ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES
文献类型:期刊论文
作者 | Su, Yang3,4; Wu, Xiaolei1,2 |
刊名 | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
出版日期 | 2022-05-01 |
卷号 | 150期号:5页码:2239-2248 |
ISSN号 | 0002-9939 |
DOI | 10.1090/proc/15784 |
英文摘要 | 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. |
资助项目 | NSFC[11571343] ; ERC[662400] ; DFG[GZ 2047/1] ; DFG[390685813] |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | AMER MATHEMATICAL SOC |
WOS记录号 | WOS:000768891900036 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60181] |
专题 | 数学所 |
通讯作者 | Su, Yang |
作者单位 | 1.Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200348, Peoples R China 2.Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, HLM, Acad Math & Syst Sci, Beijing 100190, 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. |
入库方式: OAI收割
来源:数学与系统科学研究院
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