On the relative hyperbolicity and manifold structure of certain right-angled Coxeter groups

TL;DR

This paper investigates the manifold and relative hyperbolic structures of right-angled Coxeter groups with planar nerves and applies these findings to address the quasi-isometry problem for this class.

Contribution

It provides new insights into the manifold and hyperbolic structures of right-angled Coxeter groups with planar nerves and explores their quasi-isometry classifications.

Findings

Established conditions for manifold structures in these groups.

Demonstrated relative hyperbolicity in specific cases.

Applied results to quasi-isometry classification.

Abstract

In this article, we study the manifold structure and the relatively hyperbolic structure of right-angled Coxeter groups with planar nerves. We then apply our results to the quasi-isometry problem for this class of right-angled Coxeter groups.