ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES

doi:10.1090/proc/15784

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	ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES
	Su, Yang1,2 ; Wu, Xiaolei 3,4
	2022-05-01
发表期刊	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9939
卷号	150 期号:5 页码:2239-2248
摘要	We study the finite generation of homotopy groups of closed manifolds and finite CW-complexes by relating it to the cohomology of their fundamental groups. Our main theorems are as follows: when X is a finite CW-complex of dimension n and pi(1)(X) is virtually a Poincare duality group of dimension >= n - 1, then pi(i)(X) is not finitely generated for some i unless X is homotopy equivalent to the Eilenberg-MacLane space K(pi(1)(X), 1); when M is an n-dimensional closed manifold and pi(1)(M) is virtually a Poincare duality group of dimension >= n - 1, then for some i <= [n/2], pi(i)(M) is not finitely generated, unless M itself is an aspherical manifold. These generalize theorems of M. Damian [Trans. Amer. Math. Soc. 361 (2009), pp. 1791-1809] from polycyclic groups to any virtually Poincare duality groups.
DOI	10.1090/proc/15784
收录类别	SCI
语种	英语
资助项目	NSFC[11571343] ; ERC[662400] ; DFG[GZ 2047/1] ; DFG[390685813]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000768891900036
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60182
专题	数学所
通讯作者	Su, Yang
作者单位	1.Chinese Acad Sci, HLM, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany 4.Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200348, Peoples R China
推荐引用方式 GB/T 7714	Su, Yang,Wu, Xiaolei. ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2022,150(5):2239-2248.
APA	Su, Yang,&Wu, Xiaolei.(2022).ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,150(5),2239-2248.
MLA	Su, Yang,et al."ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES".PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 150.5(2022):2239-2248.