Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Model for the Universal Space for Proper Actions of a Hyperbolic Group   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 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.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin