Mapping class groups have finite asymptotic dimension

TL;DR

This paper proves that mapping class groups of compact orientable surfaces have finite asymptotic dimension by representing them as fundamental groups of developable complexes of groups.

Contribution

It establishes the finite asymptotic dimension of mapping class groups using a novel approach involving complexes of groups.

Findings

Mapping class groups have finite asymptotic dimension.

The proof uses developable complexes of groups.

Provides new insights into geometric group theory.

Abstract

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.