Bestvina complex for group actions with a strict fundamental domain
Bestvina complex for group actions with a strict fundamental domain
We consider a strictly developable simple complex of finite groups G(Q). We show that Bestvina's construction for Coxeter groups applies in this more general setting to produce a complex that is equivariantly homotopy equivalent to the standard development. When G(Q) is non-positively curved, this implies that the Bestvina complex is a cocompact classifying space for proper actions of G of minimal dimension. As an application, we show that for groups that act properly and chamber transitively on a building of type (W, S), the dimension of the associated Bestvina complex is the virtual cohomological dimension of W.
We give further examples and applications in the context of Coxeter groups, graph products of finite groups, locally 6-large complexes of groups and groups of rational cohomological dimension at most one. Our calculations indicate that, because of its minimal cell structure, the Bestvina complex is well-suited for cohomological computations.
1277-1307
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Prytula, Tomasz P
8540bd1f-b0fd-40e8-b6d8-72c80cb05fdf
27 October 2020
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Prytula, Tomasz P
8540bd1f-b0fd-40e8-b6d8-72c80cb05fdf
Petrosyan, Nansen and Prytula, Tomasz P
(2020)
Bestvina complex for group actions with a strict fundamental domain.
Groups, Geometry and Dynamics, 14 (4), .
(doi:10.4171/GGD/581).
Abstract
We consider a strictly developable simple complex of finite groups G(Q). We show that Bestvina's construction for Coxeter groups applies in this more general setting to produce a complex that is equivariantly homotopy equivalent to the standard development. When G(Q) is non-positively curved, this implies that the Bestvina complex is a cocompact classifying space for proper actions of G of minimal dimension. As an application, we show that for groups that act properly and chamber transitively on a building of type (W, S), the dimension of the associated Bestvina complex is the virtual cohomological dimension of W.
We give further examples and applications in the context of Coxeter groups, graph products of finite groups, locally 6-large complexes of groups and groups of rational cohomological dimension at most one. Our calculations indicate that, because of its minimal cell structure, the Bestvina complex is well-suited for cohomological computations.
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Accepted/In Press date: 21 March 2019
Published date: 27 October 2020
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Local EPrints ID: 429301
URI: http://eprints.soton.ac.uk/id/eprint/429301
ISSN: 1661-7207
PURE UUID: d3af7d62-0115-4fe4-aa09-bc2011fa182a
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Date deposited: 26 Mar 2019 17:30
Last modified: 16 Mar 2024 07:42
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Author:
Tomasz P Prytula
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