Bredon cohomological finiteness conditions for generalisations of Thompson groups
Bredon cohomological finiteness conditions for generalisations of Thompson groups
We define a family of groups that generalises Thompson’s groups T and G, and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show that for a given finite subgroup Q there are finitely many conjugacy classes of finite subgroups isomorphic to Q. We consider groups of type quasi-F−−∞. This is a property slightly weaker than possessing a finite type model for the classifying space for proper actions E−−G. We give criteria for the T versions of our groups to be of type quasi-F−−∞. We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.
931-959
Martinez-Perez, C.
cb55fc61-2a74-4072-93d3-74a882ad5fdc
Nucinkis, Brita E.A.
86582f48-4da6-4868-8700-d16ea4236c86
2013
Martinez-Perez, C.
cb55fc61-2a74-4072-93d3-74a882ad5fdc
Nucinkis, Brita E.A.
86582f48-4da6-4868-8700-d16ea4236c86
Martinez-Perez, C. and Nucinkis, Brita E.A.
(2013)
Bredon cohomological finiteness conditions for generalisations of Thompson groups.
Groups, Geometry and Dynamics, 7 (4), .
Abstract
We define a family of groups that generalises Thompson’s groups T and G, and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show that for a given finite subgroup Q there are finitely many conjugacy classes of finite subgroups isomorphic to Q. We consider groups of type quasi-F−−∞. This is a property slightly weaker than possessing a finite type model for the classifying space for proper actions E−−G. We give criteria for the T versions of our groups to be of type quasi-F−−∞. We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.
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Submitted date: 3 May 2011
e-pub ahead of print date: 20 November 2013
Published date: 2013
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Local EPrints ID: 183819
URI: http://eprints.soton.ac.uk/id/eprint/183819
ISSN: 1661-7207
PURE UUID: 60835196-91e3-48c8-a779-05d3204e74c6
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Date deposited: 04 May 2011 11:13
Last modified: 14 Mar 2024 03:05
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Author:
C. Martinez-Perez
Author:
Brita E.A. Nucinkis
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