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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 28, Issue 5

Issues

Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V

Conchita Martínez-Pérez / Francesco Matucci
  • Département de Mathématiques, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, 91405 Orsay Cedex, France
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/ Brita E. A. Nucinkis
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  • Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom of Great Britain and Northern Ireland
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Published Online: 2015-10-20 | DOI: https://doi.org/10.1515/forum-2014-0176

Abstract

We consider generalisations of Thompson’s group V, denoted by Vr(Σ), which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, Vr(Σ) is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type F and that this implies that also centralisers of finite subgroups are of type F.

Keywords: Cohomological finiteness conditions; Thompson groups

MSC 2010: 20J05

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About the article


Received: 2014-10-06

Revised: 2015-02-03

Published Online: 2015-10-20

Published in Print: 2016-09-01


This work was partially funded by an LMS Scheme 4 Grant 41209. The first named author was supported by Gobierno de Aragón, European Regional Development Funds and MTM2010-19938-C03-03. The second author gratefully acknowledges the Fondation Mathématique Jacques Hadamard (ANR-10-CAMP-0151-02 – FMJH – Investissement d’Avenir) for the support received during the development of this work.


Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 909–921, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0176.

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