Volume 20, issue 2 (2020)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

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

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The Segal conjecture for infinite discrete groups

Wolfgang Lück

Algebraic & Geometric Topology 20 (2020) 965–986
Abstract

We formulate and prove a version of the Segal conjecture for infinite groups. For finite groups it reduces to the original version. The condition that G is finite is replaced in our setting by the assumption that there exists a finite model for the classifying space E ¯G for proper actions. This assumption is satisfied for instance for word hyperbolic groups or cocompact discrete subgroups of Lie groups with finitely many path components. As a consequence we get for such groups G that the zeroth stable cohomotopy of the classifying space BG is isomorphic to the I–adic completion of the ring given by the zeroth equivariant stable cohomotopy of E¯G for I the augmentation ideal.

Keywords
equivariant cohomotopy, Segal conjecture for infinite discrete groups
Mathematical Subject Classification 2010
Primary: 55P91
References
Publication
Received: 26 January 2019
Revised: 5 July 2019
Accepted: 9 August 2019
Published: 23 April 2020
Authors
Wolfgang Lück
Mathematisches Institut
Rheinische Wilhelms-Universität Bonn
Bonn
Germany
http://www.him.uni-bonn.de/lueck