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2020 The Segal conjecture for infinite discrete groups
Wolfgang Lück
Algebr. Geom. Topol. 20(2): 965-986 (2020). DOI: 10.2140/agt.2020.20.965

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.

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Wolfgang Lück. "The Segal conjecture for infinite discrete groups." Algebr. Geom. Topol. 20 (2) 965 - 986, 2020. https://doi.org/10.2140/agt.2020.20.965

Information

Received: 26 January 2019; Revised: 5 July 2019; Accepted: 9 August 2019; Published: 2020
First available in Project Euclid: 30 April 2020

MathSciNet: MR4092316
zbMATH: 07195381
Digital Object Identifier: 10.2140/agt.2020.20.965

Subjects:
Primary: 55P91

Rights: Copyright © 2020 Mathematical Sciences Publishers

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