Coxeter groups and random groups

2014/11/06 by Danny Calegari, Calegari, Danny
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1411.1506

18 pages, 14 figures; version 2 incorporates referee's corrections

openalex publication_date 2014/11/06 · arxiv created 2015/04/04 · arxiv updated 2015/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of the family, with overwhelming probability.

Related

• 3-manifolds everywhere
• Convex cocompactness for Coxeter groups
• A threshold for relative hyperbolicity in random right-angled Coxeter groups
• Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces
• Random groups are not n-cubulated