A construction of hyperbolic Coxeter groups

TL;DR

This paper presents a straightforward method to construct Gromov hyperbolic Coxeter groups with arbitrarily large virtual cohomological dimension, expanding the known examples and enabling new groups with interesting asphericity properties.

Contribution

The authors introduce a simple construction technique for hyperbolic Coxeter groups that can produce groups with large virtual cohomological dimension and novel asphericity features.

Findings

Constructed new hyperbolic Coxeter groups with large virtual cohomological dimension

Provided examples of groups with unique asphericity properties

Expanded the class of known Gromov hyperbolic Coxeter groups

Abstract

We give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct e.g. new groups having some interesting asphericity properties.