Isoperimetric inequalities for Poincaré duality groups
Isoperimetric inequalities for Poincaré duality groups
We show that every oriented n-dimensional Poincaré duality group over a ∗-ring R is amenable or satisfies a linear homological isoperimetric inequality in dimension n−1. As an application, we prove the Tits alternative for such groups when n=2. We then deduce a new proof of the fact that when n=2 and R=Z then the group in question is a surface group.
4685-4698
Kielak, Dawid
349c0efc-9537-400e-b17a-8feb7047c419
Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
November 2021
Kielak, Dawid
349c0efc-9537-400e-b17a-8feb7047c419
Kropholler, Peter
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Kielak, Dawid and Kropholler, Peter
(2021)
Isoperimetric inequalities for Poincaré duality groups.
Proceedings of the American Mathematical Society, 149 (11), .
(doi:10.1090/proc/15596).
Abstract
We show that every oriented n-dimensional Poincaré duality group over a ∗-ring R is amenable or satisfies a linear homological isoperimetric inequality in dimension n−1. As an application, we prove the Tits alternative for such groups when n=2. We then deduce a new proof of the fact that when n=2 and R=Z then the group in question is a surface group.
Text
2008.07812
- Accepted Manuscript
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Accepted/In Press date: 17 March 2021
Published date: November 2021
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Funding Information:
Received by the editors August 15, 2020, and, in revised form, January 19, 2021, March 8, 2021, and March 17, 2021. 2020 Mathematics Subject Classification. Primary 20J06, 57P10. The first author was partly supported by a grant from the German Science Foundation (DFG) within the Priority Programme SPP2026 ‘Geometry at Infinity’. This work had received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant agreement No. 850930.
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© 2021 American Mathematical Society. All rights reserved.
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Local EPrints ID: 447958
URI: http://eprints.soton.ac.uk/id/eprint/447958
ISSN: 0002-9939
PURE UUID: 1dd96e0c-8f70-4c9b-b1e4-1f941b8c6c2f
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Date deposited: 29 Mar 2021 16:30
Last modified: 06 Jun 2024 01:51
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Author:
Dawid Kielak
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