	138	NUM
ejpam-2608	394	7	,	,	PUNCT
ejpam-2608	394	8	1987	1987	NUM
ejpam-2608	394	9	.	.	PUNCT
ejpam-2608	395	1	[	[	X
ejpam-2608	395	2	9	9	NUM
ejpam-2608	395	3	]	]	X
ejpam-2608	395	4	d.	d.	PROPN
ejpam-2608	395	5	popovici	popovici	PROPN
ejpam-2608	395	6	.	.	PUNCT
ejpam-2608	396	1	aeppli	aeppli	VERB
ejpam-2608	396	2	cohomology	cohomology	NOUN
ejpam-2608	396	3	classes	class	NOUN
ejpam-2608	396	4	associated	associate	VERB
ejpam-2608	396	5	with	with	ADP
ejpam-2608	396	6	gauduchon	gauduchon	PROPN
ejpam-2608	396	7	metrics	metric	NOUN
ejpam-2608	396	8	on	on	ADP
ejpam-2608	396	9	compact	compact	ADJ
ejpam-2608	396	10	complex	complex	ADJ
ejpam-2608	396	11	manifolds	manifold	NOUN
ejpam-2608	396	12	.	.	PUNCT
ejpam-2608	397	1	arxiv	arxiv	NOUN
ejpam-2608	397	2	:	:	PUNCT
ejpam-2608	397	3	1310.3685v1	1310.3685v1	NUM
ejpam-2608	398	1	[	[	X
ejpam-2608	398	2	math.dg	math.dg	X
ejpam-2608	398	3	]	]	PUNCT
ejpam-2608	398	4	,	,	PUNCT
ejpam-2608	398	5	october	october	PROPN
ejpam-2608	398	6	2013	2013	NUM
ejpam-2608	398	7	.	.	PUNCT
ejpam-2608	399	1	[	[	X
ejpam-2608	399	2	10	10	NUM
ejpam-2608	399	3	]	]	PUNCT
ejpam-2608	399	4	m.	m.	NOUN
ejpam-2608	399	5	schweitzer	schweitzer	PROPN
ejpam-2608	399	6	.	.	PUNCT
ejpam-2608	400	1	autour	autour	PROPN
ejpam-2608	400	2	de	de	X
ejpam-2608	400	3	la	la	X
ejpam-2608	400	4	cohomologie	cohomologie	PROPN
ejpam-2608	400	5	de	de	PROPN
ejpam-2608	400	6	bott	bott	PROPN
ejpam-2608	400	7	-	-	PUNCT
ejpam-2608	400	8	chern	chern	PROPN
ejpam-2608	400	9	.	.	PUNCT
ejpam-2608	401	1	arxiv:0709.3528v1	arxiv:0709.3528v1	PUNCT
ejpam-2608	402	1	[	[	X
ejpam-2608	402	2	math.ag	math.ag	X
ejpam-2608	402	3	]	]	X
ejpam-2608	402	4	.	.	PUNCT
ejpam-2608	402	5	,	,	PUNCT
ejpam-2608	402	6	prepublication	prepublication	NOUN
ejpam-2608	402	7	de	de	X
ejpam-2608	402	8	l’institut	l’institut	PROPN
ejpam-2608	402	9	fourier(703	fourier(703	PROPN
ejpam-2608	402	10	)	)	PUNCT
ejpam-2608	402	11	,	,	PUNCT
ejpam-2608	402	12	2007	2007	NUM
ejpam-2608	402	13	.	.	PUNCT
ejpam-2608	403	1	references	reference	NOUN
ejpam-2608	403	2	454	454	NUM
ejpam-2608	403	3	[	[	X
ejpam-2608	403	4	11	11	NUM
ejpam-2608	403	5	]	]	X
ejpam-2608	403	6	l.	l.	PROPN
ejpam-2608	403	7	ugarte	ugarte	PROPN
ejpam-2608	403	8	.	.	PUNCT
ejpam-2608	404	1	hodge	hodge	PROPN
ejpam-2608	404	2	numbers	number	NOUN
ejpam-2608	404	3	of	of	ADP
ejpam-2608	404	4	a	a	DET
ejpam-2608	404	5	hypothetical	hypothetical	ADJ
ejpam-2608	404	6	complex	complex	ADJ
ejpam-2608	404	7	structure	structure	NOUN
ejpam-2608	404	8	on	on	ADP
ejpam-2608	404	9	the	the	DET
ejpam-2608	404	10	six	six	NUM
ejpam-2608	404	11	sphere	sphere	NOUN
ejpam-2608	404	12	.	.	PUNCT
ejpam-2608	405	1	geom	geom	PROPN
ejpam-2608	405	2	.	.	PUNCT
ejpam-2608	406	1	dedicata	dedicata	PROPN
ejpam-2608	406	2	,	,	PUNCT
ejpam-2608	406	3	81:173–179	81:173–179	PROPN
ejpam-2608	406	4	,	,	PUNCT
ejpam-2608	406	5	2000	2000	NUM
ejpam-2608	406	6	.	.	PUNCT
ejpam-2608	407	1	[	[	X
ejpam-2608	407	2	12	12	NUM
ejpam-2608	407	3	]	]	PUNCT
ejpam-2608	407	4	j.	j.	PROPN
ejpam-2608	407	5	varouchas	varouchas	PROPN
ejpam-2608	407	6	.	.	PROPN
ejpam-2608	408	1	proprietes	propriete	VERB
ejpam-2608	408	2	cohomologiques	cohomologiques	PROPN
ejpam-2608	408	3	d’une	d’une	PROPN
ejpam-2608	408	4	classe	classe	X
ejpam-2608	408	5	de	de	X
ejpam-2608	408	6	varietes	varietes	PROPN
ejpam-2608	408	7	analytiques	analytique	VERB
ejpam-2608	408	8	complexes	complex	NOUN
ejpam-2608	408	9	compactes	compact	VERB
ejpam-2608	408	10	.	.	PUNCT
ejpam-2608	409	1	in	in	ADP
ejpam-2608	409	2	p.	p.	PROPN
ejpam-2608	409	3	lelong	lelong	PROPN
ejpam-2608	409	4	,	,	PUNCT
ejpam-2608	409	5	p.	p.	NOUN
ejpam-2608	409	6	dolbeault	dolbeault	PROPN
ejpam-2608	409	7	,	,	PUNCT
ejpam-2608	409	8	and	and	CCONJ
ejpam-2608	409	9	h.	h.	PROPN
ejpam-2608	409	10	skoda	skoda	PROPN
ejpam-2608	409	11	,	,	PUNCT
ejpam-2608	409	12	editors	editor	NOUN
ejpam-2608	409	13	,	,	PUNCT
ejpam-2608	409	14	seminaire	seminaire	VERB
ejpam-2608	409	15	d’analyse	d’analyse	PROPN
ejpam-2608	409	16	p.	p.	PROPN
ejpam-2608	409	17	lelong	lelong	PROPN
ejpam-2608	409	18	-	-	PROPN
ejpam-2608	409	19	p.	p.	NOUN
ejpam-2608	409	20	dolbeault	dolbeault	PROPN
ejpam-2608	409	21	-	-	PUNCT
ejpam-2608	409	22	h.	h.	PROPN
ejpam-2608	409	23	skoda	skoda	PROPN
ejpam-2608	409	24	,	,	PUNCT
ejpam-2608	409	25	annees	annee	NOUN
ejpam-2608	409	26	1983/1984	1983/1984	NUM
ejpam-2608	409	27	,	,	PUNCT
ejpam-2608	409	28	lecture	lecture	NOUN
ejpam-2608	409	29	notes	note	NOUN
ejpam-2608	409	30	in	in	ADP
ejpam-2608	409	31	math	math	NOUN
ejpam-2608	409	32	.	.	PUNCT
ejpam-2608	410	1	,	,	PUNCT
ejpam-2608	410	2	volume	volume	NOUN
ejpam-2608	410	3	1198	1198	NUM
ejpam-2608	410	4	,	,	PUNCT
ejpam-2608	410	5	pages	page	NOUN
ejpam-2608	410	6	233–243	233–243	NUM
ejpam-2608	410	7	.	.	PUNCT
ejpam-2608	411	1	springer	springer	NOUN
ejpam-2608	411	2	,	,	PUNCT
ejpam-2608	411	3	1986	1986	NUM
ejpam-2608	411	4	.	.	PUNCT