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Pairings, duality, amenability and bounded cohomology

Pairings, duality, amenability and bounded cohomology
Pairings, duality, amenability and bounded cohomology
We give a new perspective on the homological characterisations of amenability given by Johnson and Ringrose in the context of bounded cohomology and by Block and Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterisations. We apply these ideas to give a new proof of non- vanishing for the bounded cohomology of a free group.
amenability, uniformly finite homology, group cohomology, bounded cohomology, duality, hochschild cohomology.
1435-9855
1513-1518
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wright, Nick
f4685b8d-7496-47dc-95f0-aba3f70fbccd

Brodzki, Jacek, Niblo, Graham A. and Wright, Nick (2012) Pairings, duality, amenability and bounded cohomology. Journal of the European Mathematical Society, 14 (5), Autumn Issue, 1513-1518. (doi:10.4171/JEMS/338).

Record type: Article

Abstract

We give a new perspective on the homological characterisations of amenability given by Johnson and Ringrose in the context of bounded cohomology and by Block and Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterisations. We apply these ideas to give a new proof of non- vanishing for the bounded cohomology of a free group.

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More information

Accepted/In Press date: 12 March 2010
Published date: 2012
Keywords: amenability, uniformly finite homology, group cohomology, bounded cohomology, duality, hochschild cohomology.
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 79402
URI: https://eprints.soton.ac.uk/id/eprint/79402
ISSN: 1435-9855
PURE UUID: 07be4cb1-f208-4b85-8ddc-c33e52db1a2e
ORCID for Graham A. Niblo: ORCID iD orcid.org/0000-0003-0648-7027
ORCID for Nick Wright: ORCID iD orcid.org/0000-0003-4884-2576

Catalogue record

Date deposited: 15 Mar 2010
Last modified: 20 Jul 2019 01:21

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