Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reflection groups of geodesic spaces and Coxeter groups   H.S.M. Coxeter showed that a group $\Gamma$ is a finite reflection group of
an Euclidean space if and only if $\Gamma$ is a finite Coxeter group. In this
paper, we define {\it reflections} of geodesic spaces in general, and we prove
that $\Gamma$ is a cocompact discrete reflection group of some geodesic space
if and only if $\Gamma$ is a Coxeter group.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat