Local Connectivity of Right-angled Coxeter group boundaries

2025/07/23 by Michael Mihalik, Mihalik, Michael, Kim Ruane +3
Mathematics · #20F55 #20F65 (primary) #20F67 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2507.17574

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide conditions on the defining graph of a right-angled Coxeter group presentation that guarantees the boundary of any CAT(0) space on which the group acts geometrically will be locally connected. This is a revised version of a published paper where we streamline some of the proofs and add figures.

Citations

• Visual Decompositions of Coxeter Groups

Related

• A classification of right-angled Coxeter groups with no 3-flats and locally connected boundary
• Right-angled Coxeter groups with totally disconnected Morse boundaries
• Right-angled Coxeter groups with non-planar boundary
• Actions of Right-Angled Coxeter Groups on the Croke Kleiner Spaces
• Connectivity of Coxeter group Morse boundaries