Every Coxeter group acts amenably on a compact space

TL;DR

This paper demonstrates that all Coxeter groups can act amenably on compact spaces and possess finite asymptotic dimension, highlighting their geometric and analytical properties.

Contribution

It establishes the amenability of Coxeter groups' actions on compact spaces and confirms their finite asymptotic dimension, advancing understanding of their geometric group theory.

Findings

Coxeter groups admit amenable actions on compact spaces

Coxeter groups have finite asymptotic dimension

Provides new insights into the geometric properties of Coxeter groups

Abstract

Coxeter groups admit amenable actions on compact spaces. Moreover, they have finite asymptotic dimension.