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2017 Equivariant vector bundles over classifying spaces for proper actions
Dieter Degrijse, Ian Leary
Algebr. Geom. Topol. 17(1): 131-156 (2017). DOI: 10.2140/agt.2017.17.131

Abstract

Let G be an infinite discrete group and let E ¯G be a classifying space for proper actions of G. Every G–equivariant vector bundle over E ¯G gives rise to a compatible collection of representations of the finite subgroups of G. We give the first examples of groups G with a cocompact classifying space for proper actions E¯ G admitting a compatible collection of representations of the finite subgroups of G that does not come from a G–equivariant (virtual) vector bundle over E ¯G. This implies that the Atiyah–Hirzebruch spectral sequence computing the G–equivariant topological K–theory of E ¯G has nonzero differentials. On the other hand, we show that for right-angled Coxeter groups this spectral sequence always collapses at the second page and compute the K–theory of the classifying space of a right-angled Coxeter group.

Citation

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Dieter Degrijse. Ian Leary. "Equivariant vector bundles over classifying spaces for proper actions." Algebr. Geom. Topol. 17 (1) 131 - 156, 2017. https://doi.org/10.2140/agt.2017.17.131

Information

Received: 1 May 2015; Revised: 19 May 2016; Accepted: 17 June 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1378.19001
MathSciNet: MR3604375
Digital Object Identifier: 10.2140/agt.2017.17.131

Subjects:
Primary: 19L47
Secondary: 20F65, 55N15, 55N91

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 1 • 2017
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