Reflection groups of geodesic spaces and Coxeter groups

2004/05/28 by Tetsuya Hosaka, Hosaka, Tetsuya
Computer Science · Mathematics · #20F55 #20F65 #57M07 #Advanced Combinatorial Mathematics #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GR #msc:20F55 #msc:20F65 #msc:57M07

paper · pdf · doi:10.48550/arxiv.math/0405552

arxiv created 2004/05/28 · openalex publication_date 2004/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Convex cocompactness for Coxeter groups
• Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces
• On reflection subgroups of finite Coxeter groups
• Reflection Groups. A Contribution to the Handbook of Algebra
• On tilings defined by discrete reflection groups