Reflection groups of geodesic spaces and Coxeter groups

Tetsuya Hosaka

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Reflection groups of geodesic spaces and Coxeter groups

Tetsuya Hosaka

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Abstract

H.S.M. Coxeter showed that a group $Γ$ is a finite reflection group of an Euclidean space if and only if $Γ$ is a finite Coxeter group. In this paper, we define {\it reflections} of geodesic spaces in general, and we prove that $Γ$ is a cocompact discrete reflection group of some geodesic space if and only if $Γ$ is a Coxeter group.

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Tetsuya Hosaka. 2004-05-28. Reflection groups of geodesic spaces and Coxeter groups. https://arxiv.org/abs/math/0405552

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