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Uncountably many quasi-isometry classes of groups of type FP

Uncountably many quasi-isometry classes of groups of type FP
Uncountably many quasi-isometry classes of groups of type FP

In an earlier paper, one of the authors constructed uncountable families of groups of type F P and of n-dimensional Poincaré duality groups for each n ≥ 4. We show that those groups com-prise uncountably many quasi-isometry classes. We deduce that for each n ≥ 4 there are uncountably many quasi-isometry classes of acyclic n-manifolds admitting free cocompact properly discontinuous discrete group actions.

0002-9327
1931-1944
Kropholler, Robert P.
4558694c-0458-4d2e-96a4-4949afbf9bff
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Soroko, Ignat
6a2dba6c-6bad-4e2d-a82e-a9f84dd755cf
Kropholler, Robert P.
4558694c-0458-4d2e-96a4-4949afbf9bff
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Soroko, Ignat
6a2dba6c-6bad-4e2d-a82e-a9f84dd755cf

Kropholler, Robert P., Leary, Ian J. and Soroko, Ignat (2020) Uncountably many quasi-isometry classes of groups of type FP. American Journal of Mathematics, 142 (6), 1931-1944. (doi:10.1353/ajm.2020.0048).

Record type: Article

Abstract

In an earlier paper, one of the authors constructed uncountable families of groups of type F P and of n-dimensional Poincaré duality groups for each n ≥ 4. We show that those groups com-prise uncountably many quasi-isometry classes. We deduce that for each n ≥ 4 there are uncountably many quasi-isometry classes of acyclic n-manifolds admitting free cocompact properly discontinuous discrete group actions.

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In preparation date: 20 December 2017
Accepted/In Press date: 9 August 2018
e-pub ahead of print date: 11 November 2020
Published date: 6 December 2020
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Identifiers

Local EPrints ID: 416670
URI: http://eprints.soton.ac.uk/id/eprint/416670
DOI: doi:10.1353/ajm.2020.0048
ISSN: 0002-9327
PURE UUID: 3ecd9859-6a83-4ff2-a300-dca5b0da72db
ORCID for Ian J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

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Date deposited: 04 Jan 2018 17:30
Last modified: 16 Mar 2024 06:03

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Author: Robert P. Kropholler
Author: Ian J. Leary ORCID iD
Author: Ignat Soroko

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