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New York Journal of Mathematics 8 (2002), 1-7.

A model for the universal space for proper actions of a hyperbolic group

David Meintrup and Thomas Schick

Published: January 3, 2002
Keywords: universal space for proper actions, Rips complex, word hyperbolic group, Gromov hyperbolic group, fixed point set, conjugacy classes of finite subgroups, finiteness properties for universal spaces, classifying space for proper actions, G-CW-complex
Subject: 20F67, 55R35, 57M07


{ Let $G$ 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 subgroup $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $\eg$ for proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.}

The first author has been supported by the DAAD

Author information:
David Meintrup:
Universit\"at der Bundeswehr, M\"unchen, Germany

Thomas Schick :
Universit\"at G\"ottingen, Germany