id	sid	tid	token	lemma	pos
ejpam-5351	1	1	european	european	PROPN
ejpam-5351	1	2	journal	journal	PROPN
ejpam-5351	1	3	of	of	ADP
ejpam-5351	1	4	pure	pure	ADJ
ejpam-5351	1	5	and	and	CCONJ
ejpam-5351	1	6	applied	apply	VERB
ejpam-5351	1	7	mathematics	mathematic	NOUN
ejpam-5351	1	8	vol	vol	NOUN
ejpam-5351	1	9	.	.	PROPN
ejpam-5351	2	1	17	17	NUM
ejpam-5351	2	2	,	,	PUNCT
ejpam-5351	2	3	no	no	INTJ
ejpam-5351	2	4	.	.	NOUN
ejpam-5351	2	5	3	3	NUM
ejpam-5351	2	6	,	,	PUNCT
ejpam-5351	2	7	2024	2024	NUM
ejpam-5351	2	8	,	,	PUNCT
ejpam-5351	2	9	2361	2361	NUM
ejpam-5351	2	10	-	-	SYM
ejpam-5351	2	11	2369	2369	NUM
ejpam-5351	2	12	issn	issn	VERB
ejpam-5351	2	13	1307	1307	NUM
ejpam-5351	2	14	-	-	SYM
ejpam-5351	2	15	5543	5543	NUM
ejpam-5351	2	16	–	–	PUNCT
ejpam-5351	2	17	ejpam.com	ejpam.com	X
ejpam-5351	2	18	published	publish	VERB
ejpam-5351	2	19	by	by	ADP
ejpam-5351	2	20	new	new	PROPN
ejpam-5351	2	21	york	york	PROPN
ejpam-5351	2	22	business	business	PROPN
ejpam-5351	2	23	global	global	PROPN
ejpam-5351	2	24	an	an	DET
ejpam-5351	2	25	outreach	outreach	NOUN
ejpam-5351	2	26	note	note	NOUN
ejpam-5351	2	27	on	on	ADP
ejpam-5351	2	28	the	the	DET
ejpam-5351	2	29	poincaré	poincaré	ADJ
ejpam-5351	2	30	conjecture	conjecture	NOUN
ejpam-5351	2	31	for	for	ADP
ejpam-5351	2	32	non	non	NOUN
ejpam-5351	2	33	-	-	NOUN
ejpam-5351	2	34	specialists	specialist	NOUN
ejpam-5351	2	35	daniele	daniele	PROPN
ejpam-5351	2	36	ettore	ettore	PROPN
ejpam-5351	2	37	otera	otera	PROPN
ejpam-5351	2	38	vilnius	vilnius	PROPN
ejpam-5351	2	39	university	university	PROPN
ejpam-5351	2	40	,	,	PUNCT
ejpam-5351	2	41	institute	institute	PROPN
ejpam-5351	2	42	of	of	ADP
ejpam-5351	2	43	data	data	PROPN
ejpam-5351	2	44	science	science	NOUN
ejpam-5351	2	45	and	and	CCONJ
ejpam-5351	2	46	digital	digital	ADJ
ejpam-5351	2	47	technologies	technology	NOUN
ejpam-5351	2	48	,	,	PUNCT
ejpam-5351	2	49	akademijos	akademijos	PROPN
ejpam-5351	2	50	st	st	PROPN
ejpam-5351	2	51	.	.	PROPN
ejpam-5351	2	52	4	4	NUM
ejpam-5351	2	53	,	,	PUNCT
ejpam-5351	2	54	lt-08663	lt-08663	NOUN
ejpam-5351	2	55	,	,	PUNCT
ejpam-5351	2	56	vilnius	vilnius	PROPN
ejpam-5351	2	57	,	,	PUNCT
ejpam-5351	2	58	lithuania	lithuania	PROPN
ejpam-5351	2	59	abstract	abstract	NOUN
ejpam-5351	2	60	.	.	PUNCT
ejpam-5351	3	1	the	the	DET
ejpam-5351	3	2	poincaré	poincaré	ADJ
ejpam-5351	3	3	conjecture	conjecture	NOUN
ejpam-5351	3	4	,	,	PUNCT
ejpam-5351	3	5	a	a	DET
ejpam-5351	3	6	problem	problem	NOUN
ejpam-5351	3	7	formulated	formulate	VERB
ejpam-5351	3	8	by	by	ADP
ejpam-5351	3	9	the	the	DET
ejpam-5351	3	10	french	french	ADJ
ejpam-5351	3	11	mathematician	mathematician	NOUN
ejpam-5351	3	12	henri	henri	PROPN
ejpam-5351	3	13	poincaré	poincaré	ADJ
ejpam-5351	3	14	more	more	ADJ
ejpam-5351	3	15	than	than	ADP
ejpam-5351	3	16	a	a	DET
ejpam-5351	3	17	century	century	NOUN
ejpam-5351	3	18	ago	ago	ADV
ejpam-5351	3	19	,	,	PUNCT
ejpam-5351	3	20	has	have	AUX
ejpam-5351	3	21	been	be	AUX
ejpam-5351	3	22	one	one	NUM
ejpam-5351	3	23	of	of	ADP
ejpam-5351	3	24	the	the	DET
ejpam-5351	3	25	main	main	ADJ
ejpam-5351	3	26	challenge	challenge	NOUN
ejpam-5351	3	27	of	of	ADP
ejpam-5351	3	28	modern	modern	ADJ
ejpam-5351	3	29	mathematics	mathematic	NOUN
ejpam-5351	3	30	.	.	PUNCT
ejpam-5351	4	1	it	it	PRON
ejpam-5351	4	2	states	state	VERB
ejpam-5351	4	3	that	that	SCONJ
ejpam-5351	4	4	any	any	DET
ejpam-5351	4	5	three	three	NUM
ejpam-5351	4	6	-	-	PUNCT
ejpam-5351	4	7	dimensional	dimensional	ADJ
ejpam-5351	4	8	space	space	NOUN
ejpam-5351	4	9	which	which	PRON
ejpam-5351	4	10	is	be	AUX
ejpam-5351	4	11	closed	close	VERB
ejpam-5351	4	12	on	on	ADP
ejpam-5351	4	13	itself	itself	PRON
ejpam-5351	4	14	and	and	CCONJ
ejpam-5351	4	15	without	without	ADP
ejpam-5351	4	16	holes	hole	NOUN
ejpam-5351	4	17	can	can	AUX
ejpam-5351	4	18	be	be	AUX
ejpam-5351	4	19	deformed	deform	VERB
ejpam-5351	4	20	into	into	ADP
ejpam-5351	4	21	a	a	DET
ejpam-5351	4	22	sphere	sphere	NOUN
ejpam-5351	4	23	of	of	ADP
ejpam-5351	4	24	dimension	dimension	NOUN
ejpam-5351	4	25	3	3	NUM
ejpam-5351	4	26	.	.	PUNCT
ejpam-5351	5	1	even	even	ADV
ejpam-5351	5	2	if	if	SCONJ
ejpam-5351	5	3	the	the	DET
ejpam-5351	5	4	conjecture	conjecture	NOUN
ejpam-5351	5	5	was	be	AUX
ejpam-5351	5	6	solved	solve	VERB
ejpam-5351	5	7	at	at	ADP
ejpam-5351	5	8	the	the	DET
ejpam-5351	5	9	beginning	beginning	NOUN
ejpam-5351	5	10	of	of	ADP
ejpam-5351	5	11	this	this	DET
ejpam-5351	5	12	century	century	NOUN
ejpam-5351	5	13	,	,	PUNCT
ejpam-5351	5	14	it	it	PRON
ejpam-5351	5	15	still	still	ADV
ejpam-5351	5	16	remains	remain	VERB
ejpam-5351	5	17	a	a	DET
ejpam-5351	5	18	mysterious	mysterious	ADJ
ejpam-5351	5	19	,	,	PUNCT
ejpam-5351	5	20	appealing	appealing	ADJ
ejpam-5351	5	21	and	and	CCONJ
ejpam-5351	5	22	intriguing	intriguing	ADJ
ejpam-5351	5	23	problem	problem	NOUN
ejpam-5351	5	24	worth	worth	ADJ
ejpam-5351	5	25	to	to	PART
ejpam-5351	5	26	be	be	AUX
ejpam-5351	5	27	further	far	ADV
ejpam-5351	5	28	studied	study	VERB
ejpam-5351	5	29	in	in	ADP
ejpam-5351	5	30	detail	detail	NOUN
ejpam-5351	5	31	.	.	PUNCT
ejpam-5351	6	1	the	the	DET
ejpam-5351	6	2	purpose	purpose	NOUN
ejpam-5351	6	3	of	of	ADP
ejpam-5351	6	4	this	this	DET
ejpam-5351	6	5	short	short	ADJ
ejpam-5351	6	6	popularizing	popularize	VERB
ejpam-5351	6	7	note	note	NOUN
ejpam-5351	6	8	is	be	AUX
ejpam-5351	6	9	,	,	PUNCT
ejpam-5351	6	10	on	on	ADP
ejpam-5351	6	11	the	the	DET
ejpam-5351	6	12	one	one	NUM
ejpam-5351	6	13	hand	hand	NOUN
ejpam-5351	6	14	,	,	PUNCT
ejpam-5351	6	15	to	to	PART
ejpam-5351	6	16	provide	provide	VERB
ejpam-5351	6	17	a	a	DET
ejpam-5351	6	18	quick	quick	ADJ
ejpam-5351	6	19	overview	overview	NOUN
ejpam-5351	6	20	for	for	ADP
ejpam-5351	6	21	non	non	NOUN
ejpam-5351	6	22	-	-	NOUN
ejpam-5351	6	23	experts	expert	NOUN
ejpam-5351	6	24	of	of	ADP
ejpam-5351	6	25	what	what	PRON
ejpam-5351	6	26	we	we	PRON
ejpam-5351	6	27	know	know	VERB
ejpam-5351	6	28	today	today	NOUN
ejpam-5351	6	29	about	about	ADP
ejpam-5351	6	30	the	the	DET
ejpam-5351	6	31	poincaré	poincaré	ADJ
ejpam-5351	6	32	conjecture	conjecture	NOUN
ejpam-5351	6	33	and	and	CCONJ
ejpam-5351	6	34	its	its	PRON
ejpam-5351	6	35	related	related	ADJ
ejpam-5351	6	36	problems	problem	NOUN
ejpam-5351	6	37	in	in	ADP
ejpam-5351	6	38	dimension	dimension	NOUN
ejpam-5351	6	39	3	3	NUM
ejpam-5351	6	40	,	,	PUNCT
ejpam-5351	6	41	and	and	CCONJ
ejpam-5351	6	42	,	,	PUNCT
ejpam-5351	6	43	on	on	ADP
ejpam-5351	6	44	the	the	DET
ejpam-5351	6	45	other	other	ADJ
ejpam-5351	6	46	hand	hand	NOUN
ejpam-5351	6	47	,	,	PUNCT
ejpam-5351	6	48	to	to	PART
ejpam-5351	6	49	explain	explain	VERB
ejpam-5351	6	50	why	why	SCONJ
ejpam-5351	6	51	it	it	PRON
ejpam-5351	6	52	has	have	AUX
ejpam-5351	6	53	represented	represent	VERB
ejpam-5351	6	54	a	a	DET
ejpam-5351	6	55	central	central	ADJ
ejpam-5351	6	56	problem	problem	NOUN
ejpam-5351	6	57	in	in	ADP
ejpam-5351	6	58	mathematics	mathematic	NOUN
ejpam-5351	6	59	.	.	PUNCT
ejpam-5351	7	1	2020	2020	NUM
ejpam-5351	7	2	mathematics	mathematic	NOUN
ejpam-5351	7	3	subject	subject	NOUN
ejpam-5351	7	4	classifications	classification	NOUN
ejpam-5351	7	5	:	:	PUNCT
ejpam-5351	7	6	57r60	57r60	NUM
ejpam-5351	7	7	,	,	PUNCT
ejpam-5351	7	8	57k35	57k35	NUM
ejpam-5351	7	9	key	key	ADJ
ejpam-5351	7	10	words	word	NOUN
ejpam-5351	7	11	and	and	CCONJ
ejpam-5351	7	12	phrases	phrase	NOUN
ejpam-5351	7	13	:	:	PUNCT
ejpam-5351	7	14	3	3	NUM
ejpam-5351	7	15	-	-	PUNCT
ejpam-5351	7	16	manifolds	manifold	NOUN
ejpam-5351	7	17	,	,	PUNCT
ejpam-5351	7	18	poincaré	poincaré	ADJ
ejpam-5351	7	19	conjecture	conjecture	NOUN
ejpam-5351	7	20	,	,	PUNCT
ejpam-5351	7	21	differential	differential	ADJ
ejpam-5351	7	22	and	and	CCONJ
ejpam-5351	7	23	geometric	geometric	ADJ
ejpam-5351	7	24	structures	structure	NOUN
ejpam-5351	7	25	1	1	NUM
ejpam-5351	7	26	.	.	PUNCT
ejpam-5351	8	1	introduction	introduction	NOUN
ejpam-5351	8	2	on	on	ADP
ejpam-5351	8	3	the	the	DET
ejpam-5351	8	4	occasion	occasion	NOUN
ejpam-5351	8	5	of	of	ADP
ejpam-5351	8	6	the	the	DET
ejpam-5351	8	7	new	new	ADJ
ejpam-5351	8	8	millennium	millennium	NOUN
ejpam-5351	8	9	,	,	PUNCT
ejpam-5351	8	10	and	and	CCONJ
ejpam-5351	8	11	a	a	DET
ejpam-5351	8	12	century	century	NOUN
ejpam-5351	8	13	after	after	SCONJ
ejpam-5351	8	14	the	the	DET
ejpam-5351	8	15	famous	famous	ADJ
ejpam-5351	8	16	international	international	ADJ
ejpam-5351	8	17	congress	congress	PROPN
ejpam-5351	8	18	of	of	ADP
ejpam-5351	8	19	mathematics	mathematic	NOUN
ejpam-5351	8	20	held	hold	VERB
ejpam-5351	8	21	in	in	ADP
ejpam-5351	8	22	paris	paris	PROPN
ejpam-5351	8	23	in	in	ADP
ejpam-5351	8	24	1900	1900	NUM
ejpam-5351	8	25	where	where	SCONJ
ejpam-5351	8	26	david	david	PROPN
ejpam-5351	8	27	hilbert	hilbert	PROPN
ejpam-5351	8	28	drew	draw	VERB
ejpam-5351	8	29	up	up	ADP
ejpam-5351	8	30	his	his	PRON
ejpam-5351	8	31	famous	famous	ADJ
ejpam-5351	8	32	list	list	NOUN
ejpam-5351	8	33	of	of	ADP
ejpam-5351	8	34	23	23	NUM
ejpam-5351	8	35	unsolved	unsolved	ADJ
ejpam-5351	8	36	mathematical	mathematical	ADJ
ejpam-5351	8	37	problems	problem	NOUN
ejpam-5351	8	38	at	at	ADP
ejpam-5351	8	39	that	that	DET
ejpam-5351	8	40	time	time	NOUN
ejpam-5351	9	1	,	,	PUNCT
ejpam-5351	9	2	the	the	DET
ejpam-5351	9	3	clay	clay	NOUN
ejpam-5351	9	4	mathematics	mathematics	PROPN
ejpam-5351	9	5	institute	institute	PROPN
ejpam-5351	9	6	in	in	ADP
ejpam-5351	9	7	cambridge	cambridge	PROPN
ejpam-5351	9	8	,	,	PUNCT
ejpam-5351	9	9	massachusetts	massachusetts	PROPN
ejpam-5351	9	10	,	,	PUNCT
ejpam-5351	9	11	chose	choose	VERB
ejpam-5351	9	12	a	a	DET
ejpam-5351	9	13	new	new	ADJ
ejpam-5351	9	14	group	group	NOUN
ejpam-5351	9	15	of	of	ADP
ejpam-5351	9	16	seven	seven	NUM
ejpam-5351	9	17	difficult	difficult	ADJ
ejpam-5351	9	18	problems	problem	NOUN
ejpam-5351	9	19	/	/	SYM
ejpam-5351	9	20	conjectures	conjecture	VERB
ejpam-5351	9	21	that	that	PRON
ejpam-5351	9	22	were	be	AUX
ejpam-5351	9	23	still	still	ADV
ejpam-5351	9	24	unsolved	unsolved	ADJ
ejpam-5351	9	25	in	in	ADP
ejpam-5351	9	26	the	the	DET
ejpam-5351	9	27	years	year	NOUN
ejpam-5351	9	28	2000	2000	NUM
ejpam-5351	9	29	,	,	PUNCT
ejpam-5351	9	30	awarding	award	VERB
ejpam-5351	9	31	a	a	DET
ejpam-5351	9	32	prize	prize	NOUN
ejpam-5351	9	33	of	of	ADP
ejpam-5351	9	34	one	one	NUM
ejpam-5351	9	35	million	million	NUM
ejpam-5351	9	36	dollars	dollar	NOUN
ejpam-5351	9	37	for	for	ADP
ejpam-5351	9	38	the	the	DET
ejpam-5351	9	39	solution	solution	NOUN
ejpam-5351	9	40	of	of	ADP
ejpam-5351	9	41	each	each	DET
ejpam-5351	9	42	one	one	NUM
ejpam-5351	9	43	of	of	ADP
ejpam-5351	9	44	them	they	PRON
ejpam-5351	9	45	.	.	PUNCT
ejpam-5351	10	1	the	the	DET
ejpam-5351	10	2	millennium	millennium	NOUN
ejpam-5351	10	3	prizes	prize	NOUN
ejpam-5351	10	4	were	be	AUX
ejpam-5351	10	5	announced	announce	VERB
ejpam-5351	10	6	once	once	ADV
ejpam-5351	10	7	again	again	ADV
ejpam-5351	10	8	in	in	ADP
ejpam-5351	10	9	paris	paris	PROPN
ejpam-5351	10	10	in	in	ADP
ejpam-5351	10	11	the	the	DET
ejpam-5351	10	12	spring	spring	NOUN
ejpam-5351	10	13	of	of	ADP
ejpam-5351	10	14	2000	2000	NUM
ejpam-5351	10	15	,	,	PUNCT
ejpam-5351	10	16	and	and	CCONJ
ejpam-5351	10	17	among	among	ADP
ejpam-5351	10	18	these	these	DET
ejpam-5351	10	19	seven	seven	NUM
ejpam-5351	10	20	great	great	ADJ
ejpam-5351	10	21	questions	question	NOUN
ejpam-5351	10	22	of	of	ADP
ejpam-5351	10	23	the	the	DET
ejpam-5351	10	24	new	new	ADJ
ejpam-5351	10	25	century	century	NOUN
ejpam-5351	10	26	stand	stand	VERB
ejpam-5351	10	27	out	out	ADP
ejpam-5351	10	28	the	the	DET
ejpam-5351	10	29	poincaré	poincaré	ADJ
ejpam-5351	10	30	conjecture	conjecture	NOUN
ejpam-5351	10	31	(	(	PUNCT
ejpam-5351	10	32	which	which	PRON
ejpam-5351	10	33	is	be	AUX
ejpam-5351	10	34	easy	easy	ADJ
ejpam-5351	10	35	to	to	PART
ejpam-5351	10	36	state	state	VERB
ejpam-5351	10	37	and	and	CCONJ
ejpam-5351	10	38	a	a	DET
ejpam-5351	10	39	century	century	NOUN
ejpam-5351	10	40	old	old	ADJ
ejpam-5351	10	41	)	)	PUNCT
ejpam-5351	10	42	,	,	PUNCT
ejpam-5351	10	43	and	and	CCONJ
ejpam-5351	10	44	the	the	DET
ejpam-5351	10	45	all	all	ADV
ejpam-5351	10	46	-	-	PUNCT
ejpam-5351	10	47	famous	famous	ADJ
ejpam-5351	10	48	riemann	riemann	PROPN
ejpam-5351	10	49	hypothesis	hypothesis	NOUN
ejpam-5351	10	50	,	,	PUNCT
ejpam-5351	10	51	formulated	formulate	VERB
ejpam-5351	10	52	in	in	ADP
ejpam-5351	10	53	1859	1859	NUM
ejpam-5351	10	54	,	,	PUNCT
ejpam-5351	10	55	the	the	DET
ejpam-5351	10	56	only	only	ADJ
ejpam-5351	10	57	conjecture	conjecture	NOUN
ejpam-5351	10	58	that	that	PRON
ejpam-5351	10	59	was	be	AUX
ejpam-5351	10	60	already	already	ADV
ejpam-5351	10	61	part	part	NOUN
ejpam-5351	10	62	of	of	ADP
ejpam-5351	10	63	hilbert	hilbert	PROPN
ejpam-5351	10	64	’s	’s	PART
ejpam-5351	10	65	23	23	NUM
ejpam-5351	10	66	problems	problem	NOUN
ejpam-5351	10	67	of	of	ADP
ejpam-5351	10	68	1900	1900	NUM
ejpam-5351	10	69	.	.	PUNCT
ejpam-5351	11	1	of	of	ADP
ejpam-5351	11	2	all	all	DET
ejpam-5351	11	3	these	these	DET
ejpam-5351	11	4	problems	problem	NOUN
ejpam-5351	11	5	,	,	PUNCT
ejpam-5351	11	6	only	only	ADV
ejpam-5351	11	7	one	one	NUM
ejpam-5351	11	8	has	have	AUX
ejpam-5351	11	9	been	be	AUX
ejpam-5351	11	10	solved	solve	VERB
ejpam-5351	11	11	in	in	ADP
ejpam-5351	11	12	the	the	DET
ejpam-5351	11	13	meantime	meantime	NOUN
ejpam-5351	11	14	:	:	PUNCT
ejpam-5351	11	15	the	the	DET
ejpam-5351	11	16	poincaré	poincaré	ADJ
ejpam-5351	11	17	conjecture	conjecture	NOUN
ejpam-5351	11	18	,	,	PUNCT
ejpam-5351	11	19	settled	settle	VERB
ejpam-5351	11	20	by	by	ADP
ejpam-5351	11	21	the	the	DET
ejpam-5351	11	22	russian	russian	ADJ
ejpam-5351	11	23	mathematician	mathematician	ADJ
ejpam-5351	11	24	grigori	grigori	PROPN
ejpam-5351	11	25	perelman	perelman	PROPN
ejpam-5351	11	26	in	in	ADP
ejpam-5351	11	27	2003	2003	NUM
ejpam-5351	11	28	[	[	X
ejpam-5351	11	29	3	3	NUM
ejpam-5351	11	30	,	,	PUNCT
ejpam-5351	11	31	4	4	NUM
ejpam-5351	11	32	]	]	PUNCT
ejpam-5351	11	33	.	.	PUNCT
ejpam-5351	12	1	the	the	DET
ejpam-5351	12	2	resolution	resolution	NOUN
ejpam-5351	12	3	of	of	ADP
ejpam-5351	12	4	this	this	DET
ejpam-5351	12	5	century	century	NOUN
ejpam-5351	12	6	-	-	PUNCT
ejpam-5351	12	7	old	old	ADJ
ejpam-5351	12	8	conjecture	conjecture	NOUN
ejpam-5351	12	9	,	,	PUNCT
ejpam-5351	12	10	along	along	ADP
ejpam-5351	12	11	with	with	ADP
ejpam-5351	12	12	the	the	DET
ejpam-5351	12	13	fact	fact	NOUN
ejpam-5351	12	14	that	that	SCONJ
ejpam-5351	12	15	he	he	PRON
ejpam-5351	12	16	refused	refuse	VERB
ejpam-5351	12	17	the	the	DET
ejpam-5351	12	18	1	1	NUM
ejpam-5351	12	19	-	-	PUNCT
ejpam-5351	12	20	million	million	NUM
ejpam-5351	12	21	prize	prize	NOUN
ejpam-5351	12	22	,	,	PUNCT
ejpam-5351	12	23	has	have	AUX
ejpam-5351	12	24	drawn	draw	VERB
ejpam-5351	12	25	the	the	DET
ejpam-5351	12	26	attention	attention	NOUN
ejpam-5351	12	27	of	of	ADP
ejpam-5351	12	28	the	the	DET
ejpam-5351	12	29	general	general	ADJ
ejpam-5351	12	30	public	public	NOUN
ejpam-5351	12	31	especially	especially	ADV
ejpam-5351	12	32	to	to	ADP
ejpam-5351	12	33	this	this	DET
ejpam-5351	12	34	problem	problem	NOUN
ejpam-5351	12	35	.	.	PUNCT
ejpam-5351	13	1	doi	doi	NOUN
ejpam-5351	13	2	:	:	PUNCT
ejpam-5351	13	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5351	https://doi.org/10.29020/nybg.ejpam.v17i3.5351	PROPN
ejpam-5351	13	4	email	email	NOUN
ejpam-5351	13	5	address	address	NOUN
ejpam-5351	13	6	:	:	PUNCT
ejpam-5351	14	1	daniele.otera@mif.vu.lt	daniele.otera@mif.vu.lt	PROPN
ejpam-5351	14	2	daniele.otera@gmail.com	daniele.otera@gmail.com	PROPN
ejpam-5351	14	3	(	(	PUNCT
ejpam-5351	14	4	d.	d.	PROPN
ejpam-5351	14	5	e.	e.	PROPN
ejpam-5351	14	6	otera	otera	PROPN
ejpam-5351	14	7	)	)	PUNCT
ejpam-5351	14	8	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5351	14	9	2361	2361	NUM
ejpam-5351	14	10	©	©	ADP
ejpam-5351	14	11	2024	2024	NUM
ejpam-5351	14	12	ejpam	ejpam	NOUN
ejpam-5351	14	13	all	all	DET
ejpam-5351	14	14	rights	right	NOUN
ejpam-5351	14	15	reserved	reserve	VERB
ejpam-5351	14	16	.	.	PUNCT
ejpam-5351	15	1	d.	d.	PROPN
ejpam-5351	15	2	e.	e.	PROPN
ejpam-5351	15	3	otera	otera	PROPN
ejpam-5351	15	4	/	/	SYM
ejpam-5351	15	5	eur	eur	PROPN
ejpam-5351	15	6	.	.	PUNCT
ejpam-5351	16	1	j.	j.	PROPN
ejpam-5351	16	2	pure	pure	PROPN
ejpam-5351	16	3	appl	appl	PROPN
ejpam-5351	16	4	.	.	PROPN
ejpam-5351	16	5	math	math	PROPN
ejpam-5351	16	6	,	,	PUNCT
ejpam-5351	16	7	17	17	NUM
ejpam-5351	16	8	(	(	PUNCT
ejpam-5351	16	9	3	3	NUM
ejpam-5351	16	10	)	)	PUNCT
ejpam-5351	16	11	(	(	PUNCT
ejpam-5351	16	12	2024	2024	NUM
ejpam-5351	16	13	)	)	PUNCT
ejpam-5351	16	14	,	,	PUNCT
ejpam-5351	16	15	2361	2361	NUM
ejpam-5351	16	16	-	-	SYM
ejpam-5351	16	17	2369	2369	NUM
ejpam-5351	16	18	2362	2362	NUM
ejpam-5351	16	19	2	2	NUM
ejpam-5351	16	20	.	.	PUNCT
ejpam-5351	16	21	preliminaries	preliminary	NOUN
ejpam-5351	16	22	since	since	SCONJ
ejpam-5351	16	23	we	we	PRON
ejpam-5351	16	24	want	want	VERB
ejpam-5351	16	25	to	to	PART
ejpam-5351	16	26	address	address	VERB
ejpam-5351	16	27	to	to	ADP
ejpam-5351	16	28	an	an	DET
ejpam-5351	16	29	audience	audience	NOUN
ejpam-5351	16	30	of	of	ADP
ejpam-5351	16	31	non	non	NOUN
ejpam-5351	16	32	-	-	NOUN
ejpam-5351	16	33	experts	expert	NOUN
ejpam-5351	16	34	,	,	PUNCT
ejpam-5351	16	35	we	we	PRON
ejpam-5351	16	36	will	will	AUX
ejpam-5351	16	37	start	start	VERB
ejpam-5351	16	38	from	from	ADP
ejpam-5351	16	39	scratch	scratch	NOUN
ejpam-5351	16	40	,	,	PUNCT
ejpam-5351	16	41	in	in	ADP
ejpam-5351	16	42	order	order	NOUN
ejpam-5351	16	43	to	to	PART
ejpam-5351	16	44	be	be	AUX
ejpam-5351	16	45	able	able	ADJ
ejpam-5351	16	46	to	to	PART
ejpam-5351	16	47	state	state	VERB
ejpam-5351	16	48	and	and	CCONJ
ejpam-5351	16	49	comment	comment	VERB
ejpam-5351	16	50	the	the	DET
ejpam-5351	16	51	poincaré	poincaré	ADJ
ejpam-5351	16	52	conjecture	conjecture	NOUN
ejpam-5351	16	53	and	and	CCONJ
ejpam-5351	16	54	its	its	PRON
ejpam-5351	16	55	generalizations	generalization	NOUN
ejpam-5351	16	56	.	.	PUNCT
ejpam-5351	17	1	2.1	2.1	NUM
ejpam-5351	17	2	.	.	PUNCT
ejpam-5351	17	3	manifolds	manifold	NOUN
ejpam-5351	17	4	we	we	PRON
ejpam-5351	17	5	need	need	VERB
ejpam-5351	17	6	to	to	PART
ejpam-5351	17	7	start	start	VERB
ejpam-5351	17	8	by	by	ADP
ejpam-5351	17	9	defining	define	VERB
ejpam-5351	17	10	and	and	CCONJ
ejpam-5351	17	11	talking	talk	VERB
ejpam-5351	17	12	about	about	ADP
ejpam-5351	17	13	the	the	DET
ejpam-5351	17	14	central	central	ADJ
ejpam-5351	17	15	topics	topic	NOUN
ejpam-5351	17	16	of	of	ADP
ejpam-5351	17	17	interest	interest	NOUN
ejpam-5351	17	18	for	for	ADP
ejpam-5351	17	19	us	we	PRON
ejpam-5351	17	20	:	:	PUNCT
ejpam-5351	17	21	manifolds	manifold	NOUN
ejpam-5351	17	22	of	of	ADP
ejpam-5351	17	23	dimension	dimension	NOUN
ejpam-5351	17	24	n	n	CCONJ
ejpam-5351	17	25	,	,	PUNCT
ejpam-5351	17	26	where	where	SCONJ
ejpam-5351	17	27	,	,	PUNCT
ejpam-5351	17	28	for	for	ADP
ejpam-5351	17	29	simplicity	simplicity	NOUN
ejpam-5351	17	30	,	,	PUNCT
ejpam-5351	17	31	we	we	PRON
ejpam-5351	17	32	will	will	AUX
ejpam-5351	17	33	consider	consider	VERB
ejpam-5351	17	34	a	a	DET
ejpam-5351	17	35	manifold	manifold	NOUN
ejpam-5351	17	36	as	as	ADP
ejpam-5351	17	37	an	an	DET
ejpam-5351	17	38	object	object	NOUN
ejpam-5351	17	39	considered	consider	VERB
ejpam-5351	17	40	in	in	ADP
ejpam-5351	17	41	a	a	DET
ejpam-5351	17	42	space	space	NOUN
ejpam-5351	17	43	of	of	ADP
ejpam-5351	17	44	dimension	dimension	NOUN
ejpam-5351	17	45	n	n	CCONJ
ejpam-5351	17	46	(	(	PUNCT
ejpam-5351	17	47	greater	great	ADJ
ejpam-5351	17	48	than	than	ADP
ejpam-5351	17	49	n	n	CCONJ
ejpam-5351	17	50	)	)	PUNCT
ejpam-5351	17	51	.	.	PUNCT
ejpam-5351	18	1	a	a	DET
ejpam-5351	18	2	manifold	manifold	NOUN
ejpam-5351	18	3	of	of	ADP
ejpam-5351	18	4	dimension	dimension	NOUN
ejpam-5351	18	5	1	1	NUM
ejpam-5351	18	6	(	(	PUNCT
ejpam-5351	18	7	n	n	NOUN
ejpam-5351	18	8	=	=	SYM
ejpam-5351	18	9	1	1	NUM
ejpam-5351	18	10	)	)	PUNCT
ejpam-5351	18	11	is	be	AUX
ejpam-5351	18	12	a	a	DET
ejpam-5351	18	13	line	line	NOUN
ejpam-5351	18	14	or	or	CCONJ
ejpam-5351	18	15	a	a	DET
ejpam-5351	18	16	curve	curve	NOUN
ejpam-5351	18	17	(	(	PUNCT
ejpam-5351	18	18	in	in	ADP
ejpam-5351	18	19	our	our	PRON
ejpam-5351	18	20	standard	standard	ADJ
ejpam-5351	18	21	plane	plane	NOUN
ejpam-5351	18	22	r2	r2	NOUN
ejpam-5351	18	23	for	for	ADP
ejpam-5351	18	24	example	example	NOUN
ejpam-5351	18	25	)	)	PUNCT
ejpam-5351	18	26	,	,	PUNCT
ejpam-5351	18	27	while	while	SCONJ
ejpam-5351	18	28	a	a	DET
ejpam-5351	18	29	manifold	manifold	NOUN
ejpam-5351	18	30	of	of	ADP
ejpam-5351	18	31	dimension	dimension	NOUN
ejpam-5351	18	32	2	2	NUM
ejpam-5351	18	33	(	(	PUNCT
ejpam-5351	18	34	n	n	NOUN
ejpam-5351	18	35	=	=	SYM
ejpam-5351	18	36	2	2	NUM
ejpam-5351	18	37	)	)	PUNCT
ejpam-5351	18	38	is	be	AUX
ejpam-5351	18	39	what	what	PRON
ejpam-5351	18	40	we	we	PRON
ejpam-5351	18	41	commonly	commonly	ADV
ejpam-5351	18	42	call	call	VERB
ejpam-5351	18	43	a	a	DET
ejpam-5351	18	44	surface	surface	NOUN
ejpam-5351	18	45	(	(	PUNCT
ejpam-5351	18	46	in	in	ADP
ejpam-5351	18	47	our	our	PRON
ejpam-5351	18	48	3	3	NUM
ejpam-5351	18	49	-	-	PUNCT
ejpam-5351	18	50	dimensional	dimensional	ADJ
ejpam-5351	18	51	space	space	NOUN
ejpam-5351	18	52	r3	r3	NOUN
ejpam-5351	18	53	)	)	PUNCT
ejpam-5351	18	54	.	.	PUNCT
ejpam-5351	19	1	with	with	ADP
ejpam-5351	19	2	more	more	ADJ
ejpam-5351	19	3	fantasy	fantasy	NOUN
ejpam-5351	19	4	and	and	CCONJ
ejpam-5351	19	5	abstraction	abstraction	NOUN
ejpam-5351	19	6	,	,	PUNCT
ejpam-5351	19	7	we	we	PRON
ejpam-5351	19	8	can	can	AUX
ejpam-5351	19	9	imagine	imagine	VERB
ejpam-5351	19	10	a	a	DET
ejpam-5351	19	11	3	3	NUM
ejpam-5351	19	12	-	-	PUNCT
ejpam-5351	19	13	dimensional	dimensional	ADJ
ejpam-5351	19	14	manifold	manifold	ADJ
ejpam-5351	19	15	m	m	NOUN
ejpam-5351	19	16	as	as	ADP
ejpam-5351	19	17	a	a	DET
ejpam-5351	19	18	subspace	subspace	NOUN
ejpam-5351	19	19	of	of	ADP
ejpam-5351	19	20	a	a	DET
ejpam-5351	19	21	space	space	NOUN
ejpam-5351	19	22	of	of	ADP
ejpam-5351	19	23	dimension	dimension	NOUN
ejpam-5351	19	24	n	n	CCONJ
ejpam-5351	19	25	≥	≥	NUM
ejpam-5351	19	26	4	4	NUM
ejpam-5351	19	27	(	(	PUNCT
ejpam-5351	19	28	imagine	imagine	VERB
ejpam-5351	19	29	r4	r4	NOUN
ejpam-5351	19	30	as	as	ADP
ejpam-5351	19	31	einstein	einstein	PROPN
ejpam-5351	19	32	’s	’s	PART
ejpam-5351	19	33	space	space	NOUN
ejpam-5351	19	34	-	-	PUNCT
ejpam-5351	19	35	time	time	NOUN
ejpam-5351	19	36	)	)	PUNCT
ejpam-5351	19	37	,	,	PUNCT
ejpam-5351	19	38	such	such	ADJ
ejpam-5351	19	39	that	that	SCONJ
ejpam-5351	19	40	,	,	PUNCT
ejpam-5351	19	41	locally	locally	ADV
ejpam-5351	19	42	,	,	PUNCT
ejpam-5351	19	43	it	it	PRON
ejpam-5351	19	44	looks	look	VERB
ejpam-5351	19	45	like	like	ADP
ejpam-5351	19	46	our	our	PRON
ejpam-5351	19	47	3	3	NUM
ejpam-5351	19	48	-	-	PUNCT
ejpam-5351	19	49	dimensional	dimensional	ADJ
ejpam-5351	19	50	space	space	NOUN
ejpam-5351	19	51	(	(	PUNCT
ejpam-5351	19	52	as	as	ADV
ejpam-5351	19	53	well	well	ADV
ejpam-5351	19	54	as	as	ADP
ejpam-5351	19	55	,	,	PUNCT
ejpam-5351	19	56	for	for	ADP
ejpam-5351	19	57	instance	instance	NOUN
ejpam-5351	19	58	,	,	PUNCT
ejpam-5351	19	59	a	a	DET
ejpam-5351	19	60	local	local	ADJ
ejpam-5351	19	61	piece	piece	NOUN
ejpam-5351	19	62	of	of	ADP
ejpam-5351	19	63	a	a	DET
ejpam-5351	19	64	surface	surface	NOUN
ejpam-5351	19	65	resembles	resemble	VERB
ejpam-5351	19	66	a	a	DET
ejpam-5351	19	67	piece	piece	NOUN
ejpam-5351	19	68	of	of	ADP
ejpam-5351	19	69	the	the	DET
ejpam-5351	19	70	real	real	ADJ
ejpam-5351	19	71	plane	plane	NOUN
ejpam-5351	19	72	)	)	PUNCT
ejpam-5351	19	73	,	,	PUNCT
ejpam-5351	19	74	and	and	CCONJ
ejpam-5351	19	75	so	so	ADV
ejpam-5351	19	76	on	on	ADV
ejpam-5351	19	77	for	for	ADP
ejpam-5351	19	78	any	any	DET
ejpam-5351	19	79	natural	natural	ADJ
ejpam-5351	19	80	number	number	NOUN
ejpam-5351	19	81	n.	n.	NOUN
ejpam-5351	19	82	just	just	ADV
ejpam-5351	19	83	like	like	ADP
ejpam-5351	19	84	prime	prime	ADJ
ejpam-5351	19	85	or	or	CCONJ
ejpam-5351	19	86	complex	complex	ADJ
ejpam-5351	19	87	numbers	number	NOUN
ejpam-5351	19	88	,	,	PUNCT
ejpam-5351	19	89	it	it	PRON
ejpam-5351	19	90	turns	turn	VERB
ejpam-5351	19	91	out	out	ADP
ejpam-5351	19	92	that	that	SCONJ
ejpam-5351	19	93	manifolds	manifold	NOUN
ejpam-5351	19	94	are	be	AUX
ejpam-5351	19	95	also	also	ADV
ejpam-5351	19	96	central	central	ADJ
ejpam-5351	19	97	objects	object	NOUN
ejpam-5351	19	98	in	in	ADP
ejpam-5351	19	99	the	the	DET
ejpam-5351	19	100	architecture	architecture	NOUN
ejpam-5351	19	101	of	of	ADP
ejpam-5351	19	102	modern	modern	ADJ
ejpam-5351	19	103	mathematics	mathematic	NOUN
ejpam-5351	19	104	.	.	PUNCT
ejpam-5351	20	1	they	they	PRON
ejpam-5351	20	2	are	be	AUX
ejpam-5351	20	3	in	in	ADP
ejpam-5351	20	4	fact	fact	NOUN
ejpam-5351	20	5	the	the	DET
ejpam-5351	20	6	basic	basic	ADJ
ejpam-5351	20	7	building	building	NOUN
ejpam-5351	20	8	blocks	block	NOUN
ejpam-5351	20	9	of	of	ADP
ejpam-5351	20	10	the	the	DET
ejpam-5351	20	11	branch	branch	NOUN
ejpam-5351	20	12	of	of	ADP
ejpam-5351	20	13	mathematics	mathematic	NOUN
ejpam-5351	20	14	called	call	VERB
ejpam-5351	20	15	topology	topology	NOUN
ejpam-5351	20	16	(	(	PUNCT
ejpam-5351	20	17	literally	literally	ADV
ejpam-5351	20	18	the	the	DET
ejpam-5351	20	19	study	study	NOUN
ejpam-5351	20	20	of	of	ADP
ejpam-5351	20	21	“	"	PUNCT
ejpam-5351	20	22	places	place	NOUN
ejpam-5351	20	23	and	and	CCONJ
ejpam-5351	20	24	forms	form	NOUN
ejpam-5351	20	25	”	"	PUNCT
ejpam-5351	20	26	)	)	PUNCT
ejpam-5351	20	27	.	.	PUNCT
ejpam-5351	21	1	and	and	CCONJ
ejpam-5351	21	2	the	the	DET
ejpam-5351	21	3	poincaré	poincaré	ADJ
ejpam-5351	21	4	conjecture	conjecture	NOUN
ejpam-5351	21	5	is	be	AUX
ejpam-5351	21	6	a	a	DET
ejpam-5351	21	7	cornerstone	cornerstone	NOUN
ejpam-5351	21	8	of	of	ADP
ejpam-5351	21	9	the	the	DET
ejpam-5351	21	10	classification	classification	NOUN
ejpam-5351	21	11	of	of	ADP
ejpam-5351	21	12	them	they	PRON
ejpam-5351	21	13	.	.	PUNCT
ejpam-5351	22	1	now	now	ADV
ejpam-5351	22	2	,	,	PUNCT
ejpam-5351	22	3	just	just	ADV
ejpam-5351	22	4	as	as	SCONJ
ejpam-5351	22	5	a	a	DET
ejpam-5351	22	6	single	single	ADJ
ejpam-5351	22	7	coordinate	coordinate	NOUN
ejpam-5351	22	8	is	be	AUX
ejpam-5351	22	9	sufficient	sufficient	ADJ
ejpam-5351	22	10	to	to	PART
ejpam-5351	22	11	identify	identify	VERB
ejpam-5351	22	12	a	a	DET
ejpam-5351	22	13	point	point	NOUN
ejpam-5351	22	14	on	on	ADP
ejpam-5351	22	15	a	a	DET
ejpam-5351	22	16	curve	curve	NOUN
ejpam-5351	22	17	,	,	PUNCT
ejpam-5351	22	18	two	two	NUM
ejpam-5351	22	19	numbers	number	NOUN
ejpam-5351	22	20	(	(	PUNCT
ejpam-5351	22	21	coordinates	coordinate	NOUN
ejpam-5351	22	22	)	)	PUNCT
ejpam-5351	22	23	are	be	AUX
ejpam-5351	22	24	needed	need	VERB
ejpam-5351	22	25	to	to	PART
ejpam-5351	22	26	identify	identify	VERB
ejpam-5351	22	27	a	a	DET
ejpam-5351	22	28	point	point	NOUN
ejpam-5351	22	29	on	on	ADP
ejpam-5351	22	30	a	a	DET
ejpam-5351	22	31	surface	surface	NOUN
ejpam-5351	22	32	.	.	PUNCT
ejpam-5351	23	1	for	for	ADP
ejpam-5351	23	2	example	example	NOUN
ejpam-5351	23	3	,	,	PUNCT
ejpam-5351	23	4	on	on	ADP
ejpam-5351	23	5	the	the	DET
ejpam-5351	23	6	earth	earth	NOUN
ejpam-5351	23	7	’s	’s	PART
ejpam-5351	23	8	surface	surface	NOUN
ejpam-5351	23	9	,	,	PUNCT
ejpam-5351	23	10	(	(	PUNCT
ejpam-5351	23	11	which	which	PRON
ejpam-5351	23	12	is	be	AUX
ejpam-5351	23	13	a	a	DET
ejpam-5351	23	14	two	two	NUM
ejpam-5351	23	15	-	-	PUNCT
ejpam-5351	23	16	dimensional	dimensional	ADJ
ejpam-5351	23	17	sphere	sphere	NOUN
ejpam-5351	23	18	s2	s2	PROPN
ejpam-5351	23	19	)	)	PUNCT
ejpam-5351	23	20	,	,	PUNCT
ejpam-5351	23	21	we	we	PRON
ejpam-5351	23	22	need	need	VERB
ejpam-5351	23	23	longitude	longitude	NOUN
ejpam-5351	23	24	and	and	CCONJ
ejpam-5351	23	25	latitude	latitude	NOUN
ejpam-5351	23	26	.	.	PUNCT
ejpam-5351	24	1	incidentally	incidentally	ADV
ejpam-5351	24	2	,	,	PUNCT
ejpam-5351	24	3	the	the	DET
ejpam-5351	24	4	fact	fact	NOUN
ejpam-5351	24	5	that	that	SCONJ
ejpam-5351	24	6	this	this	DET
ejpam-5351	24	7	parametrization	parametrization	NOUN
ejpam-5351	24	8	possesses	possess	VERB
ejpam-5351	24	9	anomalies	anomaly	NOUN
ejpam-5351	24	10	(	(	PUNCT
ejpam-5351	24	11	e.g.	e.g.	ADV
ejpam-5351	24	12	all	all	DET
ejpam-5351	24	13	meridians	meridian	NOUN
ejpam-5351	24	14	meet	meet	VERB
ejpam-5351	24	15	at	at	ADP
ejpam-5351	24	16	the	the	DET
ejpam-5351	24	17	north	north	NOUN
ejpam-5351	24	18	and	and	CCONJ
ejpam-5351	24	19	south	south	ADJ
ejpam-5351	24	20	poles	pole	NOUN
ejpam-5351	24	21	,	,	PUNCT
ejpam-5351	24	22	where	where	SCONJ
ejpam-5351	24	23	longitude	longitude	NOUN
ejpam-5351	24	24	therefore	therefore	ADV
ejpam-5351	24	25	ceases	cease	VERB
ejpam-5351	24	26	to	to	PART
ejpam-5351	24	27	be	be	AUX
ejpam-5351	24	28	well	well	ADV
ejpam-5351	24	29	defined	define	VERB
ejpam-5351	24	30	)	)	PUNCT
ejpam-5351	24	31	is	be	AUX
ejpam-5351	24	32	a	a	DET
ejpam-5351	24	33	sign	sign	NOUN
ejpam-5351	24	34	of	of	ADP
ejpam-5351	24	35	a	a	DET
ejpam-5351	24	36	basic	basic	ADJ
ejpam-5351	24	37	topological	topological	ADJ
ejpam-5351	24	38	fact	fact	NOUN
ejpam-5351	24	39	:	:	PUNCT
ejpam-5351	24	40	the	the	DET
ejpam-5351	24	41	sphere	sphere	NOUN
ejpam-5351	24	42	s2	s2	NOUN
ejpam-5351	24	43	is	be	AUX
ejpam-5351	24	44	topologically	topologically	ADV
ejpam-5351	24	45	different	different	ADJ
ejpam-5351	24	46	(	(	PUNCT
ejpam-5351	24	47	technically	technically	ADV
ejpam-5351	24	48	not	not	PART
ejpam-5351	24	49	“	"	PUNCT
ejpam-5351	24	50	homeomorphic	homeomorphic	ADJ
ejpam-5351	24	51	”	"	PUNCT
ejpam-5351	24	52	,	,	PUNCT
ejpam-5351	24	53	see	see	VERB
ejpam-5351	24	54	here	here	ADV
ejpam-5351	24	55	below	below	ADV
ejpam-5351	24	56	)	)	PUNCT
ejpam-5351	24	57	to	to	ADP
ejpam-5351	24	58	the	the	DET
ejpam-5351	24	59	torus	torus	PROPN
ejpam-5351	24	60	t	t	PROPN
ejpam-5351	24	61	2	2	NUM
ejpam-5351	24	62	,	,	PUNCT
ejpam-5351	24	63	which	which	PRON
ejpam-5351	24	64	is	be	AUX
ejpam-5351	24	65	the	the	DET
ejpam-5351	24	66	surface	surface	NOUN
ejpam-5351	24	67	of	of	ADP
ejpam-5351	24	68	a	a	DET
ejpam-5351	24	69	tyre	tyre	PROPN
ejpam-5351	24	70	.	.	PUNCT
ejpam-5351	25	1	obviously	obviously	ADV
ejpam-5351	25	2	,	,	PUNCT
ejpam-5351	25	3	the	the	DET
ejpam-5351	25	4	sphere	sphere	NOUN
ejpam-5351	25	5	s2	s2	PROPN
ejpam-5351	25	6	differs	differ	VERB
ejpam-5351	25	7	also	also	ADV
ejpam-5351	25	8	from	from	ADP
ejpam-5351	25	9	(	(	PUNCT
ejpam-5351	25	10	is	be	AUX
ejpam-5351	25	11	not	not	PART
ejpam-5351	25	12	homeomorphic	homeomorphic	ADJ
ejpam-5351	25	13	to	to	ADP
ejpam-5351	25	14	)	)	PUNCT
ejpam-5351	25	15	the	the	DET
ejpam-5351	25	16	euclidean	euclidean	ADJ
ejpam-5351	25	17	space	space	NOUN
ejpam-5351	25	18	r2	r2	NOUN
ejpam-5351	25	19	either	either	ADV
ejpam-5351	25	20	,	,	PUNCT
ejpam-5351	25	21	but	but	CCONJ
ejpam-5351	25	22	this	this	PRON
ejpam-5351	25	23	is	be	AUX
ejpam-5351	25	24	an	an	DET
ejpam-5351	25	25	easier	easy	ADJ
ejpam-5351	25	26	thing	thing	NOUN
ejpam-5351	25	27	to	to	PART
ejpam-5351	25	28	understand	understand	VERB
ejpam-5351	25	29	,	,	PUNCT
ejpam-5351	25	30	since	since	SCONJ
ejpam-5351	25	31	the	the	DET
ejpam-5351	25	32	intuitive	intuitive	ADJ
ejpam-5351	25	33	fact	fact	NOUN
ejpam-5351	25	34	that	that	SCONJ
ejpam-5351	25	35	the	the	DET
ejpam-5351	25	36	sphere	sphere	NOUN
ejpam-5351	25	37	is	be	AUX
ejpam-5351	25	38	a	a	DET
ejpam-5351	25	39	“	"	PUNCT
ejpam-5351	25	40	closed	closed	ADJ
ejpam-5351	25	41	”	"	PUNCT
ejpam-5351	25	42	surface	surface	NOUN
ejpam-5351	25	43	while	while	SCONJ
ejpam-5351	25	44	the	the	DET
ejpam-5351	25	45	plane	plane	NOUN
ejpam-5351	25	46	r2	r2	NOUN
ejpam-5351	25	47	is	be	AUX
ejpam-5351	25	48	“	"	PUNCT
ejpam-5351	25	49	open	open	ADJ
ejpam-5351	25	50	”	"	PUNCT
ejpam-5351	25	51	corresponds	correspond	NOUN
ejpam-5351	25	52	to	to	ADP
ejpam-5351	25	53	a	a	DET
ejpam-5351	25	54	topological	topological	ADJ
ejpam-5351	25	55	difference	difference	NOUN
ejpam-5351	25	56	that	that	PRON
ejpam-5351	25	57	is	be	AUX
ejpam-5351	25	58	well	well	ADV
ejpam-5351	25	59	encoded	encode	VERB
ejpam-5351	25	60	(	(	PUNCT
ejpam-5351	25	61	a	a	DET
ejpam-5351	25	62	manifold	manifold	NOUN
ejpam-5351	25	63	is	be	AUX
ejpam-5351	25	64	said	say	VERB
ejpam-5351	25	65	to	to	PART
ejpam-5351	25	66	be	be	AUX
ejpam-5351	25	67	closed	close	VERB
ejpam-5351	25	68	if	if	SCONJ
ejpam-5351	25	69	it	it	PRON
ejpam-5351	25	70	has	have	VERB
ejpam-5351	25	71	no	no	DET
ejpam-5351	25	72	boundary	boundary	NOUN
ejpam-5351	25	73	and	and	CCONJ
ejpam-5351	25	74	takes	take	VERB
ejpam-5351	25	75	up	up	ADP
ejpam-5351	25	76	a	a	DET
ejpam-5351	25	77	finite	finite	ADJ
ejpam-5351	25	78	region	region	NOUN
ejpam-5351	25	79	of	of	ADP
ejpam-5351	25	80	space	space	NOUN
ejpam-5351	25	81	)	)	PUNCT
ejpam-5351	25	82	.	.	PUNCT
ejpam-5351	26	1	we	we	PRON
ejpam-5351	26	2	end	end	VERB
ejpam-5351	26	3	this	this	DET
ejpam-5351	26	4	section	section	NOUN
ejpam-5351	26	5	by	by	ADP
ejpam-5351	26	6	giving	give	VERB
ejpam-5351	26	7	an	an	DET
ejpam-5351	26	8	idea	idea	NOUN
ejpam-5351	26	9	of	of	ADP
ejpam-5351	26	10	what	what	PRON
ejpam-5351	26	11	a	a	DET
ejpam-5351	26	12	homeomorphism	homeomorphism	NOUN
ejpam-5351	26	13	is	be	AUX
ejpam-5351	26	14	.	.	PUNCT
ejpam-5351	27	1	homeomorphisms	homeomorphisms	PROPN
ejpam-5351	27	2	are	be	AUX
ejpam-5351	27	3	equivalences	equivalence	NOUN
ejpam-5351	27	4	in	in	ADP
ejpam-5351	27	5	the	the	DET
ejpam-5351	27	6	category	category	NOUN
ejpam-5351	27	7	of	of	ADP
ejpam-5351	27	8	topological	topological	ADJ
ejpam-5351	27	9	spaces	space	NOUN
ejpam-5351	27	10	,	,	PUNCT
ejpam-5351	27	11	more	more	ADV
ejpam-5351	27	12	precisely	precisely	ADV
ejpam-5351	27	13	bijective	bijective	ADJ
ejpam-5351	27	14	and	and	CCONJ
ejpam-5351	27	15	continuous	continuous	ADJ
ejpam-5351	27	16	correspondences	correspondence	NOUN
ejpam-5351	27	17	in	in	ADP
ejpam-5351	27	18	both	both	DET
ejpam-5351	27	19	directions	direction	NOUN
ejpam-5351	27	20	.	.	PUNCT
ejpam-5351	28	1	in	in	ADP
ejpam-5351	28	2	particular	particular	ADJ
ejpam-5351	28	3	,	,	PUNCT
ejpam-5351	28	4	homeomorphisms	homeomorphisms	PROPN
ejpam-5351	28	5	are	be	AUX
ejpam-5351	28	6	those	those	DET
ejpam-5351	28	7	functions	function	NOUN
ejpam-5351	28	8	which	which	PRON
ejpam-5351	28	9	preserve	preserve	VERB
ejpam-5351	28	10	all	all	DET
ejpam-5351	28	11	the	the	DET
ejpam-5351	28	12	topological	topological	ADJ
ejpam-5351	28	13	properties	property	NOUN
ejpam-5351	28	14	of	of	ADP
ejpam-5351	28	15	a	a	DET
ejpam-5351	28	16	given	give	VERB
ejpam-5351	28	17	manifold	manifold	ADJ
ejpam-5351	28	18	(	(	PUNCT
ejpam-5351	28	19	topological	topological	ADJ
ejpam-5351	28	20	space	space	NOUN
ejpam-5351	28	21	)	)	PUNCT
ejpam-5351	28	22	.	.	PUNCT
ejpam-5351	29	1	and	and	CCONJ
ejpam-5351	29	2	it	it	PRON
ejpam-5351	29	3	turns	turn	VERB
ejpam-5351	29	4	out	out	ADP
ejpam-5351	29	5	that	that	SCONJ
ejpam-5351	29	6	two	two	NUM
ejpam-5351	29	7	manifolds	manifold	NOUN
ejpam-5351	29	8	are	be	AUX
ejpam-5351	29	9	homeomorphic	homeomorphic	ADJ
ejpam-5351	29	10	if	if	SCONJ
ejpam-5351	29	11	one	one	PRON
ejpam-5351	29	12	can	can	AUX
ejpam-5351	29	13	continuously	continuously	ADV
ejpam-5351	29	14	(	(	PUNCT
ejpam-5351	29	15	i.e.	i.e.	X
ejpam-5351	29	16	without	without	ADP
ejpam-5351	29	17	cutting	cut	VERB
ejpam-5351	29	18	or	or	CCONJ
ejpam-5351	29	19	glueing	glueing	NOUN
ejpam-5351	29	20	)	)	PUNCT
ejpam-5351	29	21	deform	deform	VERB
ejpam-5351	29	22	the	the	DET
ejpam-5351	29	23	first	first	ADJ
ejpam-5351	29	24	manifold	manifold	NOUN
ejpam-5351	29	25	into	into	ADP
ejpam-5351	29	26	the	the	DET
ejpam-5351	29	27	second	second	ADJ
ejpam-5351	29	28	one	one	NUM
ejpam-5351	29	29	.	.	PUNCT
ejpam-5351	30	1	the	the	DET
ejpam-5351	30	2	poincaré	poincaré	ADJ
ejpam-5351	30	3	conjecture	conjecture	NOUN
ejpam-5351	30	4	states	state	NOUN
ejpam-5351	30	5	that	that	SCONJ
ejpam-5351	30	6	the	the	DET
ejpam-5351	30	7	3	3	NUM
ejpam-5351	30	8	-	-	PUNCT
ejpam-5351	30	9	sphere	sphere	NOUN
ejpam-5351	30	10	is	be	AUX
ejpam-5351	30	11	the	the	DET
ejpam-5351	30	12	only	only	ADJ
ejpam-5351	30	13	three	three	NUM
ejpam-5351	30	14	-	-	PUNCT
ejpam-5351	30	15	dimensional	dimensional	ADJ
ejpam-5351	30	16	compact	compact	ADJ
ejpam-5351	30	17	manifold	manifold	NOUN
ejpam-5351	30	18	without	without	ADP
ejpam-5351	30	19	boundary	boundary	ADJ
ejpam-5351	30	20	and	and	CCONJ
ejpam-5351	30	21	without	without	ADP
ejpam-5351	30	22	‘	'	PUNCT
ejpam-5351	30	23	holes	hole	NOUN
ejpam-5351	30	24	’	'	PUNCT
ejpam-5351	30	25	,	,	PUNCT
ejpam-5351	30	26	up	up	ADP
ejpam-5351	30	27	to	to	ADP
ejpam-5351	30	28	homeomomorphisms	homeomomorphism	NOUN
ejpam-5351	30	29	,	,	PUNCT
ejpam-5351	30	30	i.e.	i.e.	X
ejpam-5351	30	31	it	it	PRON
ejpam-5351	30	32	is	be	AUX
ejpam-5351	30	33	the	the	DET
ejpam-5351	30	34	only	only	ADJ
ejpam-5351	30	35	such	such	ADJ
ejpam-5351	30	36	manifold	manifold	NOUN
ejpam-5351	30	37	where	where	SCONJ
ejpam-5351	30	38	any	any	DET
ejpam-5351	30	39	closed	closed	ADJ
ejpam-5351	30	40	path	path	NOUN
ejpam-5351	30	41	can	can	AUX
ejpam-5351	30	42	be	be	AUX
ejpam-5351	30	43	contracted	contract	VERB
ejpam-5351	30	44	to	to	PART
ejpam-5351	30	45	become	become	VERB
ejpam-5351	30	46	a	a	DET
ejpam-5351	30	47	point	point	NOUN
ejpam-5351	30	48	.	.	PUNCT
ejpam-5351	31	1	d.	d.	PROPN
ejpam-5351	31	2	e.	e.	PROPN
ejpam-5351	31	3	otera	otera	PROPN
ejpam-5351	31	4	/	/	SYM
ejpam-5351	31	5	eur	eur	PROPN
ejpam-5351	31	6	.	.	PUNCT
ejpam-5351	32	1	j.	j.	PROPN
ejpam-5351	32	2	pure	pure	PROPN
ejpam-5351	32	3	appl	appl	PROPN
ejpam-5351	32	4	.	.	PROPN
ejpam-5351	32	5	math	math	PROPN
ejpam-5351	32	6	,	,	PUNCT
ejpam-5351	32	7	17	17	NUM
ejpam-5351	32	8	(	(	PUNCT
ejpam-5351	32	9	3	3	NUM
ejpam-5351	32	10	)	)	PUNCT
ejpam-5351	32	11	(	(	PUNCT
ejpam-5351	32	12	2024	2024	NUM
ejpam-5351	32	13	)	)	PUNCT
ejpam-5351	32	14	,	,	PUNCT
ejpam-5351	32	15	2361	2361	NUM
ejpam-5351	32	16	-	-	SYM
ejpam-5351	32	17	2369	2369	NUM
ejpam-5351	32	18	2363	2363	NUM
ejpam-5351	32	19	2.2	2.2	NUM
ejpam-5351	32	20	.	.	PUNCT
ejpam-5351	33	1	from	from	ADP
ejpam-5351	33	2	the	the	DET
ejpam-5351	33	3	sphere	sphere	NOUN
ejpam-5351	33	4	s2	s2	NOUN
ejpam-5351	33	5	to	to	ADP
ejpam-5351	33	6	the	the	DET
ejpam-5351	33	7	ball	ball	NOUN
ejpam-5351	33	8	b3	b3	NOUN
ejpam-5351	33	9	the	the	DET
ejpam-5351	33	10	reader	reader	NOUN
ejpam-5351	33	11	will	will	AUX
ejpam-5351	33	12	certainly	certainly	ADV
ejpam-5351	33	13	be	be	AUX
ejpam-5351	33	14	familiar	familiar	ADJ
ejpam-5351	33	15	with	with	ADP
ejpam-5351	33	16	at	at	ADV
ejpam-5351	33	17	least	least	ADV
ejpam-5351	33	18	one	one	NUM
ejpam-5351	33	19	3	3	NUM
ejpam-5351	33	20	-	-	PUNCT
ejpam-5351	33	21	dimensional	dimensional	ADJ
ejpam-5351	33	22	manifold	manifold	ADJ
ejpam-5351	33	23	,	,	PUNCT
ejpam-5351	33	24	namely	namely	ADV
ejpam-5351	33	25	our	our	PRON
ejpam-5351	33	26	three	three	NUM
ejpam-5351	33	27	-	-	PUNCT
ejpam-5351	33	28	dimensional	dimensional	ADJ
ejpam-5351	33	29	space	space	NOUN
ejpam-5351	33	30	,	,	PUNCT
ejpam-5351	33	31	r3	r3	PROPN
ejpam-5351	33	32	,	,	PUNCT
ejpam-5351	33	33	but	but	CCONJ
ejpam-5351	33	34	we	we	PRON
ejpam-5351	33	35	can	can	AUX
ejpam-5351	33	36	construct	construct	VERB
ejpam-5351	33	37	many	many	ADJ
ejpam-5351	33	38	other	other	ADJ
ejpam-5351	33	39	ones	one	NOUN
ejpam-5351	33	40	in	in	ADP
ejpam-5351	33	41	any	any	DET
ejpam-5351	33	42	dimension	dimension	NOUN
ejpam-5351	33	43	.	.	PUNCT
ejpam-5351	34	1	indeed	indeed	ADV
ejpam-5351	34	2	,	,	PUNCT
ejpam-5351	34	3	also	also	ADV
ejpam-5351	34	4	real	real	ADJ
ejpam-5351	34	5	world	world	NOUN
ejpam-5351	34	6	mechanics	mechanic	NOUN
ejpam-5351	34	7	or	or	CCONJ
ejpam-5351	34	8	physics	physics	NOUN
ejpam-5351	34	9	force	force	NOUN
ejpam-5351	34	10	us	we	PRON
ejpam-5351	34	11	to	to	PART
ejpam-5351	34	12	move	move	VERB
ejpam-5351	34	13	from	from	ADP
ejpam-5351	34	14	dimension	dimension	NOUN
ejpam-5351	34	15	2	2	NUM
ejpam-5351	34	16	to	to	ADP
ejpam-5351	34	17	dimensions	dimension	NOUN
ejpam-5351	34	18	3	3	NUM
ejpam-5351	34	19	,	,	PUNCT
ejpam-5351	34	20	4	4	NUM
ejpam-5351	34	21	or	or	CCONJ
ejpam-5351	34	22	higher	high	ADJ
ejpam-5351	34	23	.	.	PUNCT
ejpam-5351	35	1	these	these	DET
ejpam-5351	35	2	higher	high	ADJ
ejpam-5351	35	3	dimensional	dimensional	ADJ
ejpam-5351	35	4	manifolds	manifold	NOUN
ejpam-5351	35	5	are	be	AUX
ejpam-5351	35	6	objects	object	NOUN
ejpam-5351	35	7	comparable	comparable	ADJ
ejpam-5351	35	8	to	to	ADP
ejpam-5351	35	9	surfaces	surface	NOUN
ejpam-5351	35	10	,	,	PUNCT
ejpam-5351	35	11	but	but	CCONJ
ejpam-5351	35	12	where	where	SCONJ
ejpam-5351	35	13	3	3	NUM
ejpam-5351	35	14	,	,	PUNCT
ejpam-5351	35	15	4	4	NUM
ejpam-5351	35	16	or	or	CCONJ
ejpam-5351	35	17	more	more	ADJ
ejpam-5351	35	18	(	(	PUNCT
ejpam-5351	35	19	local	local	ADJ
ejpam-5351	35	20	)	)	PUNCT
ejpam-5351	35	21	coordinates	coordinate	NOUN
ejpam-5351	35	22	are	be	AUX
ejpam-5351	35	23	needed	need	VERB
ejpam-5351	35	24	to	to	PART
ejpam-5351	35	25	identify	identify	VERB
ejpam-5351	35	26	a	a	DET
ejpam-5351	35	27	point	point	NOUN
ejpam-5351	35	28	.	.	PUNCT
ejpam-5351	36	1	for	for	ADP
ejpam-5351	36	2	example	example	NOUN
ejpam-5351	36	3	,	,	PUNCT
ejpam-5351	36	4	the	the	DET
ejpam-5351	36	5	motion	motion	NOUN
ejpam-5351	36	6	of	of	ADP
ejpam-5351	36	7	three	three	NUM
ejpam-5351	36	8	bodies	body	NOUN
ejpam-5351	36	9	subjected	subject	VERB
ejpam-5351	36	10	to	to	ADP
ejpam-5351	36	11	the	the	DET
ejpam-5351	36	12	force	force	NOUN
ejpam-5351	36	13	of	of	ADP
ejpam-5351	36	14	gravity	gravity	NOUN
ejpam-5351	36	15	can	can	AUX
ejpam-5351	36	16	be	be	AUX
ejpam-5351	36	17	studied	study	VERB
ejpam-5351	36	18	as	as	ADP
ejpam-5351	36	19	an	an	DET
ejpam-5351	36	20	18	18	NUM
ejpam-5351	36	21	-	-	PUNCT
ejpam-5351	36	22	dimensional	dimensional	ADJ
ejpam-5351	36	23	manifold	manifold	NOUN
ejpam-5351	36	24	,	,	PUNCT
ejpam-5351	36	25	each	each	DET
ejpam-5351	36	26	body	body	NOUN
ejpam-5351	36	27	being	be	AUX
ejpam-5351	36	28	defined	define	VERB
ejpam-5351	36	29	by	by	ADP
ejpam-5351	36	30	three	three	NUM
ejpam-5351	36	31	spatial	spatial	ADJ
ejpam-5351	36	32	coordinates	coordinate	NOUN
ejpam-5351	36	33	and	and	CCONJ
ejpam-5351	36	34	three	three	NUM
ejpam-5351	36	35	velocity	velocity	NOUN
ejpam-5351	36	36	coordinates	coordinate	NOUN
ejpam-5351	36	37	.	.	PUNCT
ejpam-5351	37	1	if	if	SCONJ
ejpam-5351	37	2	we	we	PRON
ejpam-5351	37	3	imagine	imagine	VERB
ejpam-5351	37	4	the	the	DET
ejpam-5351	37	5	two	two	NUM
ejpam-5351	37	6	-	-	PUNCT
ejpam-5351	37	7	dimensional	dimensional	ADJ
ejpam-5351	37	8	sphere	sphere	NOUN
ejpam-5351	37	9	as	as	ADP
ejpam-5351	37	10	the	the	DET
ejpam-5351	37	11	(	(	PUNCT
ejpam-5351	37	12	exterior	exterior	ADJ
ejpam-5351	37	13	)	)	PUNCT
ejpam-5351	37	14	surface	surface	NOUN
ejpam-5351	37	15	(	(	PUNCT
ejpam-5351	37	16	or	or	CCONJ
ejpam-5351	37	17	boundary	boundary	NOUN
ejpam-5351	37	18	)	)	PUNCT
ejpam-5351	37	19	of	of	ADP
ejpam-5351	37	20	a	a	DET
ejpam-5351	37	21	three	three	NUM
ejpam-5351	37	22	-	-	PUNCT
ejpam-5351	37	23	dimensional	dimensional	ADJ
ejpam-5351	37	24	ball	ball	NOUN
ejpam-5351	37	25	,	,	PUNCT
ejpam-5351	37	26	then	then	ADV
ejpam-5351	37	27	we	we	PRON
ejpam-5351	37	28	can	can	AUX
ejpam-5351	37	29	conceive	conceive	VERB
ejpam-5351	37	30	spheres	sphere	NOUN
ejpam-5351	37	31	in	in	ADP
ejpam-5351	37	32	three	three	NUM
ejpam-5351	37	33	,	,	PUNCT
ejpam-5351	37	34	four	four	NUM
ejpam-5351	37	35	or	or	CCONJ
ejpam-5351	37	36	more	more	ADJ
ejpam-5351	37	37	dimensions	dimension	NOUN
ejpam-5351	37	38	...	...	PUNCT
ejpam-5351	38	1	and	and	CCONJ
ejpam-5351	38	2	so	so	ADV
ejpam-5351	38	3	we	we	PRON
ejpam-5351	38	4	realize	realize	VERB
ejpam-5351	38	5	that	that	SCONJ
ejpam-5351	38	6	the	the	DET
ejpam-5351	38	7	n	n	ADV
ejpam-5351	38	8	-	-	PUNCT
ejpam-5351	38	9	dimensional	dimensional	ADJ
ejpam-5351	38	10	sphere	sphere	NOUN
ejpam-5351	38	11	is	be	AUX
ejpam-5351	38	12	the	the	DET
ejpam-5351	38	13	boundary	boundary	NOUN
ejpam-5351	38	14	of	of	ADP
ejpam-5351	38	15	the	the	DET
ejpam-5351	38	16	ball	ball	NOUN
ejpam-5351	38	17	of	of	ADP
ejpam-5351	38	18	dimension	dimension	NOUN
ejpam-5351	38	19	n	n	PROPN
ejpam-5351	39	1	+	+	NOUN
ejpam-5351	39	2	1	1	NUM
ejpam-5351	39	3	.	.	PUNCT
ejpam-5351	39	4	also	also	ADV
ejpam-5351	39	5	,	,	PUNCT
ejpam-5351	39	6	we	we	PRON
ejpam-5351	39	7	may	may	AUX
ejpam-5351	39	8	figure	figure	VERB
ejpam-5351	39	9	out	out	ADP
ejpam-5351	39	10	that	that	SCONJ
ejpam-5351	39	11	,	,	PUNCT
ejpam-5351	39	12	in	in	ADP
ejpam-5351	39	13	each	each	DET
ejpam-5351	39	14	dimension	dimension	NOUN
ejpam-5351	39	15	n	n	CCONJ
ejpam-5351	39	16	,	,	PUNCT
ejpam-5351	39	17	the	the	DET
ejpam-5351	39	18	n	n	CCONJ
ejpam-5351	39	19	-	-	PUNCT
ejpam-5351	39	20	sphere	sphere	NOUN
ejpam-5351	39	21	is	be	AUX
ejpam-5351	39	22	somehow	somehow	ADV
ejpam-5351	39	23	the	the	DET
ejpam-5351	39	24	simplest	simple	ADJ
ejpam-5351	39	25	possible	possible	ADJ
ejpam-5351	39	26	closed	closed	ADJ
ejpam-5351	39	27	manifold	manifold	ADJ
ejpam-5351	39	28	to	to	PART
ejpam-5351	39	29	study	study	VERB
ejpam-5351	39	30	.	.	PUNCT
ejpam-5351	40	1	to	to	PART
ejpam-5351	40	2	be	be	AUX
ejpam-5351	40	3	more	more	ADV
ejpam-5351	40	4	precise	precise	ADJ
ejpam-5351	40	5	,	,	PUNCT
ejpam-5351	40	6	the	the	DET
ejpam-5351	40	7	n	n	CCONJ
ejpam-5351	40	8	-	-	PUNCT
ejpam-5351	40	9	sphere	sphere	NOUN
ejpam-5351	40	10	sn	sn	PROPN
ejpam-5351	40	11	is	be	AUX
ejpam-5351	40	12	the	the	DET
ejpam-5351	40	13	set	set	NOUN
ejpam-5351	40	14	of	of	ADP
ejpam-5351	40	15	points	point	NOUN
ejpam-5351	40	16	of	of	ADP
ejpam-5351	40	17	the	the	DET
ejpam-5351	40	18	euclidean	euclidean	ADJ
ejpam-5351	40	19	rn+1	rn+1	NUM
ejpam-5351	40	20	space	space	NOUN
ejpam-5351	40	21	which	which	PRON
ejpam-5351	40	22	are	be	AUX
ejpam-5351	40	23	at	at	ADP
ejpam-5351	40	24	distance	distance	NOUN
ejpam-5351	40	25	1	1	NUM
ejpam-5351	40	26	from	from	ADP
ejpam-5351	40	27	the	the	DET
ejpam-5351	40	28	origin	origin	NOUN
ejpam-5351	40	29	,	,	PUNCT
ejpam-5351	40	30	and	and	CCONJ
ejpam-5351	40	31	elementary	elementary	ADJ
ejpam-5351	40	32	analytic	analytic	ADJ
ejpam-5351	40	33	geometry	geometry	NOUN
ejpam-5351	40	34	helps	help	VERB
ejpam-5351	40	35	us	we	PRON
ejpam-5351	40	36	by	by	ADP
ejpam-5351	40	37	providing	provide	VERB
ejpam-5351	40	38	its	its	PRON
ejpam-5351	40	39	explicit	explicit	ADJ
ejpam-5351	40	40	equation	equation	NOUN
ejpam-5351	40	41	sn	sn	NOUN
ejpam-5351	40	42	=	=	PUNCT
ejpam-5351	40	43	{	{	PUNCT
ejpam-5351	40	44	x1	x1	PROPN
ejpam-5351	40	45	,	,	PUNCT
ejpam-5351	40	46	x2	x2	PROPN
ejpam-5351	40	47	,	,	PUNCT
ejpam-5351	40	48	·	·	PUNCT
ejpam-5351	40	49	·	·	PUNCT
ejpam-5351	40	50	·	·	PUNCT
ejpam-5351	40	51	,	,	PUNCT
ejpam-5351	40	52	xn+1	xn+1	PUNCT
ejpam-5351	40	53	∈	∈	PROPN
ejpam-5351	40	54	rn+1	rn+1	VERB
ejpam-5351	40	55	such	such	ADJ
ejpam-5351	40	56	that	that	SCONJ
ejpam-5351	40	57	x21	x21	PROPN
ejpam-5351	41	1	+	+	NUM
ejpam-5351	41	2	x22	x22	NOUN
ejpam-5351	41	3	+	+	CCONJ
ejpam-5351	41	4	·	·	PUNCT
ejpam-5351	41	5	·	·	PUNCT
ejpam-5351	41	6	·	·	PUNCT
ejpam-5351	41	7	+	+	SYM
ejpam-5351	41	8	x2n+1	x2n+1	SYM
ejpam-5351	41	9	=	=	SYM
ejpam-5351	41	10	1	1	X
ejpam-5351	41	11	}	}	PUNCT
ejpam-5351	41	12	⊂	⊂	X
ejpam-5351	41	13	rn+1	rn+1	PROPN
ejpam-5351	41	14	;	;	PUNCT
ejpam-5351	41	15	while	while	SCONJ
ejpam-5351	41	16	together	together	ADV
ejpam-5351	41	17	with	with	ADP
ejpam-5351	41	18	its	its	PRON
ejpam-5351	41	19	interior	interior	ADJ
ejpam-5351	41	20	one	one	NOUN
ejpam-5351	41	21	obtains	obtain	VERB
ejpam-5351	41	22	the	the	DET
ejpam-5351	41	23	n+	n+	NUM
ejpam-5351	41	24	1	1	NUM
ejpam-5351	41	25	ball	ball	NOUN
ejpam-5351	41	26	bn+1	bn+1	NUM
ejpam-5351	41	27	expressed	express	VERB
ejpam-5351	41	28	in	in	ADP
ejpam-5351	41	29	cartesian	cartesian	ADJ
ejpam-5351	41	30	coordinates	coordinate	NOUN
ejpam-5351	41	31	as	as	ADP
ejpam-5351	41	32	bn+1	bn+1	NUM
ejpam-5351	41	33	=	=	SYM
ejpam-5351	41	34	{	{	PUNCT
ejpam-5351	41	35	x1	x1	PROPN
ejpam-5351	41	36	,	,	PUNCT
ejpam-5351	41	37	x2	x2	PROPN
ejpam-5351	41	38	,	,	PUNCT
ejpam-5351	41	39	·	·	PUNCT
ejpam-5351	41	40	·	·	PUNCT
ejpam-5351	41	41	·	·	PUNCT
ejpam-5351	41	42	,	,	PUNCT
ejpam-5351	41	43	xn+1	xn+1	PUNCT
ejpam-5351	41	44	∈	∈	PROPN
ejpam-5351	41	45	rn+1	rn+1	VERB
ejpam-5351	41	46	such	such	ADJ
ejpam-5351	41	47	that	that	SCONJ
ejpam-5351	41	48	x21	x21	PROPN
ejpam-5351	41	49	+	+	NUM
ejpam-5351	41	50	x22	x22	NOUN
ejpam-5351	41	51	+	+	CCONJ
ejpam-5351	41	52	·	·	PUNCT
ejpam-5351	41	53	·	·	PUNCT
ejpam-5351	41	54	·	·	PUNCT
ejpam-5351	42	1	+	+	SYM
ejpam-5351	42	2	x2n+1	x2n+1	SYM
ejpam-5351	42	3	≤	≤	PROPN
ejpam-5351	42	4	1	1	NUM
ejpam-5351	42	5	}	}	PUNCT
ejpam-5351	42	6	⊂	⊂	X
ejpam-5351	42	7	rn+1	rn+1	PROPN
ejpam-5351	42	8	.	.	PUNCT
ejpam-5351	43	1	let	let	VERB
ejpam-5351	43	2	us	we	PRON
ejpam-5351	43	3	now	now	ADV
ejpam-5351	43	4	imagine	imagine	VERB
ejpam-5351	43	5	a	a	DET
ejpam-5351	43	6	sphere	sphere	NOUN
ejpam-5351	43	7	s2	s2	NOUN
ejpam-5351	43	8	,	,	PUNCT
ejpam-5351	43	9	like	like	ADP
ejpam-5351	43	10	the	the	DET
ejpam-5351	43	11	surface	surface	NOUN
ejpam-5351	43	12	of	of	ADP
ejpam-5351	43	13	the	the	DET
ejpam-5351	43	14	earth	earth	NOUN
ejpam-5351	43	15	,	,	PUNCT
ejpam-5351	43	16	deprived	deprive	VERB
ejpam-5351	43	17	of	of	ADP
ejpam-5351	43	18	the	the	DET
ejpam-5351	43	19	north	north	NOUN
ejpam-5351	43	20	pole	pole	NOUN
ejpam-5351	43	21	,	,	PUNCT
ejpam-5351	43	22	namely	namely	ADV
ejpam-5351	43	23	s2	s2	VERB
ejpam-5351	43	24	−	−	NOUN
ejpam-5351	43	25	n	n	NOUN
ejpam-5351	43	26	.	.	PUNCT
ejpam-5351	44	1	with	with	ADP
ejpam-5351	44	2	a	a	DET
ejpam-5351	44	3	little	little	ADJ
ejpam-5351	44	4	more	more	ADJ
ejpam-5351	44	5	imagination	imagination	NOUN
ejpam-5351	44	6	it	it	PRON
ejpam-5351	44	7	is	be	AUX
ejpam-5351	44	8	not	not	PART
ejpam-5351	44	9	difficult	difficult	ADJ
ejpam-5351	44	10	to	to	PART
ejpam-5351	44	11	see	see	VERB
ejpam-5351	44	12	that	that	SCONJ
ejpam-5351	44	13	this	this	DET
ejpam-5351	44	14	punctured	punctured	ADJ
ejpam-5351	44	15	sphere	sphere	NOUN
ejpam-5351	44	16	is	be	AUX
ejpam-5351	44	17	,	,	PUNCT
ejpam-5351	44	18	in	in	ADP
ejpam-5351	44	19	some	some	DET
ejpam-5351	44	20	sense	sense	NOUN
ejpam-5351	44	21	,	,	PUNCT
ejpam-5351	44	22	“	"	PUNCT
ejpam-5351	44	23	contractible	contractible	ADJ
ejpam-5351	44	24	”	"	PUNCT
ejpam-5351	44	25	.	.	PUNCT
ejpam-5351	45	1	that	that	PRON
ejpam-5351	45	2	is	be	AUX
ejpam-5351	45	3	:	:	PUNCT
ejpam-5351	45	4	each	each	DET
ejpam-5351	45	5	point	point	NOUN
ejpam-5351	45	6	p	p	NOUN
ejpam-5351	45	7	of	of	ADP
ejpam-5351	45	8	s2	s2	NOUN
ejpam-5351	45	9	−n	−n	ADV
ejpam-5351	45	10	(	(	PUNCT
ejpam-5351	45	11	with	with	ADP
ejpam-5351	45	12	p	p	NOUN
ejpam-5351	45	13	different	different	ADJ
ejpam-5351	45	14	from	from	ADP
ejpam-5351	45	15	the	the	DET
ejpam-5351	45	16	south	south	ADJ
ejpam-5351	45	17	pole	pole	NOUN
ejpam-5351	45	18	)	)	PUNCT
ejpam-5351	45	19	belongs	belong	VERB
ejpam-5351	45	20	to	to	ADP
ejpam-5351	45	21	a	a	DET
ejpam-5351	45	22	single	single	ADJ
ejpam-5351	45	23	meridian	meridian	NOUN
ejpam-5351	45	24	(	(	PUNCT
ejpam-5351	45	25	this	this	PRON
ejpam-5351	45	26	is	be	AUX
ejpam-5351	45	27	not	not	PART
ejpam-5351	45	28	true	true	ADJ
ejpam-5351	45	29	for	for	ADP
ejpam-5351	45	30	both	both	CCONJ
ejpam-5351	45	31	the	the	DET
ejpam-5351	45	32	poles	pole	NOUN
ejpam-5351	45	33	)	)	PUNCT
ejpam-5351	45	34	,	,	PUNCT
ejpam-5351	45	35	and	and	CCONJ
ejpam-5351	45	36	so	so	ADV
ejpam-5351	45	37	it	it	PRON
ejpam-5351	45	38	can	can	AUX
ejpam-5351	45	39	slide	slide	VERB
ejpam-5351	45	40	continuously	continuously	ADV
ejpam-5351	45	41	along	along	ADP
ejpam-5351	45	42	this	this	DET
ejpam-5351	45	43	meridian	meridian	NOUN
ejpam-5351	45	44	until	until	SCONJ
ejpam-5351	45	45	it	it	PRON
ejpam-5351	45	46	reaches	reach	VERB
ejpam-5351	45	47	the	the	DET
ejpam-5351	45	48	south	south	ADJ
ejpam-5351	45	49	pole	pole	NOUN
ejpam-5351	45	50	.	.	PUNCT
ejpam-5351	46	1	the	the	DET
ejpam-5351	46	2	same	same	ADJ
ejpam-5351	46	3	thing	thing	NOUN
ejpam-5351	46	4	can	can	AUX
ejpam-5351	46	5	be	be	AUX
ejpam-5351	46	6	done	do	VERB
ejpam-5351	46	7	for	for	ADP
ejpam-5351	46	8	a	a	DET
ejpam-5351	46	9	sphere	sphere	NOUN
ejpam-5351	46	10	of	of	ADP
ejpam-5351	46	11	any	any	DET
ejpam-5351	46	12	dimension	dimension	NOUN
ejpam-5351	46	13	n.	n.	NOUN
ejpam-5351	46	14	and	and	CCONJ
ejpam-5351	46	15	even	even	ADV
ejpam-5351	46	16	in	in	ADP
ejpam-5351	46	17	this	this	DET
ejpam-5351	46	18	case	case	NOUN
ejpam-5351	46	19	,	,	PUNCT
ejpam-5351	46	20	the	the	DET
ejpam-5351	46	21	“	"	PUNCT
ejpam-5351	46	22	meridians	meridian	NOUN
ejpam-5351	46	23	”	"	PUNCT
ejpam-5351	46	24	of	of	ADP
ejpam-5351	46	25	sn	sn	PROPN
ejpam-5351	46	26	−n	−n	ADV
ejpam-5351	46	27	meet	meet	VERB
ejpam-5351	46	28	only	only	ADV
ejpam-5351	46	29	at	at	ADP
ejpam-5351	46	30	the	the	DET
ejpam-5351	46	31	south	south	ADJ
ejpam-5351	46	32	pole	pole	NOUN
ejpam-5351	46	33	.	.	PUNCT
ejpam-5351	47	1	but	but	CCONJ
ejpam-5351	47	2	we	we	PRON
ejpam-5351	47	3	can	can	AUX
ejpam-5351	47	4	also	also	ADV
ejpam-5351	47	5	conceive	conceive	VERB
ejpam-5351	47	6	something	something	PRON
ejpam-5351	47	7	more	more	ADV
ejpam-5351	47	8	complicated	complicated	ADJ
ejpam-5351	47	9	,	,	PUNCT
ejpam-5351	47	10	some	some	DET
ejpam-5351	47	11	kind	kind	NOUN
ejpam-5351	47	12	of	of	ADP
ejpam-5351	47	13	spheres	sphere	NOUN
ejpam-5351	47	14	σn	σn	NOUN
ejpam-5351	47	15	where	where	SCONJ
ejpam-5351	47	16	the	the	DET
ejpam-5351	47	17	continuous	continuous	ADJ
ejpam-5351	47	18	flow	flow	NOUN
ejpam-5351	47	19	from	from	ADP
ejpam-5351	47	20	σn−n	σn−n	NOUN
ejpam-5351	47	21	goes	go	VERB
ejpam-5351	47	22	towards	towards	ADP
ejpam-5351	47	23	the	the	DET
ejpam-5351	47	24	south	south	ADJ
ejpam-5351	47	25	pole	pole	NOUN
ejpam-5351	47	26	but	but	CCONJ
ejpam-5351	47	27	in	in	ADP
ejpam-5351	47	28	a	a	DET
ejpam-5351	47	29	much	much	ADV
ejpam-5351	47	30	more	more	ADV
ejpam-5351	47	31	complicated	complicated	ADJ
ejpam-5351	47	32	way	way	NOUN
ejpam-5351	47	33	,	,	PUNCT
ejpam-5351	47	34	crossing	cross	VERB
ejpam-5351	47	35	and	and	CCONJ
ejpam-5351	47	36	intersecting	intersect	VERB
ejpam-5351	47	37	not	not	PART
ejpam-5351	47	38	only	only	ADV
ejpam-5351	47	39	in	in	ADP
ejpam-5351	47	40	the	the	DET
ejpam-5351	47	41	south	south	ADJ
ejpam-5351	47	42	pole	pole	NOUN
ejpam-5351	47	43	but	but	CCONJ
ejpam-5351	47	44	also	also	ADV
ejpam-5351	47	45	elsewhere	elsewhere	ADV
ejpam-5351	47	46	.	.	PUNCT
ejpam-5351	48	1	these	these	DET
ejpam-5351	48	2	“	"	PUNCT
ejpam-5351	48	3	sorts	sort	NOUN
ejpam-5351	48	4	of	of	ADP
ejpam-5351	48	5	spheres	sphere	NOUN
ejpam-5351	48	6	”	"	PUNCT
ejpam-5351	48	7	are	be	AUX
ejpam-5351	48	8	called	call	VERB
ejpam-5351	48	9	homotopy	homotopy	NOUN
ejpam-5351	48	10	spheres	sphere	NOUN
ejpam-5351	48	11	(	(	PUNCT
ejpam-5351	48	12	they	they	PRON
ejpam-5351	48	13	are	be	AUX
ejpam-5351	48	14	objects	object	NOUN
ejpam-5351	48	15	which	which	PRON
ejpam-5351	48	16	are	be	AUX
ejpam-5351	48	17	similar	similar	ADJ
ejpam-5351	48	18	to	to	ADP
ejpam-5351	48	19	spheres	sphere	NOUN
ejpam-5351	48	20	but	but	CCONJ
ejpam-5351	48	21	different	different	ADJ
ejpam-5351	48	22	from	from	ADP
ejpam-5351	48	23	them	they	PRON
ejpam-5351	48	24	,	,	PUNCT
ejpam-5351	48	25	because	because	SCONJ
ejpam-5351	48	26	they	they	PRON
ejpam-5351	48	27	are	be	AUX
ejpam-5351	48	28	shaped	shape	VERB
ejpam-5351	48	29	in	in	ADP
ejpam-5351	48	30	a	a	DET
ejpam-5351	48	31	different	different	ADJ
ejpam-5351	48	32	way	way	NOUN
ejpam-5351	48	33	)	)	PUNCT
ejpam-5351	48	34	.	.	PUNCT
ejpam-5351	49	1	in	in	ADP
ejpam-5351	49	2	other	other	ADJ
ejpam-5351	49	3	words	word	NOUN
ejpam-5351	49	4	,	,	PUNCT
ejpam-5351	49	5	a	a	DET
ejpam-5351	49	6	homotopy	homotopy	NOUN
ejpam-5351	49	7	sphere	sphere	NOUN
ejpam-5351	49	8	is	be	AUX
ejpam-5351	49	9	a	a	DET
ejpam-5351	49	10	closed	closed	ADJ
ejpam-5351	49	11	manifold	manifold	ADJ
ejpam-5351	49	12	σn	σn	NOUN
ejpam-5351	49	13	such	such	ADJ
ejpam-5351	49	14	that	that	SCONJ
ejpam-5351	49	15	σn	σn	NOUN
ejpam-5351	49	16	−	−	PROPN
ejpam-5351	49	17	p	p	NOUN
ejpam-5351	49	18	can	can	AUX
ejpam-5351	49	19	be	be	AUX
ejpam-5351	49	20	deformed	deform	VERB
ejpam-5351	49	21	continuously	continuously	ADV
ejpam-5351	49	22	(	(	PUNCT
ejpam-5351	49	23	always	always	ADV
ejpam-5351	49	24	remaining	remain	VERB
ejpam-5351	49	25	in	in	ADP
ejpam-5351	49	26	σn	σn	NOUN
ejpam-5351	49	27	−	−	PROPN
ejpam-5351	49	28	p	p	NOUN
ejpam-5351	49	29	)	)	PUNCT
ejpam-5351	49	30	to	to	ADP
ejpam-5351	49	31	a	a	DET
ejpam-5351	49	32	point	point	NOUN
ejpam-5351	49	33	(	(	PUNCT
ejpam-5351	49	34	like	like	ADP
ejpam-5351	49	35	normal	normal	ADJ
ejpam-5351	49	36	spheres	sphere	NOUN
ejpam-5351	49	37	)	)	PUNCT
ejpam-5351	49	38	.	.	PUNCT
ejpam-5351	50	1	3	3	X
ejpam-5351	50	2	.	.	X
ejpam-5351	50	3	formulation	formulation	NOUN
ejpam-5351	50	4	of	of	ADP
ejpam-5351	50	5	the	the	DET
ejpam-5351	50	6	poincaré	poincaré	ADJ
ejpam-5351	50	7	conjecture	conjecture	NOUN
ejpam-5351	50	8	the	the	DET
ejpam-5351	50	9	poincaré	poincaré	ADJ
ejpam-5351	50	10	conjecture	conjecture	NOUN
ejpam-5351	50	11	states	state	NOUN
ejpam-5351	50	12	that	that	SCONJ
ejpam-5351	50	13	the	the	DET
ejpam-5351	50	14	only	only	ADJ
ejpam-5351	50	15	homotopy	homotopy	NOUN
ejpam-5351	50	16	sphere	sphere	NOUN
ejpam-5351	50	17	σ3	σ3	PROPN
ejpam-5351	50	18	of	of	ADP
ejpam-5351	50	19	dimension	dimension	NOUN
ejpam-5351	50	20	3	3	NUM
ejpam-5351	50	21	is	be	AUX
ejpam-5351	50	22	the	the	DET
ejpam-5351	50	23	sphere	sphere	NOUN
ejpam-5351	50	24	s3	s3	PROPN
ejpam-5351	50	25	(	(	PUNCT
ejpam-5351	50	26	up	up	ADP
ejpam-5351	50	27	to	to	ADP
ejpam-5351	50	28	homeomorphisms	homeomorphism	NOUN
ejpam-5351	50	29	)	)	PUNCT
ejpam-5351	51	1	[	[	X
ejpam-5351	51	2	7	7	NUM
ejpam-5351	51	3	]	]	PUNCT
ejpam-5351	51	4	.	.	PUNCT
ejpam-5351	52	1	in	in	ADP
ejpam-5351	52	2	other	other	ADJ
ejpam-5351	52	3	words	word	NOUN
ejpam-5351	52	4	,	,	PUNCT
ejpam-5351	52	5	this	this	PRON
ejpam-5351	52	6	means	mean	VERB
ejpam-5351	52	7	that	that	SCONJ
ejpam-5351	52	8	one	one	PRON
ejpam-5351	52	9	can	can	AUX
ejpam-5351	52	10	always	always	ADV
ejpam-5351	52	11	find	find	VERB
ejpam-5351	52	12	a	a	DET
ejpam-5351	52	13	continuous	continuous	ADJ
ejpam-5351	52	14	flow	flow	NOUN
ejpam-5351	52	15	from	from	ADP
ejpam-5351	52	16	σ3−n	σ3−n	PROPN
ejpam-5351	52	17	(	(	PUNCT
ejpam-5351	52	18	the	the	DET
ejpam-5351	52	19	north	north	NOUN
ejpam-5351	52	20	pole	pole	NOUN
ejpam-5351	52	21	)	)	PUNCT
ejpam-5351	52	22	towards	towards	ADP
ejpam-5351	52	23	the	the	DET
ejpam-5351	52	24	south	south	ADJ
ejpam-5351	52	25	pole	pole	NOUN
ejpam-5351	52	26	without	without	ADP
ejpam-5351	52	27	intersections	intersection	NOUN
ejpam-5351	52	28	,	,	PUNCT
ejpam-5351	52	29	crossovers	crossover	NOUN
ejpam-5351	52	30	or	or	CCONJ
ejpam-5351	52	31	overlaps	overlap	NOUN
ejpam-5351	52	32	,	,	PUNCT
ejpam-5351	52	33	except	except	SCONJ
ejpam-5351	52	34	at	at	ADP
ejpam-5351	52	35	the	the	DET
ejpam-5351	52	36	south	south	ADJ
ejpam-5351	52	37	pole	pole	NOUN
ejpam-5351	52	38	.	.	PUNCT
ejpam-5351	53	1	this	this	PRON
ejpam-5351	53	2	is	be	AUX
ejpam-5351	53	3	also	also	ADV
ejpam-5351	53	4	equivalent	equivalent	ADJ
ejpam-5351	53	5	to	to	ADP
ejpam-5351	53	6	saying	say	VERB
ejpam-5351	53	7	that	that	SCONJ
ejpam-5351	53	8	σ3−n	σ3−n	PROPN
ejpam-5351	53	9	=	=	SYM
ejpam-5351	53	10	r3	r3	PROPN
ejpam-5351	53	11	(	(	PUNCT
ejpam-5351	53	12	this	this	PRON
ejpam-5351	53	13	is	be	AUX
ejpam-5351	53	14	clear	clear	ADJ
ejpam-5351	53	15	for	for	ADP
ejpam-5351	53	16	s3	s3	PROPN
ejpam-5351	53	17	,	,	PUNCT
ejpam-5351	53	18	by	by	ADP
ejpam-5351	53	19	means	mean	NOUN
ejpam-5351	53	20	of	of	ADP
ejpam-5351	53	21	the	the	DET
ejpam-5351	53	22	“	"	PUNCT
ejpam-5351	53	23	stereographic	stereographic	ADJ
ejpam-5351	53	24	projection	projection	NOUN
ejpam-5351	53	25	”	"	PUNCT
ejpam-5351	53	26	)	)	PUNCT
ejpam-5351	53	27	.	.	PUNCT
ejpam-5351	54	1	d.	d.	PROPN
ejpam-5351	54	2	e.	e.	PROPN
ejpam-5351	54	3	otera	otera	PROPN
ejpam-5351	54	4	/	/	SYM
ejpam-5351	54	5	eur	eur	PROPN
ejpam-5351	54	6	.	.	PUNCT
ejpam-5351	55	1	j.	j.	PROPN
ejpam-5351	55	2	pure	pure	PROPN
ejpam-5351	55	3	appl	appl	PROPN
ejpam-5351	55	4	.	.	PROPN
ejpam-5351	55	5	math	math	PROPN
ejpam-5351	55	6	,	,	PUNCT
ejpam-5351	55	7	17	17	NUM
ejpam-5351	55	8	(	(	PUNCT
ejpam-5351	55	9	3	3	NUM
ejpam-5351	55	10	)	)	PUNCT
ejpam-5351	55	11	(	(	PUNCT
ejpam-5351	55	12	2024	2024	NUM
ejpam-5351	55	13	)	)	PUNCT
ejpam-5351	55	14	,	,	PUNCT
ejpam-5351	55	15	2361	2361	NUM
ejpam-5351	55	16	-	-	SYM
ejpam-5351	55	17	2369	2369	NUM
ejpam-5351	55	18	2364	2364	NUM
ejpam-5351	55	19	to	to	PART
ejpam-5351	55	20	be	be	AUX
ejpam-5351	55	21	more	more	ADV
ejpam-5351	55	22	precise	precise	ADJ
ejpam-5351	55	23	,	,	PUNCT
ejpam-5351	55	24	poincare	poincare	PROPN
ejpam-5351	55	25	’s	’s	PART
ejpam-5351	55	26	own	own	ADJ
ejpam-5351	55	27	formulation	formulation	NOUN
ejpam-5351	55	28	in	in	ADP
ejpam-5351	55	29	1904	1904	NUM
ejpam-5351	55	30	[	[	X
ejpam-5351	55	31	6	6	NUM
ejpam-5351	55	32	]	]	PUNCT
ejpam-5351	55	33	,	,	PUNCT
ejpam-5351	55	34	although	although	SCONJ
ejpam-5351	55	35	equivalent	equivalent	ADJ
ejpam-5351	55	36	to	to	ADP
ejpam-5351	55	37	the	the	DET
ejpam-5351	55	38	one	one	NOUN
ejpam-5351	55	39	just	just	ADV
ejpam-5351	55	40	mentioned	mention	VERB
ejpam-5351	55	41	,	,	PUNCT
ejpam-5351	55	42	was	be	AUX
ejpam-5351	55	43	a	a	DET
ejpam-5351	55	44	little	little	ADJ
ejpam-5351	55	45	bit	bit	NOUN
ejpam-5351	55	46	different	different	ADJ
ejpam-5351	55	47	:	:	PUNCT
ejpam-5351	55	48	poincaré	poincaré	ADJ
ejpam-5351	55	49	indeed	indeed	ADV
ejpam-5351	55	50	conjectured	conjecture	VERB
ejpam-5351	55	51	that	that	SCONJ
ejpam-5351	55	52	the	the	DET
ejpam-5351	55	53	only	only	ADV
ejpam-5351	55	54	closed	closed	ADJ
ejpam-5351	55	55	and	and	CCONJ
ejpam-5351	55	56	“	"	PUNCT
ejpam-5351	55	57	simply	simply	ADV
ejpam-5351	55	58	connected	connect	VERB
ejpam-5351	55	59	”	"	PUNCT
ejpam-5351	55	60	3	3	NUM
ejpam-5351	55	61	-	-	PUNCT
ejpam-5351	55	62	dimensional	dimensional	ADJ
ejpam-5351	55	63	manifold	manifold	NOUN
ejpam-5351	55	64	was	be	AUX
ejpam-5351	55	65	just	just	ADV
ejpam-5351	55	66	(	(	PUNCT
ejpam-5351	55	67	homeomorphic	homeomorphic	ADJ
ejpam-5351	55	68	to	to	ADP
ejpam-5351	55	69	)	)	PUNCT
ejpam-5351	55	70	s3	s3	PROPN
ejpam-5351	55	71	.	.	PUNCT
ejpam-5351	56	1	where	where	SCONJ
ejpam-5351	56	2	a	a	DET
ejpam-5351	56	3	manifold	manifold	ADJ
ejpam-5351	56	4	v	v	NOUN
ejpam-5351	56	5	is	be	AUX
ejpam-5351	56	6	said	say	VERB
ejpam-5351	56	7	to	to	PART
ejpam-5351	56	8	be	be	AUX
ejpam-5351	56	9	simply	simply	ADV
ejpam-5351	56	10	connected	connect	VERB
ejpam-5351	56	11	(	(	PUNCT
ejpam-5351	56	12	a	a	DET
ejpam-5351	56	13	new	new	ADJ
ejpam-5351	56	14	topological	topological	ADJ
ejpam-5351	56	15	notion	notion	NOUN
ejpam-5351	56	16	introduced	introduce	VERB
ejpam-5351	56	17	by	by	ADP
ejpam-5351	56	18	poincaré	poincaré	ADJ
ejpam-5351	56	19	himself	himself	PRON
ejpam-5351	56	20	)	)	PUNCT
ejpam-5351	56	21	if	if	SCONJ
ejpam-5351	56	22	every	every	DET
ejpam-5351	56	23	closed	closed	ADJ
ejpam-5351	56	24	curve	curve	NOUN
ejpam-5351	56	25	(	(	PUNCT
ejpam-5351	56	26	i.e.	i.e.	X
ejpam-5351	56	27	a	a	DET
ejpam-5351	56	28	loop	loop	NOUN
ejpam-5351	56	29	)	)	PUNCT
ejpam-5351	56	30	in	in	ADP
ejpam-5351	56	31	v	v	NOUN
ejpam-5351	56	32	can	can	AUX
ejpam-5351	56	33	be	be	AUX
ejpam-5351	56	34	deformed	deform	VERB
ejpam-5351	56	35	continuously	continuously	ADV
ejpam-5351	56	36	to	to	ADP
ejpam-5351	56	37	a	a	DET
ejpam-5351	56	38	point	point	NOUN
ejpam-5351	56	39	,	,	PUNCT
ejpam-5351	56	40	remaining	remain	VERB
ejpam-5351	56	41	within	within	ADP
ejpam-5351	56	42	v	v	NOUN
ejpam-5351	56	43	.	.	PUNCT
ejpam-5351	57	1	note	note	VERB
ejpam-5351	57	2	that	that	SCONJ
ejpam-5351	57	3	the	the	DET
ejpam-5351	57	4	first	first	ADJ
ejpam-5351	57	5	statement	statement	NOUN
ejpam-5351	57	6	given	give	VERB
ejpam-5351	57	7	above	above	ADV
ejpam-5351	57	8	at	at	ADP
ejpam-5351	57	9	the	the	DET
ejpam-5351	57	10	beginning	beginning	NOUN
ejpam-5351	57	11	of	of	ADP
ejpam-5351	57	12	this	this	DET
ejpam-5351	57	13	section	section	NOUN
ejpam-5351	57	14	has	have	VERB
ejpam-5351	57	15	the	the	DET
ejpam-5351	57	16	advantage	advantage	NOUN
ejpam-5351	57	17	of	of	ADP
ejpam-5351	57	18	being	be	AUX
ejpam-5351	57	19	valid	valid	ADJ
ejpam-5351	57	20	in	in	ADP
ejpam-5351	57	21	every	every	DET
ejpam-5351	57	22	dimension	dimension	NOUN
ejpam-5351	57	23	.	.	PUNCT
ejpam-5351	58	1	in	in	ADP
ejpam-5351	58	2	particular	particular	ADJ
ejpam-5351	58	3	,	,	PUNCT
ejpam-5351	58	4	one	one	PRON
ejpam-5351	58	5	can	can	AUX
ejpam-5351	58	6	formulate	formulate	VERB
ejpam-5351	58	7	the	the	DET
ejpam-5351	58	8	generalized	generalized	ADJ
ejpam-5351	58	9	poincaré	poincaré	ADJ
ejpam-5351	58	10	conjecture	conjecture	NOUN
ejpam-5351	58	11	,	,	PUNCT
ejpam-5351	58	12	which	which	PRON
ejpam-5351	58	13	says	say	VERB
ejpam-5351	58	14	that	that	SCONJ
ejpam-5351	58	15	for	for	ADP
ejpam-5351	58	16	every	every	DET
ejpam-5351	58	17	n	n	NOUN
ejpam-5351	58	18	,	,	PUNCT
ejpam-5351	58	19	a	a	DET
ejpam-5351	58	20	homotopy	homotopy	NOUN
ejpam-5351	58	21	sphere	sphere	NOUN
ejpam-5351	58	22	σn	σn	NOUN
ejpam-5351	58	23	is	be	AUX
ejpam-5351	58	24	(	(	PUNCT
ejpam-5351	58	25	homeomorphic	homeomorphic	ADJ
ejpam-5351	58	26	to	to	ADP
ejpam-5351	58	27	)	)	PUNCT
ejpam-5351	58	28	sn	sn	PROPN
ejpam-5351	58	29	.	.	PUNCT
ejpam-5351	59	1	but	but	CCONJ
ejpam-5351	59	2	the	the	DET
ejpam-5351	59	3	step	step	NOUN
ejpam-5351	59	4	from	from	ADP
ejpam-5351	59	5	n	n	NOUN
ejpam-5351	59	6	=	=	SYM
ejpam-5351	59	7	3	3	NUM
ejpam-5351	59	8	to	to	ADP
ejpam-5351	59	9	any	any	DET
ejpam-5351	59	10	n	n	CCONJ
ejpam-5351	59	11	,	,	PUNCT
ejpam-5351	59	12	appeared	appear	VERB
ejpam-5351	59	13	some	some	DET
ejpam-5351	59	14	thirty	thirty	NUM
ejpam-5351	59	15	years	year	NOUN
ejpam-5351	59	16	after	after	ADP
ejpam-5351	59	17	poincaré	poincaré	ADJ
ejpam-5351	59	18	,	,	PUNCT
ejpam-5351	59	19	and	and	CCONJ
ejpam-5351	59	20	moreover	moreover	ADV
ejpam-5351	59	21	,	,	PUNCT
ejpam-5351	59	22	no	no	DET
ejpam-5351	59	23	further	further	ADJ
ejpam-5351	59	24	progress	progress	NOUN
ejpam-5351	59	25	was	be	AUX
ejpam-5351	59	26	made	make	VERB
ejpam-5351	59	27	in	in	ADP
ejpam-5351	59	28	any	any	DET
ejpam-5351	59	29	dimension	dimension	NOUN
ejpam-5351	59	30	greater	great	ADJ
ejpam-5351	59	31	than	than	ADP
ejpam-5351	59	32	2	2	NUM
ejpam-5351	59	33	until	until	ADP
ejpam-5351	59	34	the	the	DET
ejpam-5351	59	35	1950s	1950s	NUM
ejpam-5351	59	36	.	.	PUNCT
ejpam-5351	60	1	on	on	ADP
ejpam-5351	60	2	the	the	DET
ejpam-5351	60	3	other	other	ADJ
ejpam-5351	60	4	hand	hand	NOUN
ejpam-5351	60	5	,	,	PUNCT
ejpam-5351	60	6	although	although	SCONJ
ejpam-5351	60	7	formulated	formulate	VERB
ejpam-5351	60	8	in	in	ADP
ejpam-5351	60	9	a	a	DET
ejpam-5351	60	10	very	very	ADV
ejpam-5351	60	11	different	different	ADJ
ejpam-5351	60	12	way	way	NOUN
ejpam-5351	60	13	,	,	PUNCT
ejpam-5351	60	14	the	the	DET
ejpam-5351	60	15	case	case	NOUN
ejpam-5351	60	16	n	n	NOUN
ejpam-5351	60	17	=	=	SYM
ejpam-5351	60	18	2	2	NUM
ejpam-5351	60	19	,	,	PUNCT
ejpam-5351	60	20	which	which	PRON
ejpam-5351	60	21	is	be	AUX
ejpam-5351	60	22	much	much	ADV
ejpam-5351	60	23	more	more	ADV
ejpam-5351	60	24	easy	easy	ADJ
ejpam-5351	60	25	,	,	PUNCT
ejpam-5351	60	26	was	be	AUX
ejpam-5351	60	27	already	already	ADV
ejpam-5351	60	28	known	know	VERB
ejpam-5351	60	29	since	since	SCONJ
ejpam-5351	60	30	the	the	DET
ejpam-5351	60	31	middle	middle	NOUN
ejpam-5351	60	32	of	of	ADP
ejpam-5351	60	33	the	the	DET
ejpam-5351	60	34	19th	19th	ADJ
ejpam-5351	60	35	century	century	NOUN
ejpam-5351	60	36	.	.	PUNCT
ejpam-5351	61	1	more	more	ADV
ejpam-5351	61	2	precisely	precisely	ADV
ejpam-5351	61	3	,	,	PUNCT
ejpam-5351	61	4	in	in	ADP
ejpam-5351	61	5	dimension	dimension	NOUN
ejpam-5351	61	6	2	2	NUM
ejpam-5351	61	7	,	,	PUNCT
ejpam-5351	61	8	the	the	DET
ejpam-5351	61	9	corresponding	corresponding	ADJ
ejpam-5351	61	10	statement	statement	NOUN
ejpam-5351	61	11	is	be	AUX
ejpam-5351	61	12	that	that	SCONJ
ejpam-5351	61	13	in	in	ADP
ejpam-5351	61	14	any	any	DET
ejpam-5351	61	15	closed	closed	ADJ
ejpam-5351	61	16	surface	surface	NOUN
ejpam-5351	61	17	which	which	PRON
ejpam-5351	61	18	is	be	AUX
ejpam-5351	61	19	different	different	ADJ
ejpam-5351	61	20	from	from	ADP
ejpam-5351	61	21	a	a	DET
ejpam-5351	61	22	2	2	NUM
ejpam-5351	61	23	-	-	PUNCT
ejpam-5351	61	24	sphere	sphere	NOUN
ejpam-5351	61	25	s2	s2	NOUN
ejpam-5351	61	26	one	one	NOUN
ejpam-5351	61	27	can	can	AUX
ejpam-5351	61	28	find	find	VERB
ejpam-5351	61	29	at	at	ADV
ejpam-5351	61	30	least	least	ADJ
ejpam-5351	61	31	a	a	DET
ejpam-5351	61	32	loop	loop	NOUN
ejpam-5351	61	33	which	which	PRON
ejpam-5351	61	34	can	can	AUX
ejpam-5351	61	35	not	not	PART
ejpam-5351	61	36	be	be	AUX
ejpam-5351	61	37	continuously	continuously	ADV
ejpam-5351	61	38	contracted	contract	VERB
ejpam-5351	61	39	to	to	ADP
ejpam-5351	61	40	a	a	DET
ejpam-5351	61	41	point	point	NOUN
ejpam-5351	61	42	.	.	PUNCT
ejpam-5351	62	1	this	this	DET
ejpam-5351	62	2	result	result	NOUN
ejpam-5351	62	3	actually	actually	ADV
ejpam-5351	62	4	follows	follow	VERB
ejpam-5351	62	5	from	from	ADP
ejpam-5351	62	6	a	a	DET
ejpam-5351	62	7	far	far	ADV
ejpam-5351	62	8	more	more	ADV
ejpam-5351	62	9	detailed	detailed	ADJ
ejpam-5351	62	10	and	and	CCONJ
ejpam-5351	62	11	deeper	deep	ADJ
ejpam-5351	62	12	theorem	theorem	ADJ
ejpam-5351	62	13	:	:	PUNCT
ejpam-5351	62	14	the	the	DET
ejpam-5351	62	15	classification	classification	NOUN
ejpam-5351	62	16	of	of	ADP
ejpam-5351	62	17	closed	closed	ADJ
ejpam-5351	62	18	and	and	CCONJ
ejpam-5351	62	19	connected	connect	VERB
ejpam-5351	62	20	two	two	NUM
ejpam-5351	62	21	-	-	PUNCT
ejpam-5351	62	22	dimensional	dimensional	ADJ
ejpam-5351	62	23	manifolds	manifold	NOUN
ejpam-5351	62	24	,	,	PUNCT
ejpam-5351	62	25	which	which	PRON
ejpam-5351	62	26	was	be	AUX
ejpam-5351	62	27	proved	prove	VERB
ejpam-5351	62	28	in	in	ADP
ejpam-5351	62	29	different	different	ADJ
ejpam-5351	62	30	forms	form	NOUN
ejpam-5351	62	31	since	since	SCONJ
ejpam-5351	62	32	the	the	DET
ejpam-5351	62	33	1860s	1860	NOUN
ejpam-5351	62	34	,	,	PUNCT
ejpam-5351	62	35	and	and	CCONJ
ejpam-5351	62	36	which	which	PRON
ejpam-5351	62	37	says	say	VERB
ejpam-5351	62	38	that	that	SCONJ
ejpam-5351	62	39	every	every	DET
ejpam-5351	62	40	compact	compact	ADJ
ejpam-5351	62	41	surface	surface	NOUN
ejpam-5351	62	42	is	be	AUX
ejpam-5351	62	43	homeomorphic	homeomorphic	ADJ
ejpam-5351	62	44	to	to	ADP
ejpam-5351	62	45	a	a	DET
ejpam-5351	62	46	sphere	sphere	NOUN
ejpam-5351	62	47	with	with	ADP
ejpam-5351	62	48	some	some	DET
ejpam-5351	62	49	number	number	NOUN
ejpam-5351	62	50	of	of	ADP
ejpam-5351	62	51	handles	handle	NOUN
ejpam-5351	62	52	or	or	CCONJ
ejpam-5351	62	53	cross	cross	ADJ
ejpam-5351	62	54	-	-	ADJ
ejpam-5351	62	55	caps	cap	NOUN
ejpam-5351	62	56	attached	attach	VERB
ejpam-5351	62	57	.	.	PUNCT
ejpam-5351	63	1	3.1	3.1	NUM
ejpam-5351	63	2	.	.	PUNCT
ejpam-5351	63	3	top	top	NOUN
ejpam-5351	63	4	versus	versus	ADP
ejpam-5351	63	5	diff	diff	PROPN
ejpam-5351	63	6	now	now	ADV
ejpam-5351	63	7	,	,	PUNCT
ejpam-5351	63	8	we	we	PRON
ejpam-5351	63	9	come	come	VERB
ejpam-5351	63	10	back	back	ADV
ejpam-5351	63	11	to	to	ADP
ejpam-5351	63	12	the	the	DET
ejpam-5351	63	13	sphere	sphere	NOUN
ejpam-5351	63	14	s2	s2	PROPN
ejpam-5351	63	15	,	,	PUNCT
ejpam-5351	63	16	seen	see	VERB
ejpam-5351	63	17	as	as	ADP
ejpam-5351	63	18	the	the	DET
ejpam-5351	63	19	surface	surface	NOUN
ejpam-5351	63	20	of	of	ADP
ejpam-5351	63	21	our	our	PRON
ejpam-5351	63	22	globe	globe	NOUN
ejpam-5351	63	23	b3	b3	PROPN
ejpam-5351	63	24	.	.	PUNCT
ejpam-5351	64	1	this	this	DET
ejpam-5351	64	2	object	object	NOUN
ejpam-5351	64	3	is	be	AUX
ejpam-5351	64	4	obviously	obviously	ADV
ejpam-5351	64	5	homeomorphic	homeomorphic	ADJ
ejpam-5351	64	6	,	,	PUNCT
ejpam-5351	64	7	i.e.	i.e.	X
ejpam-5351	64	8	topologically	topologically	ADV
ejpam-5351	64	9	equivalent	equivalent	ADJ
ejpam-5351	64	10	,	,	PUNCT
ejpam-5351	64	11	to	to	ADP
ejpam-5351	64	12	the	the	DET
ejpam-5351	64	13	surface	surface	NOUN
ejpam-5351	64	14	of	of	ADP
ejpam-5351	64	15	an	an	DET
ejpam-5351	64	16	ellipsoid	ellipsoid	NOUN
ejpam-5351	64	17	(	(	PUNCT
ejpam-5351	64	18	a	a	DET
ejpam-5351	64	19	rugby	rugby	NOUN
ejpam-5351	64	20	ball	ball	NOUN
ejpam-5351	64	21	)	)	PUNCT
ejpam-5351	64	22	,	,	PUNCT
ejpam-5351	64	23	but	but	CCONJ
ejpam-5351	64	24	also	also	ADV
ejpam-5351	64	25	to	to	ADP
ejpam-5351	64	26	the	the	DET
ejpam-5351	64	27	surface	surface	NOUN
ejpam-5351	64	28	of	of	ADP
ejpam-5351	64	29	a	a	DET
ejpam-5351	64	30	cube	cube	NOUN
ejpam-5351	64	31	(	(	PUNCT
ejpam-5351	64	32	because	because	SCONJ
ejpam-5351	64	33	we	we	PRON
ejpam-5351	64	34	can	can	AUX
ejpam-5351	64	35	imagine	imagine	VERB
ejpam-5351	64	36	a	a	DET
ejpam-5351	64	37	play	play	NOUN
ejpam-5351	64	38	dough	dough	NOUN
ejpam-5351	64	39	sphere	sphere	ADV
ejpam-5351	64	40	,	,	PUNCT
ejpam-5351	64	41	which	which	PRON
ejpam-5351	64	42	we	we	PRON
ejpam-5351	64	43	can	can	AUX
ejpam-5351	64	44	model	model	VERB
ejpam-5351	64	45	,	,	PUNCT
ejpam-5351	64	46	without	without	ADP
ejpam-5351	64	47	breaking	break	VERB
ejpam-5351	64	48	it	it	PRON
ejpam-5351	64	49	,	,	PUNCT
ejpam-5351	64	50	as	as	ADP
ejpam-5351	64	51	either	either	CCONJ
ejpam-5351	64	52	an	an	DET
ejpam-5351	64	53	ellipsoid	ellipsoid	NOUN
ejpam-5351	64	54	or	or	CCONJ
ejpam-5351	64	55	a	a	DET
ejpam-5351	64	56	cube	cube	NOUN
ejpam-5351	64	57	)	)	PUNCT
ejpam-5351	64	58	.	.	PUNCT
ejpam-5351	65	1	however	however	ADV
ejpam-5351	65	2	,	,	PUNCT
ejpam-5351	65	3	the	the	DET
ejpam-5351	65	4	ellipsoid	ellipsoid	NOUN
ejpam-5351	65	5	is	be	AUX
ejpam-5351	65	6	smooth	smooth	ADJ
ejpam-5351	65	7	,	,	PUNCT
ejpam-5351	65	8	like	like	ADP
ejpam-5351	65	9	the	the	DET
ejpam-5351	65	10	sphere	sphere	NOUN
ejpam-5351	65	11	,	,	PUNCT
ejpam-5351	65	12	while	while	SCONJ
ejpam-5351	65	13	the	the	DET
ejpam-5351	65	14	surface	surface	NOUN
ejpam-5351	65	15	of	of	ADP
ejpam-5351	65	16	the	the	DET
ejpam-5351	65	17	cube	cube	NOUN
ejpam-5351	65	18	is	be	AUX
ejpam-5351	65	19	not	not	PART
ejpam-5351	65	20	,	,	PUNCT
ejpam-5351	65	21	because	because	SCONJ
ejpam-5351	65	22	there	there	PRON
ejpam-5351	65	23	are	be	VERB
ejpam-5351	65	24	edges	edge	NOUN
ejpam-5351	65	25	,	,	PUNCT
ejpam-5351	65	26	corners	corner	NOUN
ejpam-5351	65	27	and	and	CCONJ
ejpam-5351	65	28	points	point	NOUN
ejpam-5351	65	29	.	.	PUNCT
ejpam-5351	66	1	hence	hence	ADV
ejpam-5351	66	2	,	,	PUNCT
ejpam-5351	66	3	we	we	PRON
ejpam-5351	66	4	can	can	AUX
ejpam-5351	66	5	say	say	VERB
ejpam-5351	66	6	that	that	SCONJ
ejpam-5351	66	7	the	the	DET
ejpam-5351	66	8	equality	equality	NOUN
ejpam-5351	66	9	between	between	ADP
ejpam-5351	66	10	the	the	DET
ejpam-5351	66	11	sphere	sphere	NOUN
ejpam-5351	66	12	and	and	CCONJ
ejpam-5351	66	13	the	the	DET
ejpam-5351	66	14	ellipsoid	ellipsoid	NOUN
ejpam-5351	66	15	is	be	AUX
ejpam-5351	66	16	realized	realize	VERB
ejpam-5351	66	17	by	by	ADP
ejpam-5351	66	18	functions	function	NOUN
ejpam-5351	66	19	that	that	PRON
ejpam-5351	66	20	possess	possess	VERB
ejpam-5351	66	21	continuous	continuous	ADJ
ejpam-5351	66	22	derivatives	derivative	NOUN
ejpam-5351	66	23	(	(	PUNCT
ejpam-5351	66	24	and	and	CCONJ
ejpam-5351	66	25	these	these	DET
ejpam-5351	66	26	functions	function	NOUN
ejpam-5351	66	27	are	be	AUX
ejpam-5351	66	28	called	call	VERB
ejpam-5351	66	29	diffeomorphisms	diffeomorphism	NOUN
ejpam-5351	66	30	=	=	SYM
ejpam-5351	66	31	differentiable	differentiable	ADJ
ejpam-5351	66	32	homeomorphisms	homeomorphism	NOUN
ejpam-5351	66	33	,	,	PUNCT
ejpam-5351	66	34	a	a	DET
ejpam-5351	66	35	more	more	ADV
ejpam-5351	66	36	restrictive	restrictive	ADJ
ejpam-5351	66	37	notion	notion	NOUN
ejpam-5351	66	38	than	than	ADP
ejpam-5351	66	39	that	that	PRON
ejpam-5351	66	40	of	of	ADP
ejpam-5351	66	41	homeomorphism	homeomorphism	PROPN
ejpam-5351	66	42	)	)	PUNCT
ejpam-5351	66	43	.	.	PUNCT
ejpam-5351	67	1	the	the	DET
ejpam-5351	67	2	sphere	sphere	NOUN
ejpam-5351	67	3	and	and	CCONJ
ejpam-5351	67	4	the	the	DET
ejpam-5351	67	5	ellipsoid	ellipsoid	NOUN
ejpam-5351	67	6	are	be	AUX
ejpam-5351	67	7	both	both	CCONJ
ejpam-5351	67	8	homeomorphic	homeomorphic	ADJ
ejpam-5351	67	9	and	and	CCONJ
ejpam-5351	67	10	diffeomorphic	diffeomorphic	ADJ
ejpam-5351	67	11	.	.	PUNCT
ejpam-5351	68	1	on	on	ADP
ejpam-5351	68	2	the	the	DET
ejpam-5351	68	3	contrary	contrary	NOUN
ejpam-5351	68	4	,	,	PUNCT
ejpam-5351	68	5	the	the	DET
ejpam-5351	68	6	topological	topological	ADJ
ejpam-5351	68	7	equivalence	equivalence	NOUN
ejpam-5351	68	8	between	between	ADP
ejpam-5351	68	9	the	the	DET
ejpam-5351	68	10	sphere	sphere	NOUN
ejpam-5351	68	11	and	and	CCONJ
ejpam-5351	68	12	the	the	DET
ejpam-5351	68	13	cube	cube	NOUN
ejpam-5351	68	14	surface	surface	NOUN
ejpam-5351	68	15	is	be	AUX
ejpam-5351	68	16	only	only	ADV
ejpam-5351	68	17	possible	possible	ADJ
ejpam-5351	68	18	through	through	ADP
ejpam-5351	68	19	simple	simple	ADJ
ejpam-5351	68	20	continuous	continuous	ADJ
ejpam-5351	68	21	functions	function	NOUN
ejpam-5351	68	22	that	that	PRON
ejpam-5351	68	23	do	do	AUX
ejpam-5351	68	24	not	not	PART
ejpam-5351	68	25	admit	admit	VERB
ejpam-5351	68	26	derivatives	derivative	NOUN
ejpam-5351	68	27	:	:	PUNCT
ejpam-5351	68	28	these	these	DET
ejpam-5351	68	29	two	two	NUM
ejpam-5351	68	30	surfaces	surface	NOUN
ejpam-5351	68	31	are	be	AUX
ejpam-5351	68	32	homeomorphic	homeomorphic	ADJ
ejpam-5351	68	33	,	,	PUNCT
ejpam-5351	68	34	but	but	CCONJ
ejpam-5351	68	35	not	not	PART
ejpam-5351	68	36	diffeomorphic	diffeomorphic	ADJ
ejpam-5351	68	37	.	.	PUNCT
ejpam-5351	69	1	the	the	DET
ejpam-5351	69	2	sphere	sphere	NOUN
ejpam-5351	69	3	is	be	AUX
ejpam-5351	69	4	smooth	smooth	ADJ
ejpam-5351	69	5	and	and	CCONJ
ejpam-5351	69	6	differentiable	differentiable	ADJ
ejpam-5351	69	7	,	,	PUNCT
ejpam-5351	69	8	while	while	SCONJ
ejpam-5351	69	9	the	the	DET
ejpam-5351	69	10	cube	cube	NOUN
ejpam-5351	69	11	is	be	AUX
ejpam-5351	69	12	not	not	PART
ejpam-5351	69	13	.	.	PUNCT
ejpam-5351	70	1	now	now	ADV
ejpam-5351	70	2	,	,	PUNCT
ejpam-5351	70	3	if	if	SCONJ
ejpam-5351	70	4	we	we	PRON
ejpam-5351	70	5	only	only	ADV
ejpam-5351	70	6	consider	consider	VERB
ejpam-5351	70	7	manifolds	manifold	NOUN
ejpam-5351	70	8	of	of	ADP
ejpam-5351	70	9	dimension	dimension	NOUN
ejpam-5351	70	10	less	less	ADV
ejpam-5351	70	11	than	than	ADP
ejpam-5351	70	12	or	or	CCONJ
ejpam-5351	70	13	equal	equal	ADJ
ejpam-5351	70	14	to	to	ADP
ejpam-5351	70	15	3	3	NUM
ejpam-5351	70	16	,	,	PUNCT
ejpam-5351	70	17	then	then	ADV
ejpam-5351	70	18	this	this	DET
ejpam-5351	70	19	distinction	distinction	NOUN
ejpam-5351	70	20	is	be	AUX
ejpam-5351	70	21	an	an	DET
ejpam-5351	70	22	unnecessary	unnecessary	ADJ
ejpam-5351	70	23	pedantry	pedantry	NOUN
ejpam-5351	70	24	,	,	PUNCT
ejpam-5351	70	25	because	because	SCONJ
ejpam-5351	70	26	in	in	ADP
ejpam-5351	70	27	those	those	DET
ejpam-5351	70	28	cases	case	NOUN
ejpam-5351	70	29	the	the	DET
ejpam-5351	70	30	categories	category	NOUN
ejpam-5351	70	31	of	of	ADP
ejpam-5351	70	32	topological	topological	ADJ
ejpam-5351	70	33	and	and	CCONJ
ejpam-5351	70	34	differentiable	differentiable	ADJ
ejpam-5351	70	35	manifolds	manifold	NOUN
ejpam-5351	70	36	coincide	coincide	NOUN
ejpam-5351	70	37	(	(	PUNCT
ejpam-5351	70	38	i.e.	i.e.	X
ejpam-5351	70	39	we	we	PRON
ejpam-5351	70	40	know	know	VERB
ejpam-5351	70	41	how	how	SCONJ
ejpam-5351	70	42	to	to	PART
ejpam-5351	70	43	round	round	VERB
ejpam-5351	70	44	off	off	ADP
ejpam-5351	70	45	edges	edge	NOUN
ejpam-5351	70	46	)	)	PUNCT
ejpam-5351	70	47	.	.	PUNCT
ejpam-5351	71	1	conversely	conversely	ADV
ejpam-5351	71	2	,	,	PUNCT
ejpam-5351	71	3	in	in	ADP
ejpam-5351	71	4	dimensions	dimension	NOUN
ejpam-5351	71	5	greater	great	ADJ
ejpam-5351	71	6	than	than	ADP
ejpam-5351	71	7	3	3	NUM
ejpam-5351	71	8	,	,	PUNCT
ejpam-5351	71	9	it	it	PRON
ejpam-5351	71	10	turns	turn	VERB
ejpam-5351	71	11	out	out	ADP
ejpam-5351	71	12	that	that	SCONJ
ejpam-5351	71	13	there	there	PRON
ejpam-5351	71	14	are	be	VERB
ejpam-5351	71	15	obstructions	obstruction	NOUN
ejpam-5351	71	16	to	to	ADP
ejpam-5351	71	17	rounding	round	VERB
ejpam-5351	71	18	objects	object	NOUN
ejpam-5351	71	19	,	,	PUNCT
ejpam-5351	71	20	and	and	CCONJ
ejpam-5351	71	21	there	there	PRON
ejpam-5351	71	22	exist	exist	VERB
ejpam-5351	71	23	examples	example	NOUN
ejpam-5351	71	24	of	of	ADP
ejpam-5351	71	25	non	non	ADJ
ejpam-5351	71	26	-	-	ADJ
ejpam-5351	71	27	smootable	smootable	ADJ
ejpam-5351	71	28	manifolds	manifold	NOUN
ejpam-5351	71	29	.	.	PUNCT
ejpam-5351	72	1	for	for	ADP
ejpam-5351	72	2	example	example	NOUN
ejpam-5351	72	3	,	,	PUNCT
ejpam-5351	72	4	in	in	ADP
ejpam-5351	72	5	1956	1956	NUM
ejpam-5351	72	6	the	the	DET
ejpam-5351	72	7	famous	famous	ADJ
ejpam-5351	72	8	mathematician	mathematician	NOUN
ejpam-5351	72	9	j.	j.	PROPN
ejpam-5351	72	10	milnor	milnor	PROPN
ejpam-5351	72	11	proved	prove	VERB
ejpam-5351	72	12	that	that	SCONJ
ejpam-5351	72	13	on	on	ADP
ejpam-5351	72	14	the	the	DET
ejpam-5351	72	15	sphere	sphere	NOUN
ejpam-5351	72	16	of	of	ADP
ejpam-5351	72	17	dimension	dimension	NOUN
ejpam-5351	72	18	7	7	NUM
ejpam-5351	72	19	coexist	coexist	NOUN
ejpam-5351	72	20	several	several	ADJ
ejpam-5351	72	21	(	(	PUNCT
ejpam-5351	72	22	actually	actually	ADV
ejpam-5351	72	23	28	28	NUM
ejpam-5351	72	24	)	)	PUNCT
ejpam-5351	72	25	differentiable	differentiable	ADJ
ejpam-5351	72	26	structures	structure	NOUN
ejpam-5351	72	27	that	that	PRON
ejpam-5351	72	28	are	be	AUX
ejpam-5351	72	29	not	not	PART
ejpam-5351	72	30	diffeomorfic	diffeomorfic	ADJ
ejpam-5351	72	31	d.	d.	PROPN
ejpam-5351	72	32	e.	e.	PROPN
ejpam-5351	72	33	otera	otera	PROPN
ejpam-5351	72	34	/	/	SYM
ejpam-5351	72	35	eur	eur	PROPN
ejpam-5351	72	36	.	.	PUNCT
ejpam-5351	73	1	j.	j.	PROPN
ejpam-5351	73	2	pure	pure	PROPN
ejpam-5351	73	3	appl	appl	PROPN
ejpam-5351	73	4	.	.	PROPN
ejpam-5351	73	5	math	math	PROPN
ejpam-5351	73	6	,	,	PUNCT
ejpam-5351	73	7	17	17	NUM
ejpam-5351	73	8	(	(	PUNCT
ejpam-5351	73	9	3	3	NUM
ejpam-5351	73	10	)	)	PUNCT
ejpam-5351	73	11	(	(	PUNCT
ejpam-5351	73	12	2024	2024	NUM
ejpam-5351	73	13	)	)	PUNCT
ejpam-5351	73	14	,	,	PUNCT
ejpam-5351	73	15	2361	2361	NUM
ejpam-5351	73	16	-	-	SYM
ejpam-5351	73	17	2369	2369	NUM
ejpam-5351	73	18	2365	2365	NUM
ejpam-5351	73	19	to	to	ADP
ejpam-5351	73	20	each	each	DET
ejpam-5351	73	21	other	other	ADJ
ejpam-5351	73	22	.	.	PUNCT
ejpam-5351	74	1	therefore	therefore	ADV
ejpam-5351	74	2	there	there	PRON
ejpam-5351	74	3	exist	exist	VERB
ejpam-5351	74	4	“	"	PUNCT
ejpam-5351	74	5	exotic	exotic	ADJ
ejpam-5351	74	6	”	"	PUNCT
ejpam-5351	74	7	spheres	sphere	NOUN
ejpam-5351	74	8	,	,	PUNCT
ejpam-5351	74	9	i.e.	i.e.	X
ejpam-5351	74	10	spheres	sphere	NOUN
ejpam-5351	74	11	admitting	admit	VERB
ejpam-5351	74	12	differential	differential	ADJ
ejpam-5351	74	13	structures	structure	NOUN
ejpam-5351	74	14	that	that	PRON
ejpam-5351	74	15	are	be	AUX
ejpam-5351	74	16	different	different	ADJ
ejpam-5351	74	17	from	from	ADP
ejpam-5351	74	18	the	the	DET
ejpam-5351	74	19	standard	standard	ADJ
ejpam-5351	74	20	one	one	NOUN
ejpam-5351	74	21	(	(	PUNCT
ejpam-5351	74	22	see	see	VERB
ejpam-5351	74	23	[	[	X
ejpam-5351	74	24	3	3	NUM
ejpam-5351	74	25	]	]	NUM
ejpam-5351	74	26	)	)	PUNCT
ejpam-5351	74	27	.	.	PUNCT
ejpam-5351	75	1	hence	hence	ADV
ejpam-5351	75	2	,	,	PUNCT
ejpam-5351	75	3	the	the	DET
ejpam-5351	75	4	general	general	ADJ
ejpam-5351	75	5	idea	idea	NOUN
ejpam-5351	75	6	at	at	ADP
ejpam-5351	75	7	the	the	DET
ejpam-5351	75	8	time	time	NOUN
ejpam-5351	75	9	was	be	AUX
ejpam-5351	75	10	that	that	SCONJ
ejpam-5351	75	11	,	,	PUNCT
ejpam-5351	75	12	as	as	ADP
ejpam-5351	75	13	the	the	DET
ejpam-5351	75	14	dimension	dimension	NOUN
ejpam-5351	75	15	increases	increase	VERB
ejpam-5351	75	16	,	,	PUNCT
ejpam-5351	75	17	the	the	DET
ejpam-5351	75	18	difficulties	difficulty	NOUN
ejpam-5351	75	19	could	could	AUX
ejpam-5351	75	20	only	only	ADV
ejpam-5351	75	21	increase	increase	VERB
ejpam-5351	75	22	too	too	ADV
ejpam-5351	75	23	.	.	PUNCT
ejpam-5351	76	1	but	but	CCONJ
ejpam-5351	76	2	then	then	ADV
ejpam-5351	76	3	,	,	PUNCT
ejpam-5351	76	4	around	around	ADP
ejpam-5351	76	5	1960	1960	NUM
ejpam-5351	76	6	,	,	PUNCT
ejpam-5351	76	7	s.	s.	PROPN
ejpam-5351	76	8	smale	smale	PROPN
ejpam-5351	76	9	realized	realize	VERB
ejpam-5351	76	10	the	the	DET
ejpam-5351	76	11	opposite	opposite	NOUN
ejpam-5351	76	12	,	,	PUNCT
ejpam-5351	76	13	and	and	CCONJ
ejpam-5351	76	14	proved	prove	VERB
ejpam-5351	76	15	at	at	ADP
ejpam-5351	76	16	once	once	ADV
ejpam-5351	76	17	the	the	DET
ejpam-5351	76	18	generalized	generalized	ADJ
ejpam-5351	76	19	poincaré	poincaré	ADJ
ejpam-5351	76	20	conjecture	conjecture	NOUN
ejpam-5351	76	21	in	in	ADP
ejpam-5351	76	22	any	any	DET
ejpam-5351	76	23	dimension	dimension	NOUN
ejpam-5351	76	24	at	at	ADV
ejpam-5351	76	25	least	least	ADJ
ejpam-5351	76	26	5	5	NUM
ejpam-5351	76	27	:	:	PUNCT
ejpam-5351	76	28	a	a	DET
ejpam-5351	76	29	manifold	manifold	NOUN
ejpam-5351	76	30	which	which	PRON
ejpam-5351	76	31	is	be	AUX
ejpam-5351	76	32	a	a	DET
ejpam-5351	76	33	homotopy	homotopy	NOUN
ejpam-5351	76	34	sphere	sphere	NOUN
ejpam-5351	76	35	σn	σn	NOUN
ejpam-5351	76	36	is	be	AUX
ejpam-5351	76	37	homeomorphic	homeomorphic	ADJ
ejpam-5351	76	38	to	to	ADP
ejpam-5351	76	39	a	a	DET
ejpam-5351	76	40	sphere	sphere	NOUN
ejpam-5351	76	41	sn	sn	PROPN
ejpam-5351	76	42	,	,	PUNCT
ejpam-5351	76	43	for	for	ADP
ejpam-5351	76	44	every	every	DET
ejpam-5351	76	45	n	n	PRON
ejpam-5351	76	46	≥	≥	NOUN
ejpam-5351	76	47	5	5	NUM
ejpam-5351	76	48	.	.	PUNCT
ejpam-5351	77	1	the	the	DET
ejpam-5351	77	2	reasons	reason	NOUN
ejpam-5351	77	3	why	why	SCONJ
ejpam-5351	77	4	the	the	DET
ejpam-5351	77	5	difficulties	difficulty	NOUN
ejpam-5351	77	6	decrease	decrease	NOUN
ejpam-5351	77	7	can	can	AUX
ejpam-5351	77	8	be	be	AUX
ejpam-5351	77	9	explained	explain	VERB
ejpam-5351	77	10	very	very	ADV
ejpam-5351	77	11	simplistically	simplistically	ADV
ejpam-5351	77	12	as	as	SCONJ
ejpam-5351	77	13	follows	follow	VERB
ejpam-5351	77	14	:	:	PUNCT
ejpam-5351	77	15	in	in	ADP
ejpam-5351	77	16	large	large	ADJ
ejpam-5351	77	17	dimensions	dimension	NOUN
ejpam-5351	77	18	,	,	PUNCT
ejpam-5351	77	19	there	there	PRON
ejpam-5351	77	20	is	be	VERB
ejpam-5351	77	21	a	a	DET
ejpam-5351	77	22	lot	lot	NOUN
ejpam-5351	77	23	of	of	ADP
ejpam-5351	77	24	empty	empty	ADJ
ejpam-5351	77	25	space	space	NOUN
ejpam-5351	77	26	to	to	PART
ejpam-5351	77	27	manoeuvre	manoeuvre	VERB
ejpam-5351	77	28	around	around	ADP
ejpam-5351	77	29	the	the	DET
ejpam-5351	77	30	problems	problem	NOUN
ejpam-5351	77	31	and	and	CCONJ
ejpam-5351	77	32	to	to	PART
ejpam-5351	77	33	develop	develop	VERB
ejpam-5351	77	34	the	the	DET
ejpam-5351	77	35	needed	need	VERB
ejpam-5351	77	36	geometric	geometric	ADJ
ejpam-5351	77	37	constructions	construction	NOUN
ejpam-5351	77	38	to	to	PART
ejpam-5351	77	39	solve	solve	VERB
ejpam-5351	77	40	them	they	PRON
ejpam-5351	77	41	and	and	CCONJ
ejpam-5351	77	42	to	to	PART
ejpam-5351	77	43	establish	establish	VERB
ejpam-5351	77	44	the	the	DET
ejpam-5351	77	45	equality	equality	NOUN
ejpam-5351	77	46	to	to	PART
ejpam-5351	77	47	be	be	AUX
ejpam-5351	77	48	proved	prove	VERB
ejpam-5351	77	49	.	.	PUNCT
ejpam-5351	78	1	while	while	SCONJ
ejpam-5351	78	2	in	in	ADP
ejpam-5351	78	3	dimensions	dimension	NOUN
ejpam-5351	78	4	smaller	small	ADJ
ejpam-5351	78	5	than	than	ADP
ejpam-5351	78	6	3	3	NUM
ejpam-5351	78	7	(	(	PUNCT
ejpam-5351	78	8	1	1	NUM
ejpam-5351	78	9	or	or	CCONJ
ejpam-5351	78	10	2	2	NUM
ejpam-5351	78	11	)	)	PUNCT
ejpam-5351	78	12	,	,	PUNCT
ejpam-5351	78	13	there	there	PRON
ejpam-5351	78	14	is	be	VERB
ejpam-5351	78	15	not	not	PART
ejpam-5351	78	16	enough	enough	ADJ
ejpam-5351	78	17	space	space	NOUN
ejpam-5351	78	18	to	to	PART
ejpam-5351	78	19	create	create	VERB
ejpam-5351	78	20	problems	problem	NOUN
ejpam-5351	78	21	.	.	PUNCT
ejpam-5351	79	1	finally	finally	ADV
ejpam-5351	79	2	,	,	PUNCT
ejpam-5351	79	3	in	in	ADP
ejpam-5351	79	4	dimension	dimension	NOUN
ejpam-5351	79	5	3	3	NUM
ejpam-5351	79	6	,	,	PUNCT
ejpam-5351	79	7	namely	namely	ADV
ejpam-5351	79	8	the	the	DET
ejpam-5351	79	9	starting	starting	NOUN
ejpam-5351	79	10	point	point	NOUN
ejpam-5351	79	11	of	of	ADP
ejpam-5351	79	12	poincaré	poincaré	ADJ
ejpam-5351	79	13	,	,	PUNCT
ejpam-5351	79	14	there	there	PRON
ejpam-5351	79	15	is	be	VERB
ejpam-5351	79	16	both	both	PRON
ejpam-5351	79	17	the	the	DET
ejpam-5351	79	18	possibility	possibility	NOUN
ejpam-5351	79	19	of	of	ADP
ejpam-5351	79	20	having	have	VERB
ejpam-5351	79	21	problems	problem	NOUN
ejpam-5351	79	22	but	but	CCONJ
ejpam-5351	79	23	also	also	ADV
ejpam-5351	79	24	very	very	ADV
ejpam-5351	79	25	little	little	ADJ
ejpam-5351	79	26	space	space	NOUN
ejpam-5351	79	27	to	to	PART
ejpam-5351	79	28	act	act	VERB
ejpam-5351	79	29	...	...	PUNCT
ejpam-5351	80	1	the	the	DET
ejpam-5351	80	2	limit	limit	NOUN
ejpam-5351	80	3	situation	situation	NOUN
ejpam-5351	80	4	is	be	AUX
ejpam-5351	80	5	dimension	dimension	NOUN
ejpam-5351	80	6	4	4	NUM
ejpam-5351	80	7	.	.	PUNCT
ejpam-5351	81	1	this	this	PRON
ejpam-5351	81	2	is	be	AUX
ejpam-5351	81	3	a	a	DET
ejpam-5351	81	4	world	world	NOUN
ejpam-5351	81	5	of	of	ADP
ejpam-5351	81	6	its	its	PRON
ejpam-5351	81	7	own	own	ADJ
ejpam-5351	81	8	,	,	PUNCT
ejpam-5351	81	9	very	very	ADV
ejpam-5351	81	10	different	different	ADJ
ejpam-5351	81	11	from	from	ADP
ejpam-5351	81	12	the	the	DET
ejpam-5351	81	13	others	other	NOUN
ejpam-5351	81	14	(	(	PUNCT
ejpam-5351	81	15	dimension	dimension	NOUN
ejpam-5351	81	16	2	2	NUM
ejpam-5351	81	17	,	,	PUNCT
ejpam-5351	81	18	3	3	NUM
ejpam-5351	81	19	or	or	CCONJ
ejpam-5351	81	20	higher	high	ADJ
ejpam-5351	81	21	dimensions	dimension	NOUN
ejpam-5351	81	22	,	,	PUNCT
ejpam-5351	81	23	see	see	VERB
ejpam-5351	81	24	[	[	X
ejpam-5351	81	25	5	5	NUM
ejpam-5351	81	26	]	]	NUM
ejpam-5351	81	27	)	)	PUNCT
ejpam-5351	81	28	.	.	PUNCT
ejpam-5351	82	1	in	in	ADP
ejpam-5351	82	2	this	this	DET
ejpam-5351	82	3	case	case	NOUN
ejpam-5351	82	4	it	it	PRON
ejpam-5351	82	5	actually	actually	ADV
ejpam-5351	82	6	took	take	VERB
ejpam-5351	82	7	a	a	DET
ejpam-5351	82	8	great	great	ADJ
ejpam-5351	82	9	tour	tour	NOUN
ejpam-5351	82	10	-	-	PUNCT
ejpam-5351	82	11	de	de	NOUN
ejpam-5351	82	12	-	-	NOUN
ejpam-5351	82	13	force	force	NOUN
ejpam-5351	82	14	to	to	PART
ejpam-5351	82	15	prove	prove	VERB
ejpam-5351	82	16	the	the	DET
ejpam-5351	82	17	poincaré	poincaré	ADJ
ejpam-5351	82	18	conjecture	conjecture	NOUN
ejpam-5351	82	19	:	:	PUNCT
ejpam-5351	82	20	in	in	ADP
ejpam-5351	82	21	1982	1982	NUM
ejpam-5351	82	22	m.	m.	NOUN
ejpam-5351	82	23	freedmann	freedmann	PROPN
ejpam-5351	82	24	proved	prove	VERB
ejpam-5351	82	25	that	that	SCONJ
ejpam-5351	82	26	σ4	σ4	NOUN
ejpam-5351	82	27	is	be	AUX
ejpam-5351	82	28	topologically	topologically	ADV
ejpam-5351	82	29	equal	equal	ADJ
ejpam-5351	82	30	(	(	PUNCT
ejpam-5351	82	31	homeomorphic	homeomorphic	ADJ
ejpam-5351	82	32	)	)	PUNCT
ejpam-5351	82	33	to	to	PART
ejpam-5351	82	34	s4	s4	VERB
ejpam-5351	82	35	.	.	PUNCT
ejpam-5351	83	1	actually	actually	ADV
ejpam-5351	83	2	,	,	PUNCT
ejpam-5351	83	3	thanks	thank	NOUN
ejpam-5351	83	4	to	to	ADP
ejpam-5351	83	5	freedmann	freedmann	PROPN
ejpam-5351	83	6	’s	’s	PART
ejpam-5351	83	7	work	work	NOUN
ejpam-5351	83	8	,	,	PUNCT
ejpam-5351	83	9	we	we	PRON
ejpam-5351	83	10	know	know	VERB
ejpam-5351	83	11	nowadays	nowadays	ADV
ejpam-5351	83	12	that	that	SCONJ
ejpam-5351	83	13	precisely	precisely	ADV
ejpam-5351	83	14	in	in	ADP
ejpam-5351	83	15	dimension	dimension	NOUN
ejpam-5351	83	16	4	4	NUM
ejpam-5351	83	17	(	(	PUNCT
ejpam-5351	83	18	the	the	DET
ejpam-5351	83	19	dimension	dimension	NOUN
ejpam-5351	83	20	of	of	ADP
ejpam-5351	83	21	our	our	PRON
ejpam-5351	83	22	space	space	NOUN
ejpam-5351	83	23	-	-	PUNCT
ejpam-5351	83	24	time	time	NOUN
ejpam-5351	83	25	)	)	PUNCT
ejpam-5351	83	26	there	there	PRON
ejpam-5351	83	27	is	be	VERB
ejpam-5351	83	28	a	a	DET
ejpam-5351	83	29	great	great	ADJ
ejpam-5351	83	30	mystery	mystery	NOUN
ejpam-5351	83	31	between	between	ADP
ejpam-5351	83	32	the	the	DET
ejpam-5351	83	33	topological	topological	ADJ
ejpam-5351	83	34	and	and	CCONJ
ejpam-5351	83	35	the	the	DET
ejpam-5351	83	36	differential	differential	ADJ
ejpam-5351	83	37	pictures	picture	NOUN
ejpam-5351	83	38	.	.	PUNCT
ejpam-5351	84	1	and	and	CCONJ
ejpam-5351	84	2	the	the	DET
ejpam-5351	84	3	smooth	smooth	ADJ
ejpam-5351	84	4	4	4	NUM
ejpam-5351	84	5	-	-	PUNCT
ejpam-5351	84	6	dimensional	dimensional	ADJ
ejpam-5351	84	7	poincaré	poincaré	ADJ
ejpam-5351	84	8	conjecture	conjecture	NOUN
ejpam-5351	84	9	is	be	AUX
ejpam-5351	84	10	still	still	ADV
ejpam-5351	84	11	an	an	DET
ejpam-5351	84	12	open	open	ADJ
ejpam-5351	84	13	problem	problem	NOUN
ejpam-5351	84	14	,	,	PUNCT
ejpam-5351	84	15	far	far	ADV
ejpam-5351	84	16	from	from	ADP
ejpam-5351	84	17	being	be	AUX
ejpam-5351	84	18	solved	solve	VERB
ejpam-5351	84	19	.	.	PUNCT
ejpam-5351	85	1	summarizing	summarizing	NOUN
ejpam-5351	85	2	,	,	PUNCT
ejpam-5351	85	3	we	we	PRON
ejpam-5351	85	4	know	know	VERB
ejpam-5351	85	5	that	that	SCONJ
ejpam-5351	85	6	the	the	DET
ejpam-5351	85	7	generalized	generalized	ADJ
ejpam-5351	85	8	poincaré	poincaré	ADJ
ejpam-5351	85	9	conjecture	conjecture	NOUN
ejpam-5351	85	10	can	can	AUX
ejpam-5351	85	11	be	be	AUX
ejpam-5351	85	12	true	true	ADJ
ejpam-5351	85	13	or	or	CCONJ
ejpam-5351	85	14	false	false	ADJ
ejpam-5351	85	15	in	in	ADP
ejpam-5351	85	16	the	the	DET
ejpam-5351	85	17	different	different	ADJ
ejpam-5351	85	18	categories	category	NOUN
ejpam-5351	85	19	(	(	PUNCT
ejpam-5351	85	20	top	top	NOUN
ejpam-5351	85	21	or	or	CCONJ
ejpam-5351	85	22	diff	diff	NOUN
ejpam-5351	85	23	)	)	PUNCT
ejpam-5351	85	24	,	,	PUNCT
ejpam-5351	85	25	depending	depend	VERB
ejpam-5351	85	26	on	on	ADP
ejpam-5351	85	27	the	the	DET
ejpam-5351	85	28	dimension	dimension	NOUN
ejpam-5351	85	29	,	,	PUNCT
ejpam-5351	85	30	thank	thank	VERB
ejpam-5351	85	31	to	to	ADP
ejpam-5351	85	32	the	the	DET
ejpam-5351	85	33	work	work	NOUN
ejpam-5351	85	34	of	of	ADP
ejpam-5351	85	35	several	several	ADJ
ejpam-5351	85	36	esteemed	esteemed	ADJ
ejpam-5351	85	37	mathematicians	mathematician	NOUN
ejpam-5351	85	38	,	,	PUNCT
ejpam-5351	85	39	such	such	ADJ
ejpam-5351	85	40	as	as	ADP
ejpam-5351	85	41	john	john	PROPN
ejpam-5351	85	42	milnor	milnor	PROPN
ejpam-5351	85	43	,	,	PUNCT
ejpam-5351	85	44	steve	steve	PROPN
ejpam-5351	85	45	smale	smale	PROPN
ejpam-5351	85	46	,	,	PUNCT
ejpam-5351	85	47	michael	michael	PROPN
ejpam-5351	85	48	freedman	freedman	PROPN
ejpam-5351	85	49	,	,	PUNCT
ejpam-5351	85	50	and	and	CCONJ
ejpam-5351	85	51	grigori	grigori	PROPN
ejpam-5351	85	52	perelman	perelman	PROPN
ejpam-5351	85	53	(	(	PUNCT
ejpam-5351	85	54	see	see	VERB
ejpam-5351	85	55	[	[	X
ejpam-5351	85	56	8	8	NUM
ejpam-5351	85	57	]	]	NUM
ejpam-5351	85	58	)	)	PUNCT
ejpam-5351	85	59	,	,	PUNCT
ejpam-5351	85	60	all	all	PRON
ejpam-5351	85	61	of	of	ADP
ejpam-5351	85	62	whom	whom	PRON
ejpam-5351	85	63	have	have	AUX
ejpam-5351	85	64	been	be	AUX
ejpam-5351	85	65	awarded	award	VERB
ejpam-5351	85	66	the	the	DET
ejpam-5351	85	67	fields	field	NOUN
ejpam-5351	85	68	medal	medal	NOUN
ejpam-5351	85	69	,	,	PUNCT
ejpam-5351	85	70	which	which	PRON
ejpam-5351	85	71	is	be	AUX
ejpam-5351	85	72	the	the	DET
ejpam-5351	85	73	most	most	ADV
ejpam-5351	85	74	prestigious	prestigious	ADJ
ejpam-5351	85	75	prize	prize	NOUN
ejpam-5351	85	76	in	in	ADP
ejpam-5351	85	77	mathematics	mathematic	NOUN
ejpam-5351	85	78	,	,	PUNCT
ejpam-5351	85	79	the	the	DET
ejpam-5351	85	80	equivalent	equivalent	NOUN
ejpam-5351	85	81	of	of	ADP
ejpam-5351	85	82	nobel	nobel	PROPN
ejpam-5351	85	83	prize	prize	PROPN
ejpam-5351	85	84	.	.	PUNCT
ejpam-5351	86	1	in	in	ADP
ejpam-5351	86	2	particular	particular	ADJ
ejpam-5351	86	3	,	,	PUNCT
ejpam-5351	86	4	in	in	ADP
ejpam-5351	86	5	the	the	DET
ejpam-5351	86	6	category	category	NOUN
ejpam-5351	86	7	top	top	NOUN
ejpam-5351	86	8	(	(	PUNCT
ejpam-5351	86	9	i.e.	i.e.	X
ejpam-5351	86	10	for	for	ADP
ejpam-5351	86	11	topological	topological	ADJ
ejpam-5351	86	12	manifolds	manifold	NOUN
ejpam-5351	86	13	)	)	PUNCT
ejpam-5351	86	14	the	the	DET
ejpam-5351	86	15	generalized	generalized	ADJ
ejpam-5351	86	16	poincaré	poincaré	ADJ
ejpam-5351	86	17	conjecture	conjecture	NOUN
ejpam-5351	86	18	is	be	AUX
ejpam-5351	86	19	true	true	ADJ
ejpam-5351	86	20	in	in	ADP
ejpam-5351	86	21	all	all	DET
ejpam-5351	86	22	dimensions	dimension	NOUN
ejpam-5351	86	23	!	!	PUNCT
ejpam-5351	87	1	whereas	whereas	SCONJ
ejpam-5351	87	2	in	in	ADP
ejpam-5351	87	3	the	the	DET
ejpam-5351	87	4	diff	diff	NOUN
ejpam-5351	87	5	category	category	NOUN
ejpam-5351	87	6	(	(	PUNCT
ejpam-5351	87	7	i.e.	i.e.	X
ejpam-5351	87	8	for	for	ADP
ejpam-5351	87	9	differential	differential	ADJ
ejpam-5351	87	10	manifolds	manifold	NOUN
ejpam-5351	87	11	)	)	PUNCT
ejpam-5351	87	12	it	it	PRON
ejpam-5351	87	13	is	be	AUX
ejpam-5351	87	14	true	true	ADJ
ejpam-5351	87	15	in	in	ADP
ejpam-5351	87	16	dimensions	dimension	NOUN
ejpam-5351	87	17	1	1	NUM
ejpam-5351	87	18	,	,	PUNCT
ejpam-5351	87	19	2	2	NUM
ejpam-5351	87	20	,	,	PUNCT
ejpam-5351	87	21	3	3	NUM
ejpam-5351	87	22	,	,	PUNCT
ejpam-5351	87	23	5	5	NUM
ejpam-5351	87	24	and	and	CCONJ
ejpam-5351	87	25	6	6	NUM
ejpam-5351	87	26	,	,	PUNCT
ejpam-5351	87	27	it	it	PRON
ejpam-5351	87	28	is	be	AUX
ejpam-5351	87	29	still	still	ADV
ejpam-5351	87	30	open	open	ADJ
ejpam-5351	87	31	in	in	ADP
ejpam-5351	87	32	dimension	dimension	NOUN
ejpam-5351	87	33	4	4	NUM
ejpam-5351	87	34	,	,	PUNCT
ejpam-5351	87	35	whereas	whereas	SCONJ
ejpam-5351	87	36	in	in	ADP
ejpam-5351	87	37	the	the	DET
ejpam-5351	87	38	other	other	ADJ
ejpam-5351	87	39	cases	case	NOUN
ejpam-5351	87	40	it	it	PRON
ejpam-5351	87	41	is	be	AUX
ejpam-5351	87	42	generally	generally	ADV
ejpam-5351	87	43	false	false	ADJ
ejpam-5351	87	44	.	.	PUNCT
ejpam-5351	88	1	notice	notice	VERB
ejpam-5351	88	2	that	that	SCONJ
ejpam-5351	88	3	,	,	PUNCT
ejpam-5351	88	4	even	even	ADV
ejpam-5351	88	5	if	if	SCONJ
ejpam-5351	88	6	the	the	DET
ejpam-5351	88	7	original	original	ADJ
ejpam-5351	88	8	poincaré	poincaré	ADJ
ejpam-5351	88	9	conjecture	conjecture	NOUN
ejpam-5351	88	10	in	in	ADP
ejpam-5351	88	11	dimension	dimension	NOUN
ejpam-5351	88	12	3	3	NUM
ejpam-5351	88	13	has	have	AUX
ejpam-5351	88	14	been	be	AUX
ejpam-5351	88	15	solved	solve	VERB
ejpam-5351	88	16	a	a	DET
ejpam-5351	88	17	century	century	NOUN
ejpam-5351	88	18	after	after	ADP
ejpam-5351	88	19	its	its	PRON
ejpam-5351	88	20	first	first	ADJ
ejpam-5351	88	21	formulation	formulation	NOUN
ejpam-5351	88	22	,	,	PUNCT
ejpam-5351	88	23	in	in	ADP
ejpam-5351	88	24	all	all	DET
ejpam-5351	88	25	that	that	DET
ejpam-5351	88	26	time	time	NOUN
ejpam-5351	88	27	,	,	PUNCT
ejpam-5351	88	28	various	various	ADJ
ejpam-5351	88	29	ways	way	NOUN
ejpam-5351	88	30	to	to	PART
ejpam-5351	88	31	attack	attack	VERB
ejpam-5351	88	32	the	the	DET
ejpam-5351	88	33	problem	problem	NOUN
ejpam-5351	88	34	have	have	AUX
ejpam-5351	88	35	been	be	AUX
ejpam-5351	88	36	developed	develop	VERB
ejpam-5351	88	37	and	and	CCONJ
ejpam-5351	88	38	tried	try	VERB
ejpam-5351	88	39	,	,	PUNCT
ejpam-5351	88	40	as	as	SCONJ
ejpam-5351	88	41	it	it	PRON
ejpam-5351	88	42	is	be	AUX
ejpam-5351	88	43	related	relate	VERB
ejpam-5351	88	44	to	to	ADP
ejpam-5351	88	45	various	various	ADJ
ejpam-5351	88	46	areas	area	NOUN
ejpam-5351	88	47	of	of	ADP
ejpam-5351	88	48	mathematics	mathematic	NOUN
ejpam-5351	88	49	,	,	PUNCT
ejpam-5351	88	50	from	from	ADP
ejpam-5351	88	51	group	group	NOUN
ejpam-5351	88	52	theory	theory	NOUN
ejpam-5351	88	53	to	to	ADP
ejpam-5351	88	54	differential	differential	ADJ
ejpam-5351	88	55	equations	equation	NOUN
ejpam-5351	88	56	,	,	PUNCT
ejpam-5351	88	57	from	from	ADP
ejpam-5351	88	58	physics	physics	NOUN
ejpam-5351	88	59	to	to	ADP
ejpam-5351	88	60	general	general	ADJ
ejpam-5351	88	61	relativity	relativity	NOUN
ejpam-5351	88	62	.	.	PUNCT
ejpam-5351	89	1	and	and	CCONJ
ejpam-5351	89	2	even	even	ADV
ejpam-5351	89	3	though	though	SCONJ
ejpam-5351	89	4	it	it	PRON
ejpam-5351	89	5	has	have	AUX
ejpam-5351	89	6	remained	remain	VERB
ejpam-5351	89	7	unproven	unproven	ADJ
ejpam-5351	89	8	for	for	ADP
ejpam-5351	89	9	a	a	DET
ejpam-5351	89	10	hundred	hundred	NUM
ejpam-5351	89	11	years	year	NOUN
ejpam-5351	89	12	,	,	PUNCT
ejpam-5351	89	13	many	many	ADJ
ejpam-5351	89	14	profound	profound	ADJ
ejpam-5351	89	15	new	new	ADJ
ejpam-5351	89	16	results	result	NOUN
ejpam-5351	89	17	have	have	AUX
ejpam-5351	89	18	emerged	emerge	VERB
ejpam-5351	89	19	from	from	ADP
ejpam-5351	89	20	the	the	DET
ejpam-5351	89	21	techniques	technique	NOUN
ejpam-5351	89	22	developed	develop	VERB
ejpam-5351	89	23	to	to	PART
ejpam-5351	89	24	solve	solve	VERB
ejpam-5351	89	25	it	it	PRON
ejpam-5351	89	26	(	(	PUNCT
ejpam-5351	89	27	see	see	VERB
ejpam-5351	89	28	[	[	X
ejpam-5351	89	29	1–4	1–4	NUM
ejpam-5351	89	30	,	,	PUNCT
ejpam-5351	89	31	8–10	8–10	NOUN
ejpam-5351	89	32	]	]	PUNCT
ejpam-5351	89	33	)	)	PUNCT
ejpam-5351	89	34	.	.	PUNCT
ejpam-5351	90	1	in	in	ADP
ejpam-5351	90	2	few	few	ADJ
ejpam-5351	90	3	words	word	NOUN
ejpam-5351	90	4	,	,	PUNCT
ejpam-5351	90	5	all	all	DET
ejpam-5351	90	6	the	the	DET
ejpam-5351	90	7	work	work	NOUN
ejpam-5351	90	8	devoted	devote	VERB
ejpam-5351	90	9	to	to	ADP
ejpam-5351	90	10	the	the	DET
ejpam-5351	90	11	conjecture	conjecture	NOUN
ejpam-5351	90	12	improved	improve	VERB
ejpam-5351	90	13	the	the	DET
ejpam-5351	90	14	deep	deep	ADJ
ejpam-5351	90	15	understanding	understanding	NOUN
ejpam-5351	90	16	of	of	ADP
ejpam-5351	90	17	the	the	DET
ejpam-5351	90	18	world	world	NOUN
ejpam-5351	90	19	of	of	ADP
ejpam-5351	90	20	3	3	NUM
ejpam-5351	90	21	-	-	PUNCT
ejpam-5351	90	22	manifolds	manifold	NOUN
ejpam-5351	90	23	.	.	PUNCT
ejpam-5351	91	1	4	4	X
ejpam-5351	91	2	.	.	X
ejpam-5351	91	3	geometric	geometric	ADJ
ejpam-5351	91	4	structures	structure	NOUN
ejpam-5351	91	5	in	in	ADP
ejpam-5351	91	6	dimension	dimension	NOUN
ejpam-5351	91	7	3	3	NUM
ejpam-5351	91	8	the	the	DET
ejpam-5351	91	9	poincaré	poincaré	ADJ
ejpam-5351	91	10	conjecture	conjecture	NOUN
ejpam-5351	91	11	is	be	AUX
ejpam-5351	91	12	a	a	DET
ejpam-5351	91	13	purely	purely	ADV
ejpam-5351	91	14	topological	topological	ADJ
ejpam-5351	91	15	problem	problem	NOUN
ejpam-5351	91	16	.	.	PUNCT
ejpam-5351	92	1	nevertheless	nevertheless	ADV
ejpam-5351	92	2	,	,	PUNCT
ejpam-5351	92	3	all	all	DET
ejpam-5351	92	4	efforts	effort	NOUN
ejpam-5351	92	5	by	by	ADP
ejpam-5351	92	6	topologists	topologist	NOUN
ejpam-5351	92	7	to	to	PART
ejpam-5351	92	8	prove	prove	VERB
ejpam-5351	92	9	it	it	PRON
ejpam-5351	92	10	have	have	AUX
ejpam-5351	92	11	failed	fail	VERB
ejpam-5351	92	12	,	,	PUNCT
ejpam-5351	92	13	and	and	CCONJ
ejpam-5351	92	14	in	in	ADP
ejpam-5351	92	15	fact	fact	NOUN
ejpam-5351	92	16	no	no	DET
ejpam-5351	92	17	topological	topological	ADJ
ejpam-5351	92	18	proof	proof	NOUN
ejpam-5351	92	19	exists	exist	VERB
ejpam-5351	92	20	to	to	ADP
ejpam-5351	92	21	this	this	DET
ejpam-5351	92	22	day	day	NOUN
ejpam-5351	92	23	.	.	PUNCT
ejpam-5351	93	1	therefore	therefore	ADV
ejpam-5351	93	2	,	,	PUNCT
ejpam-5351	93	3	for	for	ADP
ejpam-5351	93	4	its	its	PRON
ejpam-5351	93	5	resolution	resolution	NOUN
ejpam-5351	93	6	,	,	PUNCT
ejpam-5351	93	7	a	a	DET
ejpam-5351	93	8	good	good	ADJ
ejpam-5351	93	9	idea	idea	NOUN
ejpam-5351	93	10	is	be	AUX
ejpam-5351	93	11	to	to	PART
ejpam-5351	93	12	leave	leave	VERB
ejpam-5351	93	13	the	the	DET
ejpam-5351	93	14	topological	topological	ADJ
ejpam-5351	93	15	framework	framework	NOUN
ejpam-5351	93	16	,	,	PUNCT
ejpam-5351	93	17	and	and	CCONJ
ejpam-5351	93	18	to	to	PART
ejpam-5351	93	19	use	use	VERB
ejpam-5351	93	20	geometric	geometric	ADJ
ejpam-5351	93	21	or	or	CCONJ
ejpam-5351	93	22	analytic	analytic	ADJ
ejpam-5351	93	23	methods	method	NOUN
ejpam-5351	93	24	in	in	ADP
ejpam-5351	93	25	order	order	NOUN
ejpam-5351	93	26	to	to	PART
ejpam-5351	93	27	have	have	AUX
ejpam-5351	93	28	more	more	ADJ
ejpam-5351	93	29	tools	tool	NOUN
ejpam-5351	93	30	to	to	PART
ejpam-5351	93	31	attack	attack	VERB
ejpam-5351	93	32	the	the	DET
ejpam-5351	93	33	problem	problem	NOUN
ejpam-5351	93	34	.	.	PUNCT
ejpam-5351	94	1	d.	d.	PROPN
ejpam-5351	94	2	e.	e.	PROPN
ejpam-5351	94	3	otera	otera	PROPN
ejpam-5351	94	4	/	/	SYM
ejpam-5351	94	5	eur	eur	PROPN
ejpam-5351	94	6	.	.	PUNCT
ejpam-5351	95	1	j.	j.	PROPN
ejpam-5351	95	2	pure	pure	PROPN
ejpam-5351	95	3	appl	appl	PROPN
ejpam-5351	95	4	.	.	PROPN
ejpam-5351	95	5	math	math	PROPN
ejpam-5351	95	6	,	,	PUNCT
ejpam-5351	95	7	17	17	NUM
ejpam-5351	95	8	(	(	PUNCT
ejpam-5351	95	9	3	3	NUM
ejpam-5351	95	10	)	)	PUNCT
ejpam-5351	95	11	(	(	PUNCT
ejpam-5351	95	12	2024	2024	NUM
ejpam-5351	95	13	)	)	PUNCT
ejpam-5351	95	14	,	,	PUNCT
ejpam-5351	95	15	2361	2361	NUM
ejpam-5351	95	16	-	-	SYM
ejpam-5351	95	17	2369	2369	NUM
ejpam-5351	95	18	2366	2366	NUM
ejpam-5351	95	19	one	one	NUM
ejpam-5351	95	20	of	of	ADP
ejpam-5351	95	21	the	the	DET
ejpam-5351	95	22	most	most	ADV
ejpam-5351	95	23	suitable	suitable	ADJ
ejpam-5351	95	24	strategies	strategy	NOUN
ejpam-5351	95	25	is	be	AUX
ejpam-5351	95	26	to	to	PART
ejpam-5351	95	27	equip	equip	VERB
ejpam-5351	95	28	the	the	DET
ejpam-5351	95	29	manifolds	manifold	NOUN
ejpam-5351	95	30	with	with	ADP
ejpam-5351	95	31	some	some	DET
ejpam-5351	95	32	geometric	geometric	ADJ
ejpam-5351	95	33	structures	structure	NOUN
ejpam-5351	95	34	.	.	PUNCT
ejpam-5351	96	1	and	and	CCONJ
ejpam-5351	96	2	in	in	ADP
ejpam-5351	96	3	fact	fact	NOUN
ejpam-5351	96	4	,	,	PUNCT
ejpam-5351	96	5	it	it	PRON
ejpam-5351	96	6	was	be	AUX
ejpam-5351	96	7	just	just	ADV
ejpam-5351	96	8	this	this	DET
ejpam-5351	96	9	approach	approach	NOUN
ejpam-5351	96	10	that	that	PRON
ejpam-5351	96	11	has	have	AUX
ejpam-5351	96	12	proved	prove	VERB
ejpam-5351	96	13	successful	successful	ADJ
ejpam-5351	96	14	in	in	ADP
ejpam-5351	96	15	the	the	DET
ejpam-5351	96	16	end	end	NOUN
ejpam-5351	96	17	.	.	PUNCT
ejpam-5351	97	1	this	this	DET
ejpam-5351	97	2	path	path	NOUN
ejpam-5351	97	3	is	be	AUX
ejpam-5351	97	4	very	very	ADV
ejpam-5351	97	5	much	much	ADV
ejpam-5351	97	6	related	related	ADJ
ejpam-5351	97	7	to	to	ADP
ejpam-5351	97	8	another	another	DET
ejpam-5351	97	9	work	work	NOUN
ejpam-5351	97	10	by	by	ADP
ejpam-5351	97	11	poincaré	poincaré	ADJ
ejpam-5351	97	12	himself	himself	PRON
ejpam-5351	97	13	,	,	PUNCT
ejpam-5351	97	14	his	his	PRON
ejpam-5351	97	15	famous	famous	ADJ
ejpam-5351	97	16	uniformization	uniformization	NOUN
ejpam-5351	97	17	theorem	theorem	VERB
ejpam-5351	97	18	.	.	PUNCT
ejpam-5351	98	1	this	this	DET
ejpam-5351	98	2	result	result	NOUN
ejpam-5351	98	3	concerns	concern	NOUN
ejpam-5351	98	4	surfaces	surface	NOUN
ejpam-5351	98	5	(	(	PUNCT
ejpam-5351	98	6	hence	hence	ADV
ejpam-5351	98	7	we	we	PRON
ejpam-5351	98	8	are	be	AUX
ejpam-5351	98	9	in	in	ADP
ejpam-5351	98	10	dimension	dimension	NOUN
ejpam-5351	98	11	2	2	NUM
ejpam-5351	98	12	)	)	PUNCT
ejpam-5351	98	13	and	and	CCONJ
ejpam-5351	98	14	,	,	PUNCT
ejpam-5351	98	15	roughly	roughly	ADV
ejpam-5351	98	16	speaking	speak	VERB
ejpam-5351	98	17	,	,	PUNCT
ejpam-5351	98	18	tells	tell	VERB
ejpam-5351	98	19	us	we	PRON
ejpam-5351	98	20	that	that	SCONJ
ejpam-5351	98	21	on	on	ADP
ejpam-5351	98	22	each	each	DET
ejpam-5351	98	23	surface	surface	NOUN
ejpam-5351	98	24	we	we	PRON
ejpam-5351	98	25	can	can	AUX
ejpam-5351	98	26	put	put	VERB
ejpam-5351	98	27	a	a	DET
ejpam-5351	98	28	geometry	geometry	NOUN
ejpam-5351	98	29	(	(	PUNCT
ejpam-5351	98	30	i.e.	i.e.	X
ejpam-5351	98	31	a	a	DET
ejpam-5351	98	32	way	way	NOUN
ejpam-5351	98	33	of	of	ADP
ejpam-5351	98	34	measuring	measure	VERB
ejpam-5351	98	35	distances	distance	NOUN
ejpam-5351	98	36	and	and	CCONJ
ejpam-5351	98	37	angles	angle	NOUN
ejpam-5351	98	38	)	)	PUNCT
ejpam-5351	98	39	that	that	SCONJ
ejpam-5351	98	40	,	,	PUNCT
ejpam-5351	98	41	locally	locally	ADV
ejpam-5351	98	42	,	,	PUNCT
ejpam-5351	98	43	is	be	AUX
ejpam-5351	98	44	like	like	ADP
ejpam-5351	98	45	one	one	NUM
ejpam-5351	98	46	of	of	ADP
ejpam-5351	98	47	the	the	DET
ejpam-5351	98	48	three	three	NUM
ejpam-5351	98	49	classical	classical	ADJ
ejpam-5351	98	50	geometries	geometry	NOUN
ejpam-5351	98	51	with	with	ADP
ejpam-5351	98	52	constant	constant	ADJ
ejpam-5351	98	53	curvature	curvature	NOUN
ejpam-5351	98	54	:	:	PUNCT
ejpam-5351	98	55	euclidean	euclidean	ADJ
ejpam-5351	98	56	geometry	geometry	NOUN
ejpam-5351	98	57	(	(	PUNCT
ejpam-5351	98	58	the	the	DET
ejpam-5351	98	59	plane	plane	NOUN
ejpam-5351	98	60	with	with	ADP
ejpam-5351	98	61	zero	zero	NUM
ejpam-5351	98	62	curvature	curvature	NOUN
ejpam-5351	98	63	)	)	PUNCT
ejpam-5351	98	64	,	,	PUNCT
ejpam-5351	98	65	non	non	ADJ
ejpam-5351	98	66	-	-	ADJ
ejpam-5351	98	67	euclidean	euclidean	ADJ
ejpam-5351	98	68	geometry	geometry	NOUN
ejpam-5351	98	69	called	call	VERB
ejpam-5351	98	70	lobachevsky	lobachevsky	PROPN
ejpam-5351	98	71	’s	’s	PART
ejpam-5351	98	72	hyperbolic	hyperbolic	ADJ
ejpam-5351	98	73	geometry	geometry	NOUN
ejpam-5351	98	74	(	(	PUNCT
ejpam-5351	98	75	the	the	DET
ejpam-5351	98	76	one	one	NOUN
ejpam-5351	98	77	where	where	SCONJ
ejpam-5351	98	78	several	several	ADJ
ejpam-5351	98	79	lines	line	NOUN
ejpam-5351	98	80	parallel	parallel	VERB
ejpam-5351	98	81	to	to	ADP
ejpam-5351	98	82	a	a	DET
ejpam-5351	98	83	given	give	VERB
ejpam-5351	98	84	line	line	NOUN
ejpam-5351	98	85	pass	pass	VERB
ejpam-5351	98	86	through	through	ADP
ejpam-5351	98	87	a	a	DET
ejpam-5351	98	88	point	point	NOUN
ejpam-5351	98	89	,	,	PUNCT
ejpam-5351	98	90	called	call	VERB
ejpam-5351	98	91	the	the	DET
ejpam-5351	98	92	plane	plane	NOUN
ejpam-5351	98	93	with	with	ADP
ejpam-5351	98	94	negative	negative	ADJ
ejpam-5351	98	95	curvature	curvature	NOUN
ejpam-5351	98	96	-1	-1	NOUN
ejpam-5351	98	97	)	)	PUNCT
ejpam-5351	98	98	,	,	PUNCT
ejpam-5351	98	99	and	and	CCONJ
ejpam-5351	98	100	that	that	PRON
ejpam-5351	98	101	of	of	ADP
ejpam-5351	98	102	the	the	DET
ejpam-5351	98	103	round	round	ADJ
ejpam-5351	98	104	sphere	sphere	NOUN
ejpam-5351	98	105	(	(	PUNCT
ejpam-5351	98	106	called	call	VERB
ejpam-5351	98	107	elliptic	elliptic	ADJ
ejpam-5351	98	108	geometry	geometry	NOUN
ejpam-5351	98	109	with	with	ADP
ejpam-5351	98	110	positive	positive	ADJ
ejpam-5351	98	111	curvature	curvature	NOUN
ejpam-5351	98	112	+1	+1	PROPN
ejpam-5351	98	113	)	)	PUNCT
ejpam-5351	98	114	.	.	PUNCT
ejpam-5351	99	1	the	the	DET
ejpam-5351	99	2	obvious	obvious	ADJ
ejpam-5351	99	3	question	question	NOUN
ejpam-5351	99	4	is	be	AUX
ejpam-5351	99	5	now	now	ADV
ejpam-5351	99	6	:	:	PUNCT
ejpam-5351	99	7	can	can	AUX
ejpam-5351	99	8	we	we	PRON
ejpam-5351	99	9	say	say	VERB
ejpam-5351	99	10	something	something	PRON
ejpam-5351	99	11	similar	similar	ADJ
ejpam-5351	99	12	in	in	ADP
ejpam-5351	99	13	dimension	dimension	NOUN
ejpam-5351	99	14	3	3	NUM
ejpam-5351	99	15	?	?	PUNCT
ejpam-5351	100	1	in	in	ADP
ejpam-5351	100	2	the	the	DET
ejpam-5351	100	3	1970s	1970	NOUN
ejpam-5351	100	4	the	the	DET
ejpam-5351	100	5	great	great	ADJ
ejpam-5351	100	6	american	american	ADJ
ejpam-5351	100	7	mathematician	mathematician	PROPN
ejpam-5351	100	8	william	william	PROPN
ejpam-5351	100	9	thurston	thurston	PROPN
ejpam-5351	101	1	[	[	X
ejpam-5351	101	2	9	9	NUM
ejpam-5351	101	3	]	]	PUNCT
ejpam-5351	101	4	conceived	conceive	VERB
ejpam-5351	101	5	a	a	DET
ejpam-5351	101	6	very	very	ADV
ejpam-5351	101	7	spectacular	spectacular	ADJ
ejpam-5351	101	8	program	program	NOUN
ejpam-5351	101	9	in	in	ADP
ejpam-5351	101	10	order	order	NOUN
ejpam-5351	101	11	to	to	PART
ejpam-5351	101	12	“	"	PUNCT
ejpam-5351	101	13	geometrize	geometrize	VERB
ejpam-5351	101	14	”	"	PUNCT
ejpam-5351	101	15	all	all	PRON
ejpam-5351	101	16	closed	close	VERB
ejpam-5351	101	17	3	3	NUM
ejpam-5351	101	18	-	-	PUNCT
ejpam-5351	101	19	dimensional	dimensional	ADJ
ejpam-5351	101	20	manifolds	manifold	NOUN
ejpam-5351	101	21	,	,	PUNCT
ejpam-5351	101	22	as	as	SCONJ
ejpam-5351	101	23	poincaré	poincaré	ADJ
ejpam-5351	101	24	did	do	VERB
ejpam-5351	101	25	in	in	ADP
ejpam-5351	101	26	dimension	dimension	NOUN
ejpam-5351	101	27	two	two	NUM
ejpam-5351	101	28	,	,	PUNCT
ejpam-5351	101	29	with	with	ADP
ejpam-5351	101	30	the	the	DET
ejpam-5351	101	31	difference	difference	NOUN
ejpam-5351	101	32	that	that	PRON
ejpam-5351	101	33	in	in	ADP
ejpam-5351	101	34	dimension	dimension	NOUN
ejpam-5351	101	35	three	three	NUM
ejpam-5351	101	36	the	the	DET
ejpam-5351	101	37	possible	possible	ADJ
ejpam-5351	101	38	geometries	geometry	NOUN
ejpam-5351	101	39	should	should	AUX
ejpam-5351	101	40	be	be	AUX
ejpam-5351	101	41	8	8	NUM
ejpam-5351	101	42	instead	instead	ADV
ejpam-5351	101	43	of	of	ADP
ejpam-5351	101	44	3	3	NUM
ejpam-5351	101	45	,	,	PUNCT
ejpam-5351	101	46	and	and	CCONJ
ejpam-5351	101	47	among	among	ADP
ejpam-5351	101	48	them	they	PRON
ejpam-5351	101	49	,	,	PUNCT
ejpam-5351	101	50	the	the	DET
ejpam-5351	101	51	most	most	ADV
ejpam-5351	101	52	important	important	ADJ
ejpam-5351	101	53	being	be	AUX
ejpam-5351	101	54	the	the	DET
ejpam-5351	101	55	hyperbolic	hyperbolic	ADJ
ejpam-5351	101	56	one	one	NOUN
ejpam-5351	101	57	.	.	PUNCT
ejpam-5351	102	1	4.1	4.1	NUM
ejpam-5351	102	2	.	.	PUNCT
ejpam-5351	102	3	curvature	curvature	VERB
ejpam-5351	102	4	in	in	ADP
ejpam-5351	102	5	order	order	NOUN
ejpam-5351	102	6	to	to	PART
ejpam-5351	102	7	provide	provide	VERB
ejpam-5351	102	8	a	a	DET
ejpam-5351	102	9	geometry	geometry	NOUN
ejpam-5351	102	10	to	to	ADP
ejpam-5351	102	11	a	a	DET
ejpam-5351	102	12	manifold	manifold	ADJ
ejpam-5351	102	13	,	,	PUNCT
ejpam-5351	102	14	a	a	DET
ejpam-5351	102	15	natural	natural	ADJ
ejpam-5351	102	16	procedure	procedure	NOUN
ejpam-5351	102	17	is	be	AUX
ejpam-5351	102	18	to	to	PART
ejpam-5351	102	19	specify	specify	VERB
ejpam-5351	102	20	,	,	PUNCT
ejpam-5351	102	21	at	at	ADP
ejpam-5351	102	22	each	each	DET
ejpam-5351	102	23	point	point	NOUN
ejpam-5351	102	24	of	of	ADP
ejpam-5351	102	25	the	the	DET
ejpam-5351	102	26	manifold	manifold	NOUN
ejpam-5351	102	27	,	,	PUNCT
ejpam-5351	102	28	how	how	SCONJ
ejpam-5351	102	29	the	the	DET
ejpam-5351	102	30	distance	distance	NOUN
ejpam-5351	102	31	between	between	ADP
ejpam-5351	102	32	two	two	NUM
ejpam-5351	102	33	very	very	ADV
ejpam-5351	102	34	close	close	ADJ
ejpam-5351	102	35	points	point	NOUN
ejpam-5351	102	36	is	be	AUX
ejpam-5351	102	37	expressed	express	VERB
ejpam-5351	102	38	.	.	PUNCT
ejpam-5351	103	1	in	in	ADP
ejpam-5351	103	2	a	a	DET
ejpam-5351	103	3	more	more	ADV
ejpam-5351	103	4	mathematical	mathematical	ADJ
ejpam-5351	103	5	way	way	NOUN
ejpam-5351	103	6	,	,	PUNCT
ejpam-5351	103	7	one	one	PRON
ejpam-5351	103	8	must	must	AUX
ejpam-5351	103	9	specify	specify	VERB
ejpam-5351	103	10	,	,	PUNCT
ejpam-5351	103	11	at	at	ADP
ejpam-5351	103	12	each	each	DET
ejpam-5351	103	13	point	point	NOUN
ejpam-5351	103	14	,	,	PUNCT
ejpam-5351	103	15	the	the	DET
ejpam-5351	103	16	“	"	PUNCT
ejpam-5351	103	17	metric	metric	ADJ
ejpam-5351	103	18	tensor	tensor	NOUN
ejpam-5351	103	19	”	"	PUNCT
ejpam-5351	103	20	.	.	PUNCT
ejpam-5351	104	1	introduced	introduce	VERB
ejpam-5351	104	2	by	by	ADP
ejpam-5351	104	3	the	the	DET
ejpam-5351	104	4	german	german	ADJ
ejpam-5351	104	5	mathematician	mathematician	ADJ
ejpam-5351	104	6	bernhard	bernhard	PROPN
ejpam-5351	104	7	riemann	riemann	PROPN
ejpam-5351	104	8	in	in	ADP
ejpam-5351	104	9	the	the	DET
ejpam-5351	104	10	19th	19th	ADJ
ejpam-5351	104	11	century	century	NOUN
ejpam-5351	104	12	,	,	PUNCT
ejpam-5351	104	13	this	this	DET
ejpam-5351	104	14	tensor	tensor	NOUN
ejpam-5351	104	15	(	(	PUNCT
ejpam-5351	104	16	a	a	DET
ejpam-5351	104	17	generalization	generalization	NOUN
ejpam-5351	104	18	of	of	ADP
ejpam-5351	104	19	the	the	DET
ejpam-5351	104	20	notion	notion	NOUN
ejpam-5351	104	21	of	of	ADP
ejpam-5351	104	22	vector	vector	NOUN
ejpam-5351	104	23	)	)	PUNCT
ejpam-5351	104	24	is	be	AUX
ejpam-5351	104	25	used	use	VERB
ejpam-5351	104	26	to	to	PART
ejpam-5351	104	27	determine	determine	VERB
ejpam-5351	104	28	lengths	length	NOUN
ejpam-5351	104	29	,	,	PUNCT
ejpam-5351	104	30	angles	angle	NOUN
ejpam-5351	104	31	,	,	PUNCT
ejpam-5351	104	32	areas	area	NOUN
ejpam-5351	104	33	,	,	PUNCT
ejpam-5351	104	34	volumes	volume	NOUN
ejpam-5351	104	35	,	,	PUNCT
ejpam-5351	104	36	etc	etc	X
ejpam-5351	104	37	.	.	X
ejpam-5351	104	38	on	on	ADP
ejpam-5351	104	39	the	the	DET
ejpam-5351	104	40	given	give	VERB
ejpam-5351	104	41	manifold	manifold	NOUN
ejpam-5351	104	42	.	.	PUNCT
ejpam-5351	105	1	for	for	ADP
ejpam-5351	105	2	a	a	DET
ejpam-5351	105	3	manifold	manifold	NOUN
ejpam-5351	105	4	of	of	ADP
ejpam-5351	105	5	dimension	dimension	NOUN
ejpam-5351	105	6	n	n	CCONJ
ejpam-5351	105	7	,	,	PUNCT
ejpam-5351	105	8	it	it	PRON
ejpam-5351	105	9	is	be	AUX
ejpam-5351	105	10	a	a	DET
ejpam-5351	105	11	table	table	NOUN
ejpam-5351	105	12	of	of	ADP
ejpam-5351	105	13	n2	n2	ADJ
ejpam-5351	105	14	numbers	number	NOUN
ejpam-5351	105	15	(	(	PUNCT
ejpam-5351	105	16	a	a	DET
ejpam-5351	105	17	matrix	matrix	NOUN
ejpam-5351	105	18	n×	n×	CCONJ
ejpam-5351	105	19	n	n	CCONJ
ejpam-5351	105	20	)	)	PUNCT
ejpam-5351	105	21	,	,	PUNCT
ejpam-5351	105	22	which	which	PRON
ejpam-5351	105	23	is	be	AUX
ejpam-5351	105	24	used	use	VERB
ejpam-5351	105	25	to	to	PART
ejpam-5351	105	26	calculate	calculate	VERB
ejpam-5351	105	27	the	the	DET
ejpam-5351	105	28	curvature	curvature	NOUN
ejpam-5351	105	29	of	of	ADP
ejpam-5351	105	30	the	the	DET
ejpam-5351	105	31	manifold	manifold	NOUN
ejpam-5351	105	32	.	.	PUNCT
ejpam-5351	106	1	in	in	ADP
ejpam-5351	106	2	dimension	dimension	NOUN
ejpam-5351	106	3	2	2	NUM
ejpam-5351	106	4	,	,	PUNCT
ejpam-5351	106	5	the	the	DET
ejpam-5351	106	6	curvature	curvature	NOUN
ejpam-5351	106	7	of	of	ADP
ejpam-5351	106	8	a	a	DET
ejpam-5351	106	9	surface	surface	NOUN
ejpam-5351	106	10	is	be	AUX
ejpam-5351	106	11	an	an	DET
ejpam-5351	106	12	intuitive	intuitive	ADJ
ejpam-5351	106	13	notion	notion	NOUN
ejpam-5351	106	14	,	,	PUNCT
ejpam-5351	106	15	made	make	VERB
ejpam-5351	106	16	rigorous	rigorous	ADJ
ejpam-5351	106	17	by	by	ADP
ejpam-5351	106	18	the	the	DET
ejpam-5351	106	19	german	german	ADJ
ejpam-5351	106	20	mathematician	mathematician	NOUN
ejpam-5351	106	21	friedrich	friedrich	PROPN
ejpam-5351	106	22	gauss	gauss	PROPN
ejpam-5351	106	23	around	around	ADP
ejpam-5351	106	24	1830	1830	NUM
ejpam-5351	106	25	.	.	PUNCT
ejpam-5351	107	1	he	he	PRON
ejpam-5351	107	2	defined	define	VERB
ejpam-5351	107	3	the	the	DET
ejpam-5351	107	4	curvature	curvature	NOUN
ejpam-5351	107	5	r	r	NOUN
ejpam-5351	107	6	as	as	ADP
ejpam-5351	107	7	a	a	DET
ejpam-5351	107	8	number	number	NOUN
ejpam-5351	107	9	obtained	obtain	VERB
ejpam-5351	107	10	by	by	ADP
ejpam-5351	107	11	an	an	DET
ejpam-5351	107	12	expression	expression	NOUN
ejpam-5351	107	13	r(p	r(p	NOUN
ejpam-5351	107	14	)	)	PUNCT
ejpam-5351	107	15	of	of	ADP
ejpam-5351	107	16	the	the	DET
ejpam-5351	107	17	curvature	curvature	NOUN
ejpam-5351	107	18	of	of	ADP
ejpam-5351	107	19	a	a	DET
ejpam-5351	107	20	surface	surface	NOUN
ejpam-5351	107	21	at	at	ADP
ejpam-5351	107	22	its	its	PRON
ejpam-5351	107	23	point	point	NOUN
ejpam-5351	107	24	p.	p.	NOUN
ejpam-5351	107	25	and	and	CCONJ
ejpam-5351	107	26	this	this	DET
ejpam-5351	107	27	number	number	NOUN
ejpam-5351	107	28	defines	define	NOUN
ejpam-5351	107	29	and	and	CCONJ
ejpam-5351	107	30	measures	measure	NOUN
ejpam-5351	107	31	the	the	DET
ejpam-5351	107	32	“	"	PUNCT
ejpam-5351	107	33	gap	gap	NOUN
ejpam-5351	107	34	”	"	PUNCT
ejpam-5351	107	35	between	between	ADP
ejpam-5351	107	36	the	the	DET
ejpam-5351	107	37	geometry	geometry	NOUN
ejpam-5351	107	38	of	of	ADP
ejpam-5351	107	39	the	the	DET
ejpam-5351	107	40	surface	surface	NOUN
ejpam-5351	107	41	near	near	ADP
ejpam-5351	107	42	the	the	DET
ejpam-5351	107	43	point	point	NOUN
ejpam-5351	107	44	p	p	NOUN
ejpam-5351	107	45	and	and	CCONJ
ejpam-5351	107	46	the	the	DET
ejpam-5351	107	47	euclidean	euclidean	ADJ
ejpam-5351	107	48	classical	classical	ADJ
ejpam-5351	107	49	geometry	geometry	NOUN
ejpam-5351	107	50	(	(	PUNCT
ejpam-5351	107	51	the	the	DET
ejpam-5351	107	52	geometry	geometry	NOUN
ejpam-5351	107	53	of	of	ADP
ejpam-5351	107	54	the	the	DET
ejpam-5351	107	55	standard	standard	ADJ
ejpam-5351	107	56	plane	plane	NOUN
ejpam-5351	107	57	)	)	PUNCT
ejpam-5351	107	58	.	.	PUNCT
ejpam-5351	108	1	for	for	ADP
ejpam-5351	108	2	instance	instance	NOUN
ejpam-5351	108	3	,	,	PUNCT
ejpam-5351	108	4	the	the	DET
ejpam-5351	108	5	curvature	curvature	NOUN
ejpam-5351	108	6	of	of	ADP
ejpam-5351	108	7	a	a	DET
ejpam-5351	108	8	two	two	NUM
ejpam-5351	108	9	-	-	PUNCT
ejpam-5351	108	10	dimensional	dimensional	ADJ
ejpam-5351	108	11	sphere	sphere	NOUN
ejpam-5351	108	12	is	be	AUX
ejpam-5351	108	13	positive	positive	ADJ
ejpam-5351	108	14	,	,	PUNCT
ejpam-5351	108	15	that	that	PRON
ejpam-5351	108	16	of	of	ADP
ejpam-5351	108	17	a	a	DET
ejpam-5351	108	18	plane	plane	NOUN
ejpam-5351	108	19	(	(	PUNCT
ejpam-5351	108	20	or	or	CCONJ
ejpam-5351	108	21	a	a	DET
ejpam-5351	108	22	cylinder	cylinder	NOUN
ejpam-5351	108	23	or	or	CCONJ
ejpam-5351	108	24	a	a	DET
ejpam-5351	108	25	cone	cone	NOUN
ejpam-5351	108	26	)	)	PUNCT
ejpam-5351	108	27	is	be	AUX
ejpam-5351	108	28	zero	zero	NUM
ejpam-5351	108	29	,	,	PUNCT
ejpam-5351	108	30	while	while	SCONJ
ejpam-5351	108	31	that	that	PRON
ejpam-5351	108	32	of	of	ADP
ejpam-5351	108	33	the	the	DET
ejpam-5351	108	34	surface	surface	NOUN
ejpam-5351	108	35	of	of	ADP
ejpam-5351	108	36	a	a	DET
ejpam-5351	108	37	saddle	saddle	NOUN
ejpam-5351	108	38	has	have	VERB
ejpam-5351	108	39	negative	negative	ADJ
ejpam-5351	108	40	curvature	curvature	NOUN
ejpam-5351	108	41	.	.	PUNCT
ejpam-5351	109	1	if	if	SCONJ
ejpam-5351	109	2	the	the	DET
ejpam-5351	109	3	curvature	curvature	NOUN
ejpam-5351	109	4	is	be	AUX
ejpam-5351	109	5	independent	independent	ADJ
ejpam-5351	109	6	on	on	ADP
ejpam-5351	109	7	the	the	DET
ejpam-5351	109	8	point	point	NOUN
ejpam-5351	109	9	p	p	NOUN
ejpam-5351	109	10	of	of	ADP
ejpam-5351	109	11	the	the	DET
ejpam-5351	109	12	surface	surface	NOUN
ejpam-5351	109	13	,	,	PUNCT
ejpam-5351	109	14	as	as	ADP
ejpam-5351	109	15	in	in	ADP
ejpam-5351	109	16	these	these	DET
ejpam-5351	109	17	examples	example	NOUN
ejpam-5351	109	18	,	,	PUNCT
ejpam-5351	109	19	we	we	PRON
ejpam-5351	109	20	speak	speak	VERB
ejpam-5351	109	21	of	of	ADP
ejpam-5351	109	22	elliptic	elliptic	ADJ
ejpam-5351	109	23	geometry	geometry	NOUN
ejpam-5351	109	24	,	,	PUNCT
ejpam-5351	109	25	euclidean	euclidean	ADJ
ejpam-5351	109	26	geometry	geometry	NOUN
ejpam-5351	109	27	,	,	PUNCT
ejpam-5351	109	28	and	and	CCONJ
ejpam-5351	109	29	hyperbolic	hyperbolic	ADJ
ejpam-5351	109	30	geometry	geometry	NOUN
ejpam-5351	109	31	.	.	PUNCT
ejpam-5351	110	1	notice	notice	VERB
ejpam-5351	110	2	that	that	SCONJ
ejpam-5351	110	3	,	,	PUNCT
ejpam-5351	110	4	these	these	DET
ejpam-5351	110	5	three	three	NUM
ejpam-5351	110	6	different	different	ADJ
ejpam-5351	110	7	geometries	geometry	NOUN
ejpam-5351	110	8	differ	differ	VERB
ejpam-5351	110	9	in	in	ADP
ejpam-5351	110	10	the	the	DET
ejpam-5351	110	11	shape	shape	NOUN
ejpam-5351	110	12	of	of	ADP
ejpam-5351	110	13	their	their	PRON
ejpam-5351	110	14	triangles	triangle	NOUN
ejpam-5351	110	15	(	(	PUNCT
ejpam-5351	110	16	in	in	ADP
ejpam-5351	110	17	particular	particular	ADJ
ejpam-5351	110	18	in	in	ADP
ejpam-5351	110	19	the	the	DET
ejpam-5351	110	20	sum	sum	NOUN
ejpam-5351	110	21	of	of	ADP
ejpam-5351	110	22	the	the	DET
ejpam-5351	110	23	inner	inner	ADJ
ejpam-5351	110	24	angles	angle	NOUN
ejpam-5351	110	25	):	):	PUNCT
ejpam-5351	110	26	triangles	triangle	NOUN
ejpam-5351	110	27	in	in	ADP
ejpam-5351	110	28	the	the	DET
ejpam-5351	110	29	surface	surface	NOUN
ejpam-5351	110	30	of	of	ADP
ejpam-5351	110	31	the	the	DET
ejpam-5351	110	32	sphere	sphere	NOUN
ejpam-5351	110	33	are	be	AUX
ejpam-5351	110	34	fat	fat	ADJ
ejpam-5351	110	35	,	,	PUNCT
ejpam-5351	110	36	those	those	PRON
ejpam-5351	110	37	in	in	ADP
ejpam-5351	110	38	the	the	DET
ejpam-5351	110	39	plane	plane	NOUN
ejpam-5351	110	40	are	be	AUX
ejpam-5351	110	41	standard	standard	ADJ
ejpam-5351	110	42	,	,	PUNCT
ejpam-5351	110	43	while	while	SCONJ
ejpam-5351	110	44	in	in	ADP
ejpam-5351	110	45	the	the	DET
ejpam-5351	110	46	hyperbolic	hyperbolic	ADJ
ejpam-5351	110	47	case	case	NOUN
ejpam-5351	110	48	they	they	PRON
ejpam-5351	110	49	are	be	AUX
ejpam-5351	110	50	slim	slim	ADJ
ejpam-5351	110	51	.	.	PUNCT
ejpam-5351	111	1	around	around	ADP
ejpam-5351	111	2	1850	1850	NUM
ejpam-5351	111	3	,	,	PUNCT
ejpam-5351	111	4	riemann	riemann	PROPN
ejpam-5351	111	5	generalized	generalize	VERB
ejpam-5351	111	6	the	the	DET
ejpam-5351	111	7	notion	notion	NOUN
ejpam-5351	111	8	of	of	ADP
ejpam-5351	111	9	curvature	curvature	NOUN
ejpam-5351	111	10	to	to	ADP
ejpam-5351	111	11	manifolds	manifold	NOUN
ejpam-5351	111	12	of	of	ADP
ejpam-5351	111	13	any	any	DET
ejpam-5351	111	14	dimension	dimension	NOUN
ejpam-5351	111	15	n.	n.	NOUN
ejpam-5351	112	1	but	but	CCONJ
ejpam-5351	112	2	when	when	SCONJ
ejpam-5351	112	3	n	n	X
ejpam-5351	112	4	is	be	AUX
ejpam-5351	112	5	greater	great	ADJ
ejpam-5351	112	6	than	than	ADP
ejpam-5351	112	7	or	or	CCONJ
ejpam-5351	112	8	equal	equal	ADJ
ejpam-5351	112	9	to	to	ADP
ejpam-5351	112	10	3	3	NUM
ejpam-5351	112	11	,	,	PUNCT
ejpam-5351	112	12	it	it	PRON
ejpam-5351	112	13	is	be	AUX
ejpam-5351	112	14	no	no	ADV
ejpam-5351	112	15	longer	long	ADV
ejpam-5351	112	16	just	just	ADV
ejpam-5351	112	17	a	a	DET
ejpam-5351	112	18	number	number	NOUN
ejpam-5351	112	19	,	,	PUNCT
ejpam-5351	112	20	as	as	ADP
ejpam-5351	112	21	in	in	ADP
ejpam-5351	112	22	the	the	DET
ejpam-5351	112	23	case	case	NOUN
ejpam-5351	112	24	of	of	ADP
ejpam-5351	112	25	gauss	gauss	NOUN
ejpam-5351	112	26	,	,	PUNCT
ejpam-5351	112	27	but	but	CCONJ
ejpam-5351	112	28	a	a	DET
ejpam-5351	112	29	tensor	tensor	NOUN
ejpam-5351	112	30	.	.	PUNCT
ejpam-5351	113	1	let	let	VERB
ejpam-5351	113	2	us	we	PRON
ejpam-5351	113	3	suppose	suppose	VERB
ejpam-5351	113	4	that	that	SCONJ
ejpam-5351	113	5	in	in	ADP
ejpam-5351	113	6	the	the	DET
ejpam-5351	113	7	neighborhood	neighborhood	NOUN
ejpam-5351	113	8	of	of	ADP
ejpam-5351	113	9	a	a	DET
ejpam-5351	113	10	point	point	NOUN
ejpam-5351	113	11	p	p	NOUN
ejpam-5351	113	12	of	of	ADP
ejpam-5351	113	13	a	a	DET
ejpam-5351	113	14	manifold	manifold	ADJ
ejpam-5351	113	15	v	v	NOUN
ejpam-5351	113	16	n	n	CCONJ
ejpam-5351	113	17	,	,	PUNCT
ejpam-5351	113	18	we	we	PRON
ejpam-5351	113	19	have	have	AUX
ejpam-5351	113	20	chosen	choose	VERB
ejpam-5351	113	21	a	a	DET
ejpam-5351	113	22	local	local	ADJ
ejpam-5351	113	23	system	system	NOUN
ejpam-5351	113	24	of	of	ADP
ejpam-5351	113	25	coordinates	coordinate	NOUN
ejpam-5351	113	26	x1	x1	PROPN
ejpam-5351	113	27	,	,	PUNCT
ejpam-5351	113	28	x2	x2	PROPN
ejpam-5351	113	29	,	,	PUNCT
ejpam-5351	113	30	·	·	PUNCT
ejpam-5351	113	31	·	·	PUNCT
ejpam-5351	114	1	·	·	PUNCT
ejpam-5351	114	2	,	,	PUNCT
ejpam-5351	114	3	xn	xn	PROPN
ejpam-5351	114	4	.	.	PUNCT
ejpam-5351	115	1	the	the	DET
ejpam-5351	115	2	riemann	riemann	PROPN
ejpam-5351	115	3	curvature	curvature	NOUN
ejpam-5351	115	4	at	at	ADP
ejpam-5351	115	5	a	a	DET
ejpam-5351	115	6	point	point	NOUN
ejpam-5351	115	7	p	p	NOUN
ejpam-5351	115	8	of	of	ADP
ejpam-5351	115	9	v	v	NUM
ejpam-5351	115	10	n	n	VERB
ejpam-5351	115	11	is	be	AUX
ejpam-5351	115	12	expressed	express	VERB
ejpam-5351	115	13	as	as	ADP
ejpam-5351	115	14	a	a	DET
ejpam-5351	115	15	table	table	NOUN
ejpam-5351	115	16	of	of	ADP
ejpam-5351	115	17	n4	n4	PROPN
ejpam-5351	115	18	numbers	number	NOUN
ejpam-5351	115	19	,	,	PUNCT
ejpam-5351	115	20	each	each	PRON
ejpam-5351	115	21	directly	directly	ADV
ejpam-5351	115	22	dependent	dependent	ADJ
ejpam-5351	115	23	on	on	ADP
ejpam-5351	115	24	the	the	DET
ejpam-5351	115	25	(	(	PUNCT
ejpam-5351	115	26	riemannian	riemannian	ADJ
ejpam-5351	115	27	)	)	PUNCT
ejpam-5351	115	28	metric	metric	NOUN
ejpam-5351	115	29	defined	define	VERB
ejpam-5351	115	30	on	on	ADP
ejpam-5351	115	31	the	the	DET
ejpam-5351	115	32	manifold	manifold	ADJ
ejpam-5351	115	33	itself	itself	PRON
ejpam-5351	115	34	,	,	PUNCT
ejpam-5351	115	35	and	and	CCONJ
ejpam-5351	115	36	its	its	PRON
ejpam-5351	115	37	derivatives	derivative	NOUN
ejpam-5351	115	38	.	.	PUNCT
ejpam-5351	116	1	d.	d.	PROPN
ejpam-5351	116	2	e.	e.	PROPN
ejpam-5351	116	3	otera	otera	PROPN
ejpam-5351	116	4	/	/	SYM
ejpam-5351	116	5	eur	eur	PROPN
ejpam-5351	116	6	.	.	PUNCT
ejpam-5351	117	1	j.	j.	PROPN
ejpam-5351	117	2	pure	pure	PROPN
ejpam-5351	117	3	appl	appl	PROPN
ejpam-5351	117	4	.	.	PROPN
ejpam-5351	117	5	math	math	PROPN
ejpam-5351	117	6	,	,	PUNCT
ejpam-5351	117	7	17	17	NUM
ejpam-5351	117	8	(	(	PUNCT
ejpam-5351	117	9	3	3	NUM
ejpam-5351	117	10	)	)	PUNCT
ejpam-5351	117	11	(	(	PUNCT
ejpam-5351	117	12	2024	2024	NUM
ejpam-5351	117	13	)	)	PUNCT
ejpam-5351	117	14	,	,	PUNCT
ejpam-5351	117	15	2361	2361	NUM
ejpam-5351	117	16	-	-	SYM
ejpam-5351	117	17	2369	2369	NUM
ejpam-5351	117	18	2367	2367	NUM
ejpam-5351	117	19	note	note	NOUN
ejpam-5351	117	20	that	that	SCONJ
ejpam-5351	117	21	riemann	riemann	PROPN
ejpam-5351	117	22	’s	’s	PART
ejpam-5351	117	23	ideas	idea	NOUN
ejpam-5351	117	24	have	have	AUX
ejpam-5351	117	25	long	long	ADV
ejpam-5351	117	26	seemed	seem	VERB
ejpam-5351	117	27	far	far	ADV
ejpam-5351	117	28	too	too	ADV
ejpam-5351	117	29	abstract	abstract	ADJ
ejpam-5351	117	30	.	.	PUNCT
ejpam-5351	118	1	yet	yet	ADV
ejpam-5351	118	2	,	,	PUNCT
ejpam-5351	118	3	it	it	PRON
ejpam-5351	118	4	is	be	AUX
ejpam-5351	118	5	precisely	precisely	ADV
ejpam-5351	118	6	on	on	ADP
ejpam-5351	118	7	these	these	DET
ejpam-5351	118	8	notions	notion	NOUN
ejpam-5351	118	9	that	that	SCONJ
ejpam-5351	118	10	the	the	DET
ejpam-5351	118	11	general	general	ADJ
ejpam-5351	118	12	relativity	relativity	NOUN
ejpam-5351	118	13	,	,	PUNCT
ejpam-5351	118	14	einstein	einstein	PROPN
ejpam-5351	118	15	’s	’s	PART
ejpam-5351	118	16	great	great	ADJ
ejpam-5351	118	17	masterpiece	masterpiece	NOUN
ejpam-5351	118	18	,	,	PUNCT
ejpam-5351	118	19	is	be	AUX
ejpam-5351	118	20	based	base	VERB
ejpam-5351	118	21	.	.	PUNCT
ejpam-5351	119	1	4.2	4.2	NUM
ejpam-5351	119	2	.	.	PUNCT
ejpam-5351	120	1	the	the	DET
ejpam-5351	120	2	geometrization	geometrization	NOUN
ejpam-5351	120	3	conjecture	conjecture	VERB
ejpam-5351	120	4	more	more	ADJ
ejpam-5351	120	5	than	than	ADP
ejpam-5351	120	6	a	a	DET
ejpam-5351	120	7	century	century	NOUN
ejpam-5351	120	8	after	after	ADP
ejpam-5351	120	9	riemann	riemann	PROPN
ejpam-5351	120	10	’s	’s	PART
ejpam-5351	120	11	innovations	innovation	NOUN
ejpam-5351	120	12	,	,	PUNCT
ejpam-5351	120	13	the	the	DET
ejpam-5351	120	14	geometer	geometer	NOUN
ejpam-5351	120	15	w.	w.	PROPN
ejpam-5351	120	16	thurston	thurston	PROPN
ejpam-5351	120	17	proposed	propose	VERB
ejpam-5351	120	18	a	a	DET
ejpam-5351	120	19	new	new	ADJ
ejpam-5351	120	20	vast	vast	ADJ
ejpam-5351	120	21	classification	classification	NOUN
ejpam-5351	120	22	project	project	NOUN
ejpam-5351	120	23	in	in	ADP
ejpam-5351	120	24	dimension	dimension	NOUN
ejpam-5351	120	25	3	3	NUM
ejpam-5351	120	26	,	,	PUNCT
ejpam-5351	120	27	started	start	VERB
ejpam-5351	120	28	in	in	ADP
ejpam-5351	120	29	the	the	DET
ejpam-5351	120	30	1970s	1970	NOUN
ejpam-5351	120	31	,	,	PUNCT
ejpam-5351	120	32	in	in	ADP
ejpam-5351	120	33	order	order	NOUN
ejpam-5351	120	34	to	to	PART
ejpam-5351	120	35	prove	prove	VERB
ejpam-5351	120	36	the	the	DET
ejpam-5351	120	37	poincaré	poincaré	ADJ
ejpam-5351	120	38	conjecture	conjecture	NOUN
ejpam-5351	120	39	and	and	CCONJ
ejpam-5351	120	40	to	to	PART
ejpam-5351	120	41	deeply	deeply	ADV
ejpam-5351	120	42	understand	understand	VERB
ejpam-5351	120	43	the	the	DET
ejpam-5351	120	44	set	set	NOUN
ejpam-5351	120	45	of	of	ADP
ejpam-5351	120	46	closed	closed	ADJ
ejpam-5351	120	47	3	3	NUM
ejpam-5351	120	48	-	-	PUNCT
ejpam-5351	120	49	manifolds	manifold	NOUN
ejpam-5351	120	50	.	.	PUNCT
ejpam-5351	121	1	thurston	thurston	PROPN
ejpam-5351	121	2	started	start	VERB
ejpam-5351	121	3	highlighting	highlight	VERB
ejpam-5351	121	4	,	,	PUNCT
ejpam-5351	121	5	in	in	ADP
ejpam-5351	121	6	dimension	dimension	NOUN
ejpam-5351	121	7	3	3	NUM
ejpam-5351	121	8	,	,	PUNCT
ejpam-5351	121	9	eight	eight	NUM
ejpam-5351	121	10	geometries	geometry	NOUN
ejpam-5351	121	11	which	which	PRON
ejpam-5351	121	12	are	be	AUX
ejpam-5351	121	13	particularly	particularly	ADV
ejpam-5351	121	14	symmetric	symmetric	ADJ
ejpam-5351	121	15	,	,	PUNCT
ejpam-5351	121	16	three	three	NUM
ejpam-5351	121	17	of	of	ADP
ejpam-5351	121	18	which	which	PRON
ejpam-5351	121	19	are	be	AUX
ejpam-5351	121	20	those	those	PRON
ejpam-5351	121	21	already	already	ADV
ejpam-5351	121	22	defined	define	VERB
ejpam-5351	121	23	in	in	ADP
ejpam-5351	121	24	the	the	DET
ejpam-5351	121	25	case	case	NOUN
ejpam-5351	121	26	of	of	ADP
ejpam-5351	121	27	surfaces	surface	NOUN
ejpam-5351	121	28	.	.	PUNCT
ejpam-5351	122	1	he	he	PRON
ejpam-5351	122	2	therefore	therefore	ADV
ejpam-5351	122	3	devised	devise	VERB
ejpam-5351	122	4	the	the	DET
ejpam-5351	122	5	so	so	ADV
ejpam-5351	122	6	-	-	PUNCT
ejpam-5351	122	7	called	call	VERB
ejpam-5351	122	8	geometrization	geometrization	NOUN
ejpam-5351	122	9	conjecture	conjecture	NOUN
ejpam-5351	122	10	,	,	PUNCT
ejpam-5351	122	11	according	accord	VERB
ejpam-5351	122	12	to	to	ADP
ejpam-5351	122	13	which	which	PRON
ejpam-5351	122	14	any	any	DET
ejpam-5351	122	15	closed	closed	ADJ
ejpam-5351	122	16	manifold	manifold	NOUN
ejpam-5351	122	17	of	of	ADP
ejpam-5351	122	18	dimension	dimension	NOUN
ejpam-5351	122	19	3	3	NUM
ejpam-5351	122	20	can	can	AUX
ejpam-5351	122	21	be	be	AUX
ejpam-5351	122	22	broken	break	VERB
ejpam-5351	122	23	,	,	PUNCT
ejpam-5351	122	24	in	in	ADP
ejpam-5351	122	25	a	a	DET
ejpam-5351	122	26	unique	unique	ADJ
ejpam-5351	122	27	way	way	NOUN
ejpam-5351	122	28	,	,	PUNCT
ejpam-5351	122	29	into	into	ADP
ejpam-5351	122	30	a	a	DET
ejpam-5351	122	31	finite	finite	ADJ
ejpam-5351	122	32	number	number	NOUN
ejpam-5351	122	33	of	of	ADP
ejpam-5351	122	34	pieces	piece	NOUN
ejpam-5351	122	35	,	,	PUNCT
ejpam-5351	122	36	each	each	PRON
ejpam-5351	122	37	of	of	ADP
ejpam-5351	122	38	which	which	PRON
ejpam-5351	122	39	supports	support	VERB
ejpam-5351	122	40	one	one	NUM
ejpam-5351	122	41	of	of	ADP
ejpam-5351	122	42	the	the	DET
ejpam-5351	122	43	8	8	NUM
ejpam-5351	122	44	geometries	geometry	NOUN
ejpam-5351	122	45	.	.	PUNCT
ejpam-5351	123	1	it	it	PRON
ejpam-5351	123	2	is	be	AUX
ejpam-5351	123	3	thus	thus	ADV
ejpam-5351	123	4	a	a	DET
ejpam-5351	123	5	generalization	generalization	NOUN
ejpam-5351	123	6	,	,	PUNCT
ejpam-5351	123	7	in	in	ADP
ejpam-5351	123	8	dimension	dimension	NOUN
ejpam-5351	123	9	3	3	NUM
ejpam-5351	123	10	,	,	PUNCT
ejpam-5351	123	11	of	of	ADP
ejpam-5351	123	12	poincaré	poincaré	ADJ
ejpam-5351	123	13	’s	’s	PART
ejpam-5351	123	14	uniformization	uniformization	NOUN
ejpam-5351	123	15	theorem	theorem	NOUN
ejpam-5351	123	16	for	for	ADP
ejpam-5351	123	17	surfaces	surface	NOUN
ejpam-5351	123	18	mentioned	mention	VERB
ejpam-5351	123	19	above	above	ADV
ejpam-5351	123	20	.	.	PUNCT
ejpam-5351	124	1	(	(	PUNCT
ejpam-5351	124	2	for	for	ADP
ejpam-5351	124	3	his	his	PRON
ejpam-5351	124	4	work	work	NOUN
ejpam-5351	124	5	in	in	ADP
ejpam-5351	124	6	the	the	DET
ejpam-5351	124	7	field	field	NOUN
ejpam-5351	124	8	of	of	ADP
ejpam-5351	124	9	topology	topology	NOUN
ejpam-5351	124	10	and	and	CCONJ
ejpam-5351	124	11	geometry	geometry	NOUN
ejpam-5351	124	12	in	in	ADP
ejpam-5351	124	13	dimension	dimension	NOUN
ejpam-5351	124	14	3	3	NUM
ejpam-5351	124	15	,	,	PUNCT
ejpam-5351	124	16	thurston	thurston	PROPN
ejpam-5351	124	17	also	also	ADV
ejpam-5351	124	18	received	receive	VERB
ejpam-5351	124	19	the	the	DET
ejpam-5351	124	20	fields	field	NOUN
ejpam-5351	124	21	medal	medal	NOUN
ejpam-5351	124	22	)	)	PUNCT
ejpam-5351	124	23	.	.	PUNCT
ejpam-5351	125	1	now	now	ADV
ejpam-5351	125	2	,	,	PUNCT
ejpam-5351	125	3	the	the	DET
ejpam-5351	125	4	geometrization	geometrization	NOUN
ejpam-5351	125	5	conjecture	conjecture	NOUN
ejpam-5351	125	6	is	be	AUX
ejpam-5351	125	7	a	a	DET
ejpam-5351	125	8	far	far	ADV
ejpam-5351	125	9	more	more	ADV
ejpam-5351	125	10	general	general	ADJ
ejpam-5351	125	11	result	result	NOUN
ejpam-5351	125	12	than	than	ADP
ejpam-5351	125	13	poincaré	poincaré	ADJ
ejpam-5351	125	14	conjecture	conjecture	NOUN
ejpam-5351	125	15	.	.	PUNCT
ejpam-5351	126	1	in	in	ADP
ejpam-5351	126	2	fact	fact	NOUN
ejpam-5351	126	3	,	,	PUNCT
ejpam-5351	126	4	thurston	thurston	PROPN
ejpam-5351	126	5	’s	’s	PART
ejpam-5351	126	6	conjecture	conjecture	NOUN
ejpam-5351	126	7	states	state	NOUN
ejpam-5351	126	8	,	,	PUNCT
ejpam-5351	126	9	among	among	ADP
ejpam-5351	126	10	other	other	ADJ
ejpam-5351	126	11	things	thing	NOUN
ejpam-5351	126	12	,	,	PUNCT
ejpam-5351	126	13	that	that	SCONJ
ejpam-5351	126	14	among	among	ADP
ejpam-5351	126	15	the	the	DET
ejpam-5351	126	16	8	8	NUM
ejpam-5351	126	17	special	special	ADJ
ejpam-5351	126	18	geometries	geometry	NOUN
ejpam-5351	126	19	,	,	PUNCT
ejpam-5351	126	20	the	the	DET
ejpam-5351	126	21	only	only	ADJ
ejpam-5351	126	22	one	one	NUM
ejpam-5351	126	23	that	that	PRON
ejpam-5351	126	24	a	a	DET
ejpam-5351	126	25	closed	closed	ADJ
ejpam-5351	126	26	and	and	CCONJ
ejpam-5351	126	27	simply	simply	ADV
ejpam-5351	126	28	connected	connect	VERB
ejpam-5351	126	29	3	3	NUM
ejpam-5351	126	30	-	-	NUM
ejpam-5351	126	31	manifold	manifold	ADJ
ejpam-5351	126	32	may	may	AUX
ejpam-5351	126	33	carry	carry	VERB
ejpam-5351	126	34	is	be	AUX
ejpam-5351	126	35	that	that	PRON
ejpam-5351	126	36	of	of	ADP
ejpam-5351	126	37	constant	constant	ADJ
ejpam-5351	126	38	curvature	curvature	NOUN
ejpam-5351	126	39	+1	+1	PROPN
ejpam-5351	126	40	.	.	PUNCT
ejpam-5351	127	1	and	and	CCONJ
ejpam-5351	127	2	it	it	PRON
ejpam-5351	127	3	is	be	AUX
ejpam-5351	127	4	known	know	VERB
ejpam-5351	127	5	that	that	SCONJ
ejpam-5351	127	6	a	a	DET
ejpam-5351	127	7	closed	closed	ADJ
ejpam-5351	127	8	and	and	CCONJ
ejpam-5351	127	9	simply	simply	ADV
ejpam-5351	127	10	connected	connect	VERB
ejpam-5351	127	11	3	3	NUM
ejpam-5351	127	12	-	-	PUNCT
ejpam-5351	127	13	manifold	manifold	ADJ
ejpam-5351	127	14	equipped	equip	VERB
ejpam-5351	127	15	with	with	ADP
ejpam-5351	127	16	a	a	DET
ejpam-5351	127	17	metric	metric	NOUN
ejpam-5351	127	18	of	of	ADP
ejpam-5351	127	19	constant	constant	ADJ
ejpam-5351	127	20	curvature	curvature	NOUN
ejpam-5351	127	21	+1	+1	PROPN
ejpam-5351	127	22	is	be	AUX
ejpam-5351	127	23	topologically	topologically	ADV
ejpam-5351	127	24	equivalent	equivalent	ADJ
ejpam-5351	127	25	to	to	ADP
ejpam-5351	127	26	a	a	DET
ejpam-5351	127	27	sphere	sphere	NOUN
ejpam-5351	127	28	.	.	PUNCT
ejpam-5351	128	1	thus	thus	ADV
ejpam-5351	128	2	,	,	PUNCT
ejpam-5351	128	3	one	one	PRON
ejpam-5351	128	4	can	can	AUX
ejpam-5351	128	5	prove	prove	VERB
ejpam-5351	128	6	the	the	DET
ejpam-5351	128	7	poincaré	poincaré	ADJ
ejpam-5351	128	8	conjecture	conjecture	NOUN
ejpam-5351	128	9	also	also	ADV
ejpam-5351	128	10	by	by	ADP
ejpam-5351	128	11	solving	solve	VERB
ejpam-5351	128	12	thurston	thurston	PROPN
ejpam-5351	128	13	’s	’s	PART
ejpam-5351	128	14	conjecture	conjecture	NOUN
ejpam-5351	128	15	.	.	PUNCT
ejpam-5351	129	1	4.3	4.3	NUM
ejpam-5351	129	2	.	.	PUNCT
ejpam-5351	130	1	the	the	DET
ejpam-5351	130	2	ricci	ricci	PROPN
ejpam-5351	130	3	flow	flow	NOUN
ejpam-5351	130	4	consider	consider	VERB
ejpam-5351	130	5	a	a	DET
ejpam-5351	130	6	manifold	manifold	NOUN
ejpam-5351	130	7	equipped	equip	VERB
ejpam-5351	130	8	with	with	ADP
ejpam-5351	130	9	a	a	DET
ejpam-5351	130	10	metric	metric	NOUN
ejpam-5351	130	11	.	.	PUNCT
ejpam-5351	131	1	is	be	AUX
ejpam-5351	131	2	it	it	PRON
ejpam-5351	131	3	possible	possible	ADJ
ejpam-5351	131	4	to	to	PART
ejpam-5351	131	5	find	find	VERB
ejpam-5351	131	6	a	a	DET
ejpam-5351	131	7	process	process	NOUN
ejpam-5351	131	8	that	that	PRON
ejpam-5351	131	9	modifies	modify	VERB
ejpam-5351	131	10	its	its	PRON
ejpam-5351	131	11	geometry	geometry	NOUN
ejpam-5351	131	12	to	to	PART
ejpam-5351	131	13	make	make	VERB
ejpam-5351	131	14	it	it	PRON
ejpam-5351	131	15	as	as	ADV
ejpam-5351	131	16	symmetric	symmetric	ADJ
ejpam-5351	131	17	as	as	ADP
ejpam-5351	131	18	possible	possible	ADJ
ejpam-5351	131	19	?	?	PUNCT
ejpam-5351	132	1	the	the	DET
ejpam-5351	132	2	idea	idea	NOUN
ejpam-5351	132	3	is	be	AUX
ejpam-5351	132	4	to	to	PART
ejpam-5351	132	5	continuously	continuously	ADV
ejpam-5351	132	6	deform	deform	VERB
ejpam-5351	132	7	the	the	DET
ejpam-5351	132	8	metric	metric	NOUN
ejpam-5351	132	9	at	at	ADP
ejpam-5351	132	10	each	each	DET
ejpam-5351	132	11	point	point	NOUN
ejpam-5351	132	12	p	p	NOUN
ejpam-5351	132	13	of	of	ADP
ejpam-5351	132	14	the	the	DET
ejpam-5351	132	15	manifold	manifold	NOUN
ejpam-5351	132	16	so	so	SCONJ
ejpam-5351	132	17	that	that	SCONJ
ejpam-5351	132	18	the	the	DET
ejpam-5351	132	19	average	average	ADJ
ejpam-5351	132	20	curvature	curvature	NOUN
ejpam-5351	132	21	at	at	ADP
ejpam-5351	132	22	point	point	NOUN
ejpam-5351	132	23	p	p	NOUN
ejpam-5351	132	24	decreases	decrease	NOUN
ejpam-5351	132	25	.	.	PUNCT
ejpam-5351	133	1	this	this	PRON
ejpam-5351	133	2	brings	bring	VERB
ejpam-5351	133	3	us	we	PRON
ejpam-5351	133	4	to	to	ADP
ejpam-5351	133	5	the	the	DET
ejpam-5351	133	6	work	work	NOUN
ejpam-5351	133	7	of	of	ADP
ejpam-5351	133	8	r.	r.	PROPN
ejpam-5351	133	9	hamilton	hamilton	PROPN
ejpam-5351	133	10	in	in	ADP
ejpam-5351	133	11	the	the	DET
ejpam-5351	133	12	1980s	1980	NOUN
ejpam-5351	133	13	[	[	X
ejpam-5351	133	14	2	2	NUM
ejpam-5351	133	15	]	]	PUNCT
ejpam-5351	133	16	.	.	PUNCT
ejpam-5351	134	1	he	he	PRON
ejpam-5351	134	2	introduced	introduce	VERB
ejpam-5351	134	3	an	an	DET
ejpam-5351	134	4	equation	equation	NOUN
ejpam-5351	134	5	(	(	PUNCT
ejpam-5351	134	6	a	a	DET
ejpam-5351	134	7	non	non	ADJ
ejpam-5351	134	8	-	-	ADJ
ejpam-5351	134	9	linear	linear	ADJ
ejpam-5351	134	10	partial	partial	ADJ
ejpam-5351	134	11	differential	differential	NOUN
ejpam-5351	134	12	equation	equation	NOUN
ejpam-5351	134	13	)	)	PUNCT
ejpam-5351	134	14	called	call	VERB
ejpam-5351	134	15	the	the	DET
ejpam-5351	134	16	ricci	ricci	PROPN
ejpam-5351	134	17	flow	flow	NOUN
ejpam-5351	134	18	,	,	PUNCT
ejpam-5351	134	19	which	which	PRON
ejpam-5351	134	20	turns	turn	VERB
ejpam-5351	134	21	out	out	ADP
ejpam-5351	134	22	to	to	PART
ejpam-5351	134	23	be	be	AUX
ejpam-5351	134	24	very	very	ADV
ejpam-5351	134	25	useful	useful	ADJ
ejpam-5351	134	26	[	[	X
ejpam-5351	134	27	4	4	NUM
ejpam-5351	134	28	]	]	PUNCT
ejpam-5351	134	29	.	.	PUNCT
ejpam-5351	135	1	on	on	ADP
ejpam-5351	135	2	a	a	DET
ejpam-5351	135	3	3	3	NUM
ejpam-5351	135	4	-	-	NUM
ejpam-5351	135	5	manifold	manifold	ADJ
ejpam-5351	135	6	,	,	PUNCT
ejpam-5351	135	7	we	we	PRON
ejpam-5351	135	8	can	can	AUX
ejpam-5351	135	9	define	define	VERB
ejpam-5351	135	10	a	a	DET
ejpam-5351	135	11	time	time	NOUN
ejpam-5351	135	12	-	-	PUNCT
ejpam-5351	135	13	dependent	dependent	ADJ
ejpam-5351	135	14	metric	metric	NOUN
ejpam-5351	135	15	,	,	PUNCT
ejpam-5351	135	16	and	and	CCONJ
ejpam-5351	135	17	,	,	PUNCT
ejpam-5351	135	18	at	at	ADP
ejpam-5351	135	19	each	each	DET
ejpam-5351	135	20	instant	instant	NOUN
ejpam-5351	135	21	of	of	ADP
ejpam-5351	135	22	time	time	NOUN
ejpam-5351	135	23	,	,	PUNCT
ejpam-5351	135	24	we	we	PRON
ejpam-5351	135	25	can	can	AUX
ejpam-5351	135	26	associate	associate	VERB
ejpam-5351	135	27	to	to	ADP
ejpam-5351	135	28	this	this	DET
ejpam-5351	135	29	metric	metric	NOUN
ejpam-5351	135	30	a	a	DET
ejpam-5351	135	31	certain	certain	ADJ
ejpam-5351	135	32	curvature	curvature	NOUN
ejpam-5351	135	33	,	,	PUNCT
ejpam-5351	135	34	the	the	DET
ejpam-5351	135	35	so	so	ADV
ejpam-5351	135	36	-	-	PUNCT
ejpam-5351	135	37	called	call	VERB
ejpam-5351	135	38	ricci	ricci	PROPN
ejpam-5351	135	39	curvature	curvature	NOUN
ejpam-5351	135	40	,	,	PUNCT
ejpam-5351	135	41	which	which	PRON
ejpam-5351	135	42	corresponds	correspond	VERB
ejpam-5351	135	43	to	to	ADP
ejpam-5351	135	44	a	a	DET
ejpam-5351	135	45	sort	sort	NOUN
ejpam-5351	135	46	of	of	ADP
ejpam-5351	135	47	average	average	NOUN
ejpam-5351	135	48	of	of	ADP
ejpam-5351	135	49	riemann	riemann	PROPN
ejpam-5351	135	50	curvatures	curvature	NOUN
ejpam-5351	135	51	.	.	PUNCT
ejpam-5351	136	1	the	the	DET
ejpam-5351	136	2	metric	metric	NOUN
ejpam-5351	136	3	and	and	CCONJ
ejpam-5351	136	4	the	the	DET
ejpam-5351	136	5	curvature	curvature	NOUN
ejpam-5351	136	6	,	,	PUNCT
ejpam-5351	136	7	being	be	AUX
ejpam-5351	136	8	two	two	NUM
ejpam-5351	136	9	tensors	tensor	NOUN
ejpam-5351	136	10	of	of	ADP
ejpam-5351	136	11	the	the	DET
ejpam-5351	136	12	same	same	ADJ
ejpam-5351	136	13	type	type	NOUN
ejpam-5351	136	14	,	,	PUNCT
ejpam-5351	136	15	can	can	AUX
ejpam-5351	136	16	be	be	AUX
ejpam-5351	136	17	entered	enter	VERB
ejpam-5351	136	18	into	into	ADP
ejpam-5351	136	19	an	an	DET
ejpam-5351	136	20	equation	equation	NOUN
ejpam-5351	136	21	that	that	PRON
ejpam-5351	136	22	dictates	dictate	VERB
ejpam-5351	136	23	that	that	SCONJ
ejpam-5351	136	24	the	the	DET
ejpam-5351	136	25	instantaneous	instantaneous	ADJ
ejpam-5351	136	26	rate	rate	NOUN
ejpam-5351	136	27	of	of	ADP
ejpam-5351	136	28	change	change	NOUN
ejpam-5351	136	29	of	of	ADP
ejpam-5351	136	30	the	the	DET
ejpam-5351	136	31	metric	metric	ADJ
ejpam-5351	136	32	corresponds	correspond	NOUN
ejpam-5351	136	33	to	to	ADP
ejpam-5351	136	34	the	the	DET
ejpam-5351	136	35	opposite	opposite	NOUN
ejpam-5351	136	36	of	of	ADP
ejpam-5351	136	37	the	the	DET
ejpam-5351	136	38	change	change	NOUN
ejpam-5351	136	39	of	of	ADP
ejpam-5351	136	40	the	the	DET
ejpam-5351	136	41	ricci	ricci	PROPN
ejpam-5351	136	42	curvature	curvature	NOUN
ejpam-5351	136	43	.	.	PUNCT
ejpam-5351	137	1	imposing	impose	VERB
ejpam-5351	137	2	the	the	DET
ejpam-5351	137	3	ricci	ricci	PROPN
ejpam-5351	137	4	flow	flow	NOUN
ejpam-5351	137	5	equation	equation	NOUN
ejpam-5351	137	6	means	mean	VERB
ejpam-5351	137	7	evolving	evolve	VERB
ejpam-5351	137	8	the	the	DET
ejpam-5351	137	9	metric	metric	NOUN
ejpam-5351	137	10	toward	toward	ADP
ejpam-5351	137	11	a	a	DET
ejpam-5351	137	12	more	more	ADV
ejpam-5351	137	13	regular	regular	ADJ
ejpam-5351	137	14	and	and	CCONJ
ejpam-5351	137	15	symmetric	symmetric	ADJ
ejpam-5351	137	16	geometry	geometry	NOUN
ejpam-5351	137	17	over	over	ADP
ejpam-5351	137	18	time	time	NOUN
ejpam-5351	137	19	.	.	PUNCT
ejpam-5351	138	1	in	in	ADP
ejpam-5351	138	2	dimension	dimension	NOUN
ejpam-5351	138	3	2	2	NUM
ejpam-5351	138	4	,	,	PUNCT
ejpam-5351	138	5	hamilton	hamilton	PROPN
ejpam-5351	138	6	proved	prove	VERB
ejpam-5351	138	7	that	that	SCONJ
ejpam-5351	138	8	the	the	DET
ejpam-5351	138	9	ricci	ricci	PROPN
ejpam-5351	138	10	flow	flow	NOUN
ejpam-5351	138	11	for	for	ADP
ejpam-5351	138	12	any	any	DET
ejpam-5351	138	13	metric	metric	NOUN
ejpam-5351	138	14	in	in	ADP
ejpam-5351	138	15	a	a	DET
ejpam-5351	138	16	surface	surface	NOUN
ejpam-5351	138	17	evolves	evolve	VERB
ejpam-5351	138	18	,	,	PUNCT
ejpam-5351	138	19	in	in	ADP
ejpam-5351	138	20	finite	finite	ADJ
ejpam-5351	138	21	time	time	NOUN
ejpam-5351	138	22	,	,	PUNCT
ejpam-5351	138	23	toward	toward	ADP
ejpam-5351	138	24	a	a	DET
ejpam-5351	138	25	metric	metric	NOUN
ejpam-5351	138	26	of	of	ADP
ejpam-5351	138	27	constant	constant	ADJ
ejpam-5351	138	28	curvature	curvature	NOUN
ejpam-5351	138	29	.	.	PUNCT
ejpam-5351	139	1	in	in	ADP
ejpam-5351	139	2	dimension	dimension	NOUN
ejpam-5351	139	3	3	3	NUM
ejpam-5351	139	4	,	,	PUNCT
ejpam-5351	139	5	things	thing	NOUN
ejpam-5351	139	6	are	be	AUX
ejpam-5351	139	7	far	far	ADV
ejpam-5351	139	8	more	more	ADV
ejpam-5351	139	9	difficult	difficult	ADJ
ejpam-5351	139	10	,	,	PUNCT
ejpam-5351	139	11	because	because	SCONJ
ejpam-5351	139	12	the	the	DET
ejpam-5351	139	13	flow	flow	NOUN
ejpam-5351	139	14	may	may	AUX
ejpam-5351	139	15	“	"	PUNCT
ejpam-5351	139	16	explode	explode	VERB
ejpam-5351	139	17	”	"	PUNCT
ejpam-5351	139	18	,	,	PUNCT
ejpam-5351	139	19	making	make	VERB
ejpam-5351	139	20	infinite	infinite	ADJ
ejpam-5351	139	21	quantities	quantity	NOUN
ejpam-5351	139	22	appear	appear	VERB
ejpam-5351	139	23	.	.	PUNCT
ejpam-5351	140	1	hamilton	hamilton	PROPN
ejpam-5351	140	2	’s	’s	PART
ejpam-5351	140	3	abstract	abstract	ADJ
ejpam-5351	140	4	program	program	NOUN
ejpam-5351	140	5	,	,	PUNCT
ejpam-5351	140	6	developed	develop	VERB
ejpam-5351	140	7	and	and	CCONJ
ejpam-5351	140	8	completed	complete	VERB
ejpam-5351	140	9	by	by	ADP
ejpam-5351	140	10	perelman	perelman	NOUN
ejpam-5351	140	11	,	,	PUNCT
ejpam-5351	140	12	consists	consist	VERB
ejpam-5351	140	13	just	just	ADV
ejpam-5351	140	14	in	in	ADP
ejpam-5351	140	15	proving	prove	VERB
ejpam-5351	140	16	that	that	SCONJ
ejpam-5351	140	17	,	,	PUNCT
ejpam-5351	140	18	as	as	ADP
ejpam-5351	140	19	a	a	DET
ejpam-5351	140	20	consequence	consequence	NOUN
ejpam-5351	140	21	of	of	ADP
ejpam-5351	140	22	these	these	DET
ejpam-5351	140	23	explosions	explosion	NOUN
ejpam-5351	140	24	,	,	PUNCT
ejpam-5351	140	25	the	the	DET
ejpam-5351	140	26	manifold	manifold	ADJ
ejpam-5351	140	27	v	v	ADP
ejpam-5351	140	28	3	3	NUM
ejpam-5351	140	29	breaks	break	NOUN
ejpam-5351	140	30	into	into	ADP
ejpam-5351	140	31	pieces	piece	NOUN
ejpam-5351	140	32	on	on	ADP
ejpam-5351	140	33	which	which	PRON
ejpam-5351	140	34	the	the	DET
ejpam-5351	140	35	ricci	ricci	PROPN
ejpam-5351	140	36	flow	flow	NOUN
ejpam-5351	140	37	may	may	AUX
ejpam-5351	140	38	continue	continue	VERB
ejpam-5351	140	39	to	to	PART
ejpam-5351	140	40	evolve	evolve	VERB
ejpam-5351	140	41	,	,	PUNCT
ejpam-5351	140	42	and	and	CCONJ
ejpam-5351	140	43	that	that	SCONJ
ejpam-5351	140	44	,	,	PUNCT
ejpam-5351	140	45	after	after	ADP
ejpam-5351	140	46	a	a	DET
ejpam-5351	140	47	references	reference	NOUN
ejpam-5351	140	48	2368	2368	NUM
ejpam-5351	140	49	finite	finite	NOUN
ejpam-5351	140	50	amount	amount	NOUN
ejpam-5351	140	51	of	of	ADP
ejpam-5351	140	52	time	time	NOUN
ejpam-5351	140	53	and	and	CCONJ
ejpam-5351	140	54	a	a	DET
ejpam-5351	140	55	finite	finite	ADJ
ejpam-5351	140	56	number	number	NOUN
ejpam-5351	140	57	of	of	ADP
ejpam-5351	140	58	explosions	explosion	NOUN
ejpam-5351	140	59	,	,	PUNCT
ejpam-5351	140	60	one	one	PRON
ejpam-5351	140	61	obtains	obtain	VERB
ejpam-5351	140	62	the	the	DET
ejpam-5351	140	63	starting	start	VERB
ejpam-5351	140	64	manifold	manifold	ADJ
ejpam-5351	140	65	decomposed	decompose	VERB
ejpam-5351	140	66	into	into	ADP
ejpam-5351	140	67	pieces	piece	NOUN
ejpam-5351	140	68	,	,	PUNCT
ejpam-5351	140	69	each	each	PRON
ejpam-5351	140	70	endowed	endow	VERB
ejpam-5351	140	71	with	with	ADP
ejpam-5351	140	72	one	one	NUM
ejpam-5351	140	73	of	of	ADP
ejpam-5351	140	74	thurston	thurston	PROPN
ejpam-5351	140	75	’s	’s	PART
ejpam-5351	140	76	8	8	NUM
ejpam-5351	140	77	geometries	geometry	NOUN
ejpam-5351	140	78	.	.	PUNCT
ejpam-5351	141	1	perelman	perelman	PROPN
ejpam-5351	141	2	finally	finally	ADV
ejpam-5351	141	3	managed	manage	VERB
ejpam-5351	141	4	,	,	PUNCT
ejpam-5351	141	5	with	with	ADP
ejpam-5351	141	6	fine	fine	ADJ
ejpam-5351	141	7	methods	method	NOUN
ejpam-5351	141	8	of	of	ADP
ejpam-5351	141	9	non	non	ADJ
ejpam-5351	141	10	-	-	ADJ
ejpam-5351	141	11	linear	linear	ADJ
ejpam-5351	141	12	analysis	analysis	NOUN
ejpam-5351	141	13	,	,	PUNCT
ejpam-5351	141	14	to	to	PART
ejpam-5351	141	15	control	control	VERB
ejpam-5351	141	16	the	the	DET
ejpam-5351	141	17	explosions	explosion	NOUN
ejpam-5351	141	18	of	of	ADP
ejpam-5351	141	19	the	the	DET
ejpam-5351	141	20	ricci	ricci	PROPN
ejpam-5351	141	21	flow	flow	NOUN
ejpam-5351	141	22	,	,	PUNCT
ejpam-5351	141	23	and	and	CCONJ
ejpam-5351	141	24	to	to	PART
ejpam-5351	141	25	demonstrate	demonstrate	VERB
ejpam-5351	141	26	that	that	SCONJ
ejpam-5351	141	27	the	the	DET
ejpam-5351	141	28	whole	whole	ADJ
ejpam-5351	141	29	process	process	NOUN
ejpam-5351	141	30	of	of	ADP
ejpam-5351	141	31	the	the	DET
ejpam-5351	141	32	ricci	ricci	PROPN
ejpam-5351	141	33	flow	flow	NOUN
ejpam-5351	141	34	extinguishes	extinguish	VERB
ejpam-5351	141	35	in	in	ADP
ejpam-5351	141	36	a	a	DET
ejpam-5351	141	37	finite	finite	ADJ
ejpam-5351	141	38	time	time	NOUN
ejpam-5351	141	39	,	,	PUNCT
ejpam-5351	141	40	thus	thus	ADV
ejpam-5351	141	41	completing	complete	VERB
ejpam-5351	141	42	hamilton	hamilton	PROPN
ejpam-5351	141	43	’s	’s	PART
ejpam-5351	141	44	strategy	strategy	NOUN
ejpam-5351	141	45	,	,	PUNCT
ejpam-5351	141	46	and	and	CCONJ
ejpam-5351	141	47	proving	prove	VERB
ejpam-5351	141	48	both	both	CCONJ
ejpam-5351	141	49	the	the	DET
ejpam-5351	141	50	geometrization	geometrization	NOUN
ejpam-5351	141	51	of	of	ADP
ejpam-5351	141	52	thurston	thurston	PROPN
ejpam-5351	141	53	for	for	ADP
ejpam-5351	141	54	3	3	NUM
ejpam-5351	141	55	-	-	PUNCT
ejpam-5351	141	56	manifolds	manifold	NOUN
ejpam-5351	141	57	,	,	PUNCT
ejpam-5351	141	58	and	and	CCONJ
ejpam-5351	141	59	the	the	DET
ejpam-5351	141	60	poincaré	poincaré	ADJ
ejpam-5351	141	61	conjecture	conjecture	NOUN
ejpam-5351	141	62	!	!	PUNCT
ejpam-5351	142	1	5	5	X
ejpam-5351	142	2	.	.	X
ejpam-5351	142	3	conclusion	conclusion	NOUN
ejpam-5351	142	4	mathematicians	mathematician	NOUN
ejpam-5351	142	5	call	call	VERB
ejpam-5351	142	6	“	"	PUNCT
ejpam-5351	142	7	open	open	ADJ
ejpam-5351	142	8	problems	problem	NOUN
ejpam-5351	142	9	”	"	PUNCT
ejpam-5351	142	10	those	those	PRON
ejpam-5351	142	11	on	on	ADP
ejpam-5351	142	12	which	which	PRON
ejpam-5351	142	13	they	they	PRON
ejpam-5351	142	14	struggle	struggle	VERB
ejpam-5351	142	15	unsuccessfully	unsuccessfully	ADV
ejpam-5351	142	16	for	for	ADP
ejpam-5351	142	17	a	a	DET
ejpam-5351	142	18	long	long	ADJ
ejpam-5351	142	19	time	time	NOUN
ejpam-5351	142	20	.	.	PUNCT
ejpam-5351	143	1	but	but	CCONJ
ejpam-5351	143	2	an	an	DET
ejpam-5351	143	3	open	open	ADJ
ejpam-5351	143	4	problem	problem	NOUN
ejpam-5351	143	5	is	be	AUX
ejpam-5351	143	6	not	not	PART
ejpam-5351	143	7	just	just	ADV
ejpam-5351	143	8	a	a	DET
ejpam-5351	143	9	simple	simple	ADJ
ejpam-5351	143	10	unsolved	unsolved	ADJ
ejpam-5351	143	11	problem	problem	NOUN
ejpam-5351	143	12	.	.	PUNCT
ejpam-5351	144	1	in	in	ADP
ejpam-5351	144	2	fact	fact	NOUN
ejpam-5351	144	3	various	various	ADJ
ejpam-5351	144	4	new	new	ADJ
ejpam-5351	144	5	results	result	NOUN
ejpam-5351	144	6	are	be	AUX
ejpam-5351	144	7	demonstrated	demonstrate	VERB
ejpam-5351	144	8	by	by	ADP
ejpam-5351	144	9	mathematicians	mathematician	NOUN
ejpam-5351	144	10	every	every	DET
ejpam-5351	144	11	year	year	NOUN
ejpam-5351	144	12	,	,	PUNCT
ejpam-5351	144	13	and	and	CCONJ
ejpam-5351	144	14	numerous	numerous	ADJ
ejpam-5351	144	15	new	new	ADJ
ejpam-5351	144	16	questions	question	NOUN
ejpam-5351	144	17	arise	arise	VERB
ejpam-5351	144	18	also	also	ADV
ejpam-5351	144	19	every	every	DET
ejpam-5351	144	20	year	year	NOUN
ejpam-5351	144	21	,	,	PUNCT
ejpam-5351	144	22	but	but	CCONJ
ejpam-5351	144	23	(	(	PUNCT
ejpam-5351	144	24	almost	almost	ADV
ejpam-5351	144	25	)	)	PUNCT
ejpam-5351	144	26	none	none	NOUN
ejpam-5351	144	27	of	of	ADP
ejpam-5351	144	28	them	they	PRON
ejpam-5351	144	29	receive	receive	VERB
ejpam-5351	144	30	such	such	DET
ejpam-5351	144	31	a	a	DET
ejpam-5351	144	32	designation	designation	NOUN
ejpam-5351	144	33	.	.	PUNCT
ejpam-5351	145	1	an	an	DET
ejpam-5351	145	2	open	open	ADJ
ejpam-5351	145	3	problem	problem	NOUN
ejpam-5351	145	4	is	be	AUX
ejpam-5351	145	5	a	a	DET
ejpam-5351	145	6	problem	problem	NOUN
ejpam-5351	145	7	regarded	regard	VERB
ejpam-5351	145	8	as	as	ADP
ejpam-5351	145	9	exceptional	exceptional	ADJ
ejpam-5351	145	10	,	,	PUNCT
ejpam-5351	145	11	noble	noble	ADJ
ejpam-5351	145	12	,	,	PUNCT
ejpam-5351	145	13	elusive	elusive	ADJ
ejpam-5351	145	14	,	,	PUNCT
ejpam-5351	145	15	but	but	CCONJ
ejpam-5351	145	16	whose	whose	DET
ejpam-5351	145	17	comprehension	comprehension	NOUN
ejpam-5351	145	18	is	be	AUX
ejpam-5351	145	19	fundamental	fundamental	ADJ
ejpam-5351	145	20	for	for	ADP
ejpam-5351	145	21	the	the	DET
ejpam-5351	145	22	development	development	NOUN
ejpam-5351	145	23	of	of	ADP
ejpam-5351	145	24	the	the	DET
ejpam-5351	145	25	research	research	NOUN
ejpam-5351	145	26	fields	field	NOUN
ejpam-5351	145	27	that	that	PRON
ejpam-5351	145	28	surround	surround	VERB
ejpam-5351	145	29	it	it	PRON
ejpam-5351	145	30	.	.	PUNCT
ejpam-5351	146	1	the	the	DET
ejpam-5351	146	2	poincaré	poincaré	ADJ
ejpam-5351	146	3	conjecture	conjecture	NOUN
ejpam-5351	146	4	was	be	AUX
ejpam-5351	146	5	the	the	DET
ejpam-5351	146	6	prototype	prototype	NOUN
ejpam-5351	146	7	of	of	ADP
ejpam-5351	146	8	such	such	DET
ejpam-5351	146	9	a	a	DET
ejpam-5351	146	10	problem	problem	NOUN
ejpam-5351	146	11	.	.	PUNCT
ejpam-5351	147	1	it	it	PRON
ejpam-5351	147	2	was	be	AUX
ejpam-5351	147	3	really	really	ADV
ejpam-5351	147	4	a	a	DET
ejpam-5351	147	5	venerable	venerable	ADJ
ejpam-5351	147	6	major	major	ADJ
ejpam-5351	147	7	question	question	NOUN
ejpam-5351	147	8	both	both	PRON
ejpam-5351	147	9	in	in	ADP
ejpam-5351	147	10	classical	classical	ADJ
ejpam-5351	147	11	and	and	CCONJ
ejpam-5351	147	12	modern	modern	ADJ
ejpam-5351	147	13	mathematics	mathematic	NOUN
ejpam-5351	147	14	.	.	PUNCT
ejpam-5351	148	1	thanks	thank	NOUN
ejpam-5351	148	2	to	to	ADP
ejpam-5351	148	3	it	it	PRON
ejpam-5351	148	4	,	,	PUNCT
ejpam-5351	148	5	mathematics	mathematic	NOUN
ejpam-5351	148	6	has	have	AUX
ejpam-5351	148	7	evolved	evolve	VERB
ejpam-5351	148	8	in	in	ADP
ejpam-5351	148	9	different	different	ADJ
ejpam-5351	148	10	branches	branch	NOUN
ejpam-5351	148	11	:	:	PUNCT
ejpam-5351	148	12	from	from	ADP
ejpam-5351	148	13	the	the	DET
ejpam-5351	148	14	birth	birth	NOUN
ejpam-5351	148	15	of	of	ADP
ejpam-5351	148	16	algebraic	algebraic	ADJ
ejpam-5351	148	17	topology	topology	NOUN
ejpam-5351	148	18	to	to	ADP
ejpam-5351	148	19	the	the	DET
ejpam-5351	148	20	deep	deep	ADJ
ejpam-5351	148	21	and	and	CCONJ
ejpam-5351	148	22	vast	vast	ADJ
ejpam-5351	148	23	world	world	NOUN
ejpam-5351	148	24	of	of	ADP
ejpam-5351	148	25	higher	high	ADJ
ejpam-5351	148	26	dimensional	dimensional	ADJ
ejpam-5351	148	27	geometry	geometry	NOUN
ejpam-5351	148	28	and	and	CCONJ
ejpam-5351	148	29	topology	topology	NOUN
ejpam-5351	148	30	.	.	PUNCT
ejpam-5351	149	1	and	and	CCONJ
ejpam-5351	149	2	,	,	PUNCT
ejpam-5351	149	3	at	at	ADP
ejpam-5351	149	4	the	the	DET
ejpam-5351	149	5	end	end	NOUN
ejpam-5351	149	6	,	,	PUNCT
ejpam-5351	149	7	with	with	ADP
ejpam-5351	149	8	the	the	DET
ejpam-5351	149	9	help	help	NOUN
ejpam-5351	149	10	of	of	ADP
ejpam-5351	149	11	fine	fine	ADJ
ejpam-5351	149	12	and	and	CCONJ
ejpam-5351	149	13	sophisticated	sophisticated	ADJ
ejpam-5351	149	14	analytic	analytic	ADJ
ejpam-5351	149	15	tools	tool	NOUN
ejpam-5351	149	16	,	,	PUNCT
ejpam-5351	149	17	to	to	ADP
ejpam-5351	149	18	the	the	DET
ejpam-5351	149	19	growth	growth	NOUN
ejpam-5351	149	20	of	of	ADP
ejpam-5351	149	21	geometric	geometric	ADJ
ejpam-5351	149	22	analysis	analysis	NOUN
ejpam-5351	149	23	.	.	PUNCT
ejpam-5351	150	1	references	reference	NOUN
ejpam-5351	150	2	[	[	X
ejpam-5351	150	3	1	1	X
ejpam-5351	150	4	]	]	PUNCT
ejpam-5351	150	5	d.	d.	PROPN
ejpam-5351	150	6	gabai	gabai	PROPN
ejpam-5351	150	7	.	.	PUNCT
ejpam-5351	151	1	valentin	valentin	PROPN
ejpam-5351	151	2	poénaru	poénaru	PROPN
ejpam-5351	151	3	’s	’s	PART
ejpam-5351	151	4	program	program	NOUN
ejpam-5351	151	5	for	for	ADP
ejpam-5351	151	6	the	the	DET
ejpam-5351	151	7	poincaré	poincaré	ADJ
ejpam-5351	151	8	conjecture	conjecture	NOUN
ejpam-5351	151	9	.	.	PUNCT
ejpam-5351	152	1	in	in	ADP
ejpam-5351	152	2	st	st	PROPN
ejpam-5351	152	3	yau	yau	PROPN
ejpam-5351	152	4	,	,	PUNCT
ejpam-5351	152	5	editor	editor	NOUN
ejpam-5351	152	6	,	,	PUNCT
ejpam-5351	152	7	geometry	geometry	NOUN
ejpam-5351	152	8	topology	topology	NOUN
ejpam-5351	152	9	and	and	CCONJ
ejpam-5351	152	10	physics	physics	NOUN
ejpam-5351	152	11	for	for	ADP
ejpam-5351	152	12	raoul	raoul	PROPN
ejpam-5351	152	13	bott	bott	PROPN
ejpam-5351	152	14	,	,	PUNCT
ejpam-5351	152	15	pages	page	VERB
ejpam-5351	152	16	139–169	139–169	NUM
ejpam-5351	152	17	.	.	PUNCT
ejpam-5351	153	1	international	international	ADJ
ejpam-5351	153	2	press	press	NOUN
ejpam-5351	153	3	,	,	PUNCT
ejpam-5351	153	4	1994	1994	NUM
ejpam-5351	153	5	.	.	PUNCT
ejpam-5351	154	1	[	[	X
ejpam-5351	154	2	2	2	NUM
ejpam-5351	154	3	]	]	PUNCT
ejpam-5351	154	4	r.	r.	PROPN
ejpam-5351	154	5	hamilton	hamilton	PROPN
ejpam-5351	154	6	.	.	PUNCT
ejpam-5351	155	1	three	three	NUM
ejpam-5351	155	2	-	-	PUNCT
ejpam-5351	155	3	manifolds	manifold	NOUN
ejpam-5351	155	4	with	with	ADP
ejpam-5351	155	5	positive	positive	ADJ
ejpam-5351	155	6	ricci	ricci	PROPN
ejpam-5351	155	7	curvature	curvature	NOUN
ejpam-5351	155	8	.	.	PUNCT
ejpam-5351	156	1	j.	j.	PROPN
ejpam-5351	156	2	differ	differ	VERB
ejpam-5351	156	3	.	.	PUNCT
ejpam-5351	157	1	geom	geom	PROPN
ejpam-5351	157	2	.	.	PROPN
ejpam-5351	157	3	,	,	PUNCT
ejpam-5351	157	4	17(2):255–306	17(2):255–306	PROPN
ejpam-5351	157	5	,	,	PUNCT
ejpam-5351	157	6	1982	1982	NUM
ejpam-5351	157	7	.	.	PUNCT
ejpam-5351	158	1	[	[	X
ejpam-5351	158	2	3	3	X
ejpam-5351	158	3	]	]	X
ejpam-5351	158	4	j.p	j.p	PROPN
ejpam-5351	158	5	.	.	PROPN
ejpam-5351	158	6	morgan	morgan	PROPN
ejpam-5351	158	7	.	.	PUNCT
ejpam-5351	159	1	recent	recent	ADJ
ejpam-5351	159	2	progress	progress	NOUN
ejpam-5351	159	3	on	on	ADP
ejpam-5351	159	4	the	the	DET
ejpam-5351	159	5	poincaré	poincaré	ADJ
ejpam-5351	159	6	conjecture	conjecture	NOUN
ejpam-5351	159	7	and	and	CCONJ
ejpam-5351	159	8	the	the	DET
ejpam-5351	159	9	classification	classification	NOUN
ejpam-5351	159	10	of	of	ADP
ejpam-5351	159	11	3	3	NUM
ejpam-5351	159	12	-	-	PUNCT
ejpam-5351	159	13	manifolds	manifold	NOUN
ejpam-5351	159	14	.	.	PUNCT
ejpam-5351	160	1	bull	bull	NOUN
ejpam-5351	160	2	.	.	PUNCT
ejpam-5351	161	1	ams	am	NOUN
ejpam-5351	161	2	,	,	PUNCT
ejpam-5351	161	3	42:57–78	42:57–78	NUM
ejpam-5351	161	4	,	,	PUNCT
ejpam-5351	161	5	2004	2004	NUM
ejpam-5351	161	6	.	.	PUNCT
ejpam-5351	162	1	[	[	X
ejpam-5351	162	2	4	4	NUM
ejpam-5351	162	3	]	]	X
ejpam-5351	162	4	j.p	j.p	PROPN
ejpam-5351	162	5	.	.	PROPN
ejpam-5351	162	6	morgan	morgan	PROPN
ejpam-5351	162	7	and	and	CCONJ
ejpam-5351	162	8	g.	g.	PROPN
ejpam-5351	162	9	tian	tian	PROPN
ejpam-5351	162	10	.	.	PUNCT
ejpam-5351	163	1	ricci	ricci	PROPN
ejpam-5351	163	2	flow	flow	NOUN
ejpam-5351	163	3	and	and	CCONJ
ejpam-5351	163	4	the	the	DET
ejpam-5351	163	5	poincaré	poincaré	ADJ
ejpam-5351	163	6	conjecture	conjecture	NOUN
ejpam-5351	163	7	.	.	PUNCT
ejpam-5351	164	1	clay	clay	NOUN
ejpam-5351	164	2	mathematics	mathematics	PROPN
ejpam-5351	164	3	monographs	monograph	NOUN
ejpam-5351	164	4	.	.	PUNCT
ejpam-5351	165	1	vol	vol	NOUN
ejpam-5351	165	2	.	.	PUNCT
ejpam-5351	166	1	3	3	X
ejpam-5351	166	2	.	.	X
ejpam-5351	166	3	providence	providence	NOUN
ejpam-5351	166	4	,	,	PUNCT
ejpam-5351	166	5	ri	ri	PROPN
ejpam-5351	166	6	:	:	PUNCT
ejpam-5351	166	7	american	american	PROPN
ejpam-5351	166	8	mathematical	mathematical	PROPN
ejpam-5351	166	9	society	society	NOUN
ejpam-5351	166	10	,	,	PUNCT
ejpam-5351	166	11	2007	2007	NUM
ejpam-5351	166	12	.	.	PUNCT
ejpam-5351	167	1	[	[	X
ejpam-5351	167	2	5	5	X
ejpam-5351	167	3	]	]	PUNCT
ejpam-5351	167	4	v.	v.	PROPN
ejpam-5351	167	5	poénaru	poénaru	PROPN
ejpam-5351	167	6	.	.	PUNCT
ejpam-5351	168	1	the	the	DET
ejpam-5351	168	2	problems	problem	NOUN
ejpam-5351	168	3	of	of	ADP
ejpam-5351	168	4	dimension	dimension	NOUN
ejpam-5351	168	5	four	four	NUM
ejpam-5351	168	6	,	,	PUNCT
ejpam-5351	168	7	and	and	CCONJ
ejpam-5351	168	8	some	some	DET
ejpam-5351	168	9	ramifications	ramification	NOUN
ejpam-5351	168	10	.	.	PUNCT
ejpam-5351	169	1	mathematics	mathematic	NOUN
ejpam-5351	169	2	,	,	PUNCT
ejpam-5351	169	3	11(18	11(18	NUM
ejpam-5351	169	4	)	)	PUNCT
ejpam-5351	169	5	,	,	PUNCT
ejpam-5351	169	6	2023	2023	NUM
ejpam-5351	169	7	.	.	PUNCT
ejpam-5351	170	1	[	[	X
ejpam-5351	170	2	6	6	NUM
ejpam-5351	170	3	]	]	PUNCT
ejpam-5351	170	4	h.	h.	PROPN
ejpam-5351	170	5	poincaré.	poincaré.	PROPN
ejpam-5351	170	6	cinquième	cinquième	PROPN
ejpam-5351	170	7	complément	complément	PROPN
ejpam-5351	171	1	à	à	PROPN
ejpam-5351	171	2	l’analysis	l’analysis	PROPN
ejpam-5351	171	3	situs	situs	PROPN
ejpam-5351	171	4	.	.	PUNCT
ejpam-5351	171	5	rendiconti	rendiconti	PROPN
ejpam-5351	171	6	del	del	PROPN
ejpam-5351	171	7	circolo	circolo	PROPN
ejpam-5351	171	8	matematico	matematico	NOUN
ejpam-5351	171	9	di	di	NOUN
ejpam-5351	171	10	palermo	palermo	NOUN
ejpam-5351	171	11	,	,	PUNCT
ejpam-5351	171	12	18:45–110	18:45–110	NUM
ejpam-5351	171	13	,	,	PUNCT
ejpam-5351	171	14	1904	1904	NUM
ejpam-5351	171	15	.	.	PUNCT
ejpam-5351	172	1	[	[	X
ejpam-5351	172	2	7	7	X
ejpam-5351	172	3	]	]	X
ejpam-5351	172	4	h.	h.	PROPN
ejpam-5351	172	5	poincaré.	poincaré.	PROPN
ejpam-5351	172	6	papers	paper	NOUN
ejpam-5351	172	7	on	on	ADP
ejpam-5351	172	8	topology	topology	NOUN
ejpam-5351	172	9	:	:	PUNCT
ejpam-5351	172	10	analysis	analysis	NOUN
ejpam-5351	172	11	situs	situs	PROPN
ejpam-5351	172	12	and	and	CCONJ
ejpam-5351	172	13	its	its	PRON
ejpam-5351	172	14	five	five	NUM
ejpam-5351	172	15	supplements	supplement	NOUN
ejpam-5351	172	16	.	.	PUNCT
ejpam-5351	173	1	history	history	NOUN
ejpam-5351	173	2	of	of	ADP
ejpam-5351	173	3	mathematics	mathematic	NOUN
ejpam-5351	173	4	.	.	PUNCT
ejpam-5351	174	1	vol	vol	NOUN
ejpam-5351	174	2	.	.	PUNCT
ejpam-5351	175	1	37	37	NUM
ejpam-5351	175	2	,	,	PUNCT
ejpam-5351	175	3	american	american	PROPN
ejpam-5351	175	4	mathematical	mathematical	PROPN
ejpam-5351	175	5	society	society	NOUN
ejpam-5351	175	6	,	,	PUNCT
ejpam-5351	175	7	2010	2010	NUM
ejpam-5351	175	8	.	.	PUNCT
ejpam-5351	176	1	references	reference	NOUN
ejpam-5351	176	2	2369	2369	NUM
ejpam-5351	176	3	[	[	X
ejpam-5351	176	4	8	8	NUM
ejpam-5351	176	5	]	]	PUNCT
ejpam-5351	176	6	j.	j.	PROPN
ejpam-5351	176	7	stillwell	stillwell	PROPN
ejpam-5351	176	8	.	.	PUNCT
ejpam-5351	177	1	poincaré	poincaré	ADJ
ejpam-5351	177	2	and	and	CCONJ
ejpam-5351	177	3	the	the	DET
ejpam-5351	177	4	early	early	ADJ
ejpam-5351	177	5	history	history	NOUN
ejpam-5351	177	6	of	of	ADP
ejpam-5351	177	7	3	3	NUM
ejpam-5351	177	8	-	-	PUNCT
ejpam-5351	177	9	manifolds	manifold	NOUN
ejpam-5351	177	10	.	.	PUNCT
ejpam-5351	178	1	bull	bull	NOUN
ejpam-5351	178	2	.	.	PUNCT
ejpam-5351	179	1	ams	am	NOUN
ejpam-5351	179	2	,	,	PUNCT
ejpam-5351	179	3	49(4):555–576	49(4):555–576	NOUN
ejpam-5351	179	4	,	,	PUNCT
ejpam-5351	179	5	2012	2012	NUM
ejpam-5351	179	6	.	.	PUNCT
ejpam-5351	180	1	[	[	X
ejpam-5351	180	2	9	9	NUM
ejpam-5351	180	3	]	]	SYM
ejpam-5351	180	4	w.p	w.p	PROPN
ejpam-5351	180	5	.	.	PROPN
ejpam-5351	180	6	thurston	thurston	PROPN
ejpam-5351	180	7	.	.	PUNCT
ejpam-5351	181	1	three	three	NUM
ejpam-5351	181	2	-	-	PUNCT
ejpam-5351	181	3	dimensional	dimensional	ADJ
ejpam-5351	181	4	geometry	geometry	NOUN
ejpam-5351	181	5	and	and	CCONJ
ejpam-5351	181	6	topology	topology	NOUN
ejpam-5351	181	7	.	.	PUNCT
ejpam-5351	182	1	vol	vol	NOUN
ejpam-5351	182	2	.	.	PROPN
ejpam-5351	183	1	1	1	NUM
ejpam-5351	183	2	.	.	X
ejpam-5351	183	3	princeton	princeton	PROPN
ejpam-5351	183	4	mathematical	mathematical	PROPN
ejpam-5351	183	5	series	series	PROPN
ejpam-5351	183	6	.	.	PUNCT
ejpam-5351	184	1	35	35	NUM
ejpam-5351	184	2	.	.	X
ejpam-5351	185	1	princeton	princeton	PROPN
ejpam-5351	185	2	,	,	PUNCT
ejpam-5351	185	3	nj	nj	PROPN
ejpam-5351	185	4	:	:	PUNCT
ejpam-5351	185	5	princeton	princeton	PROPN
ejpam-5351	185	6	university	university	PROPN
ejpam-5351	185	7	press	press	NOUN
ejpam-5351	185	8	,	,	PUNCT
ejpam-5351	185	9	1997	1997	NUM
ejpam-5351	185	10	.	.	PUNCT
ejpam-5351	186	1	[	[	X
ejpam-5351	186	2	10	10	NUM
ejpam-5351	186	3	]	]	X
ejpam-5351	186	4	j.h.c	j.h.c	NOUN
ejpam-5351	186	5	.	.	PUNCT
ejpam-5351	186	6	whitehead	whitehead	PROPN
ejpam-5351	186	7	.	.	PUNCT
ejpam-5351	187	1	a	a	DET
ejpam-5351	187	2	certain	certain	ADJ
ejpam-5351	187	3	open	open	ADJ
ejpam-5351	187	4	manifold	manifold	NOUN
ejpam-5351	187	5	whose	whose	DET
ejpam-5351	187	6	group	group	NOUN
ejpam-5351	187	7	is	be	AUX
ejpam-5351	187	8	unity	unity	NOUN
ejpam-5351	187	9	.	.	PUNCT
ejpam-5351	188	1	q.	q.	PROPN
ejpam-5351	188	2	j.	j.	PROPN
ejpam-5351	188	3	math	math	PROPN
ejpam-5351	188	4	.	.	PROPN
ejpam-5351	188	5	,	,	PUNCT
ejpam-5351	188	6	oxf	oxf	PROPN
ejpam-5351	188	7	.	.	PUNCT
ejpam-5351	189	1	ser	ser	PROPN
ejpam-5351	189	2	.	.	PROPN
ejpam-5351	189	3	,	,	PUNCT
ejpam-5351	189	4	6:268–279	6:268–279	PROPN
ejpam-5351	189	5	,	,	PUNCT
ejpam-5351	189	6	1935	1935	NUM
ejpam-5351	189	7	.	.	PUNCT