Relative hyperbolicity and right-angled Coxeter groups

TL;DR

This paper demonstrates that right-angled Coxeter groups exhibit relative hyperbolicity with respect to certain rank-2 parabolic subgroups, providing insights into their geometric structure.

Contribution

It establishes the relative hyperbolicity of right-angled Coxeter groups relative to specific parabolic subgroups, extending understanding of their geometric properties.

Findings

Right-angled Coxeter groups are relatively hyperbolic.

Identification of natural rank-2 parabolic subgroups.

Application of Farb's definition of relative hyperbolicity.

Abstract

We show that right-angled Coxeter groups are relatively hyperbolic in the sense defined by Farb, relative to a natural collection of rank-2 parabolic subgroups.