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29 March 2024
 
  » arxiv » math.MG/0209163

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A Model for the Universal Space for Proper Actions of a Hyperbolic Group
David Meintrup Thomas Schick ;
Date 13 Sep 2002
Journal New York J. Math.}, 8:1--7 (electronic), 2002
Subject Metric Geometry; Geometric Topology MSC-class: 20F67 (hyperbolic groups), 55R35 (classifying spaces), 57M07 | math.MG math.GT
AffiliationUniversitaet der Bundeswehr Muenchen) Thomas Schick (Universitaet Goettingen
AbstractLet $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroups $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $e.g.$ of proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.
Source arXiv, math.MG/0209163
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