Divergence in right-angled Coxeter groups

TL;DR

This paper investigates the divergence properties of 2-dimensional right-angled Coxeter groups, characterizing those with linear and quadratic divergence and constructing examples with divergence of any polynomial degree, using the Davis complex structure.

Contribution

It provides a complete characterization of divergence types in 2D right-angled Coxeter groups and constructs groups with arbitrary polynomial divergence degrees.

Findings

Characterization of linear and quadratic divergence in these groups

Construction of groups with divergence polynomial of any degree

Use of Davis complex walls in proofs

Abstract

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.