Right-angled Coxeter groups with Menger curve boundary

Abstract

We find a sufficient condition for a nerve of a hyperbolic right-angled Coxeter group, under which the boundary of the group is homeomorphic to the Menger curve. We show that this condition is satisfied by many triangulations of surfaces with boundary and other 2-complexes, as well as by some triangulations of disks $D^n$ for arbitrary $n\ge 3$.

This is the accepted version of the following article: Right-angled Coxeter groups with Menger curve boundary, which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.12609