Reflection groups of geodesic spaces and Coxeter groups

Details Reflection groups of geodesic spaces and Coxeter groups Reflection groups of geodesic spaces and Coxeter groups

2004-05-28

arxiv.org/abs/math/0405552v1

Mathematics

Group Theory

Scientific paper

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.

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