Chen, Lei (2021) Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action. Bulletin of the London Mathematical Society, 53 (1). pp. 75-81. ISSN 0024-6093. doi:10.1112/blms.12399. 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.
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| Additional Information: | © 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Issue Online: 01 February 2021; Version of Record online: 20 July 2020; Manuscript revised: 05 June 2020; Manuscript received: 25 October 2019. 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. | |||||||||
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| Issue or Number: | 1 | |||||||||
| Classification Code: | 2010 Mathematics Subject Classification: 57S05, 57S25, 37C85 (primary) | |||||||||
| DOI: | 10.1112/blms.12399 | |||||||||
| Record Number: | CaltechAUTHORS:20200730-083233007 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200730-083233007 | |||||||||
| Official Citation: | Chen, L. (2021), Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action. Bull. London Math. Soc., 53: 75-81. https://doi.org/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: | 16 Nov 2021 18:33 |
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