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Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action

Chen, Lei (2020) Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action. Bulletin of the London Mathematical Society . ISSN 0024-6093. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20200730-083233007

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Abstract

In this paper, we study the action of Homeo₀ (M), the identity component of the group of homeomorphisms of an n-dimensional manifold M with an F_p-free action, on another manifold N of dimension n+k < 2n. We prove that if M is not an F_p-homology sphere, then N≅M×K for a homology manifold K such that the action of Homeo₀ (M) on M is standard and on K is trivial. In particular, for M = S_n a sphere, any nontrivial action is a generalization of the "coning-off" construction.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/blms.12399DOIArticle
https://arxiv.org/abs/1909.12515arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Lei0000-0002-5941-7914
Additional Information:© 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Received 25 October 2019; revised 5 June 2020. Version of Record online: 20 July 2020. This work is supported by NSF grant number DMS-2005409. We thank Shmuel Weinberger, Kathryn Mann and Benson Farb for helpful discussion. We also would like to thank the anonymous referee for comments.
Funders:
Funding AgencyGrant Number
NSFDMS‐2005409
Classification Code:2010 Mathematics Subject Classification: 57S05, 57S25, 37C85 (primary)
Record Number:CaltechAUTHORS:20200730-083233007
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200730-083233007
Official Citation:Chen, L. (2020), Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action. Bull. London Math. Soc.. doi:10.1112/blms.12399
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104654
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Jul 2020 15:41
Last Modified:30 Jul 2020 15:41

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