Local Connectivity of Right-angled Coxeter group boundaries

TL;DR

This paper establishes specific conditions on the defining graph of right-angled Coxeter groups that ensure their boundaries are locally connected in any CAT(0) space they act on, refining previous proofs.

Contribution

It identifies new graph-based criteria guaranteeing local connectivity of boundaries for right-angled Coxeter groups, improving proof clarity and presentation.

Findings

Boundary local connectivity is guaranteed under new graph conditions

Streamlined proofs and added figures enhance understanding

Provides a revised, clearer version of previous results

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.