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Reference: Kar, A, Kropholler, P and Nikolov, N et al., (2016). On growth of homology torsion in amenable groups. Mathematical Proceedings of the Cambridge Philosophical Society, 162 (2), 337-351.Citable link to this page:


On growth of homology torsion in amenable groups

Abstract: Suppose an amenable group G is acting freely on a simply connected simplicial complex (Formula presented.) with compact quotient X. Fix n ≥ 1, assume (Formula presented.) and let (Hi ) be a Farber chain in G. We prove that the torsion of the integral homology in dimension n of (Formula presented.) grows subexponentially in [G : Hi ]. This fails if X is not compact. We provide the first examples of amenable groups for which torsion in homology grows faster than any given function. These examples include some solvable groups of derived length 3 which is the minimal possible.

Publication status:PublishedPeer Review status:Peer reviewedVersion:Accepted manuscriptDate of acceptance:2016 Funder: Engineering and Physical Sciences Research Council   Notes:COPYRIGHT: © Cambridge Philosophical Society 2016. This is the accepted manuscript version of the article. The final version is available online from Cambridge University Press at: [10.1017/S030500411600058X]

Bibliographic Details

Publisher: Cambridge University Press

Publisher Website: http://www.cambridge.org/uk/

Journal: Mathematical Proceedings of the Cambridge Philosophical Societysee more from them

Publication Website: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society

Volume: 162

Issue: 2

Extent: 337-351

Issue Date: 2016-07-14


Doi: https://doi.org/10.1017/S030500411600058X

Eissn: 1469-8064

Issn: 0305-0041

Uuid: uuid:6f10f61a-df42-4fd2-8bd7-30cf536f126f

Urn: uri:6f10f61a-df42-4fd2-8bd7-30cf536f126f

Pubs-id: pubs:527431 Item Description

Type: journal-article;

Version: Accepted manuscriptKeywords: math.GR math.GR math.AT math.KT Article in Press


Author: Kar, A - - - Kropholler, P - - - Nikolov, N - institutionUniversity of Oxford Oxford, MPLS, Mathematical Institute - - - - Biblio

Source: https://ora.ox.ac.uk/objects/uuid:6f10f61a-df42-4fd2-8bd7-30cf536f126f


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