Equivariant vector bundles over classifying spaces for proper actions
Equivariant vector bundles over classifying spaces for proper actions
We give the first examples of discrete groups G for which there exist compatible collections of representations over the finite subgroups of G that do not come from any G-equivariant (virtual) vector bundle on the classifying space for proper actions of G. This implies that the Atiyah-Hirzebruch spectral sequence for computing the equivariant topological K-theory of the classifying space for proper actions of G has non-zero differentials. We show that this cannot happen for right-angled Coxeter groups, and we compute K-theory for these groups.
131-156
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
26 January 2017
Degrijse, Dieter
fb33133b-fe90-42a5-8214-409c210906df
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Degrijse, Dieter and Leary, Ian J.
(2017)
Equivariant vector bundles over classifying spaces for proper actions.
Algebraic & Geometric Topology, 17 (1), .
(doi:10.2140/agt.2017.17.131).
Abstract
We give the first examples of discrete groups G for which there exist compatible collections of representations over the finite subgroups of G that do not come from any G-equivariant (virtual) vector bundle on the classifying space for proper actions of G. This implies that the Atiyah-Hirzebruch spectral sequence for computing the equivariant topological K-theory of the classifying space for proper actions of G has non-zero differentials. We show that this cannot happen for right-angled Coxeter groups, and we compute K-theory for these groups.
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Submitted date: 28 April 2015
Accepted/In Press date: 17 June 2016
e-pub ahead of print date: 26 January 2017
Published date: 26 January 2017
Organisations:
Pure Mathematics
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Local EPrints ID: 376599
URI: http://eprints.soton.ac.uk/id/eprint/376599
ISSN: 1472-2747
PURE UUID: 5987748b-0870-47b0-8091-ec9715157242
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Date deposited: 05 May 2015 15:01
Last modified: 15 Mar 2024 03:36
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Author:
Dieter Degrijse
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