Projective reflection groups of finite covolume

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Balthazar Fléchelles, Seunghoon Hwang
DOI: 10.48550/arxiv.2601.22067
Cited by: 0

Abstract

We show that the Coxeter polytopes that have finite volume in their Vinberg domains are exactly the quasiperfect Coxeter polytopes of negative type, i.e. the Coxeter polytopes that are contained in their properly convex Vinberg domain, at the exception of some vertices that are C^1 points of the boundary. As a corollary, we show that for reflection groups à la Vinberg, the Vinberg domain is the only invariant properly convex domain if and only if the action is of finite covolume on the Vinberg domain and the dimension is at least 2.

Fields of Study & Subjects

Geometric and Algebraic Topology Advanced Algebra and Geometry Mathematics and Applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
29 January 2026
Language
EN
Document type
Preprint