The University of Southampton
University of Southampton Institutional Repository

Uncountably many groups of type FP

Uncountably many groups of type FP
Uncountably many groups of type FP
We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ 2, and compactly-supported cohomology of these groups. For each n at least four we construct a closed aspherical n-manifold that admits an uncountable family of acyclic regular coverings with non-isomorphic covering groups.
0024-6115
246-276
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e

Leary, Ian J. (2018) Uncountably many groups of type FP. Proceedings of the London Mathematical Society, 117 (2), 246-276. (doi:10.1112/plms.12135).

Record type: Article

Abstract

We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ 2, and compactly-supported cohomology of these groups. For each n at least four we construct a closed aspherical n-manifold that admits an uncountable family of acyclic regular coverings with non-isomorphic covering groups.

Text
uctblefp.pdf - Author's Original
Download (360kB)
Text
uctblefp - Author's Original
Download (309kB)
Text
uctblefp.pdf - Accepted Manuscript
Download (302kB)

More information

In preparation date: 21 December 2015
Submitted date: 21 February 2017
Accepted/In Press date: 20 February 2018
e-pub ahead of print date: 30 March 2018
Published date: August 2018
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 385273
URI: http://eprints.soton.ac.uk/id/eprint/385273
ISSN: 0024-6115
PURE UUID: 92e7ee87-be3e-40b1-8ce7-444ffe958d9a
ORCID for Ian J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

Catalogue record

Date deposited: 18 Jan 2016 14:37
Last modified: 15 Mar 2024 03:36

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×