Quotients of mapping class groups from $\text{Out}(F_n)$

TL;DR

This paper provides a concise proof that mapping class groups can involve any finite group, utilizing free quotients of surface groups and existing results, thus simplifying previous complex proofs.

Contribution

It offers a streamlined proof of a known result about the universality of finite groups within mapping class groups, connecting it with free quotients and Gilman's work.

Findings

Mapping class groups involve all finite groups

Simplified proof approach using free quotients

Connections to Gilman's results and Dunfield-Thurston

Abstract

We give a short proof of Masbaum and Reid's result that mapping class groups involve any finite group, appealing to free quotients of surface groups and a result of Gilman, following Dunfield-Thurston.