The asymptotic dimension of quotients by finite groups

TL;DR

This paper proves that for a proper metric space acted upon by a finite group, the quotient space's asymptotic dimension remains unchanged from the original space, highlighting a key invariance property.

Contribution

It establishes that the asymptotic dimension is preserved under quotients by finite groups acting by isometries on proper metric spaces.

Findings

Asymptotic dimension of $F\backslash X$ equals that of $X$

Finite group actions do not alter the asymptotic dimension

Provides a fundamental invariance result for geometric group theory

Abstract

Let $X$ be a proper metric space and let $F$ be a finite group acting on $X$ by isometries. We show that the asymptotic dimension of $F\backslash X$ is the same as the asymptotic dimension of $X$.