A Model for the Universal Space for Proper Actions of a Hyperbolic Group

By David Meintrup, Thomas Schick. 2002

59 citations recorded by the source corpus.

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 iscontractible for every finite subgroup H of G. Thisisthe 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 hasonly finitely many conjugacy classes of finite subgroups.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f737539db810c55a71a26acf6c7a25213a794857

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Survey on Classifying Spaces for Families of Subgroups (2003, unknown): “The following result is proved in [60], [61].”
The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, background): “If G is word hyperbolic in the sense of Gromov, then the Rips-complex is a finite model [216, 217].”
Injective hulls of certain discrete metric spaces and groups (2011, background): “A corresponding result holds for the Rips complex PD(ΓS), provided the maximal simplex diameter D is chosen sufficiently large (see [28]).”
The K-theoretic Farrell–Jones conjecture for hyperbolic groups (2007, background): “Moreover, the barycentric subdivision of Pd(G) is a G-CW-complex which is for large enough d a model for the classifying space for proper G-actions (see [47]), but we will not use this fact.”