Volume 17, issue 1 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Equivariant vector bundles over classifying spaces for proper actions

Dieter Degrijse and Ian J Leary

Algebraic & Geometric Topology 17 (2017) 131–156
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.

Keywords
equivariant vector bundles, classifying spaces for proper actions
Mathematical Subject Classification 2010
Primary: 19L47
Secondary: 20F65, 55N15, 55N91
References
Publication
Received: 1 May 2015
Revised: 19 May 2016
Accepted: 17 June 2016
Published: 26 January 2017
Authors
Dieter Degrijse
Department of Mathematical Sciences
University of Copenhagen
Universitetsparken
2100 Copenhagen
Denmark
School of Mathematics, Statistics & Applied Mathematics
NUI Galway
University Road
Galway
Ireland
Ian J Leary
School of Mathematical Sciences
University of Southampton
Southhampton
SO17 1BJ
United Kingdom