An explicit presentation for asymptotically rigid mapping class groups

TL;DR

This paper provides explicit presentations for asymptotically rigid mapping class groups by expressing them as quotients of fundamental groups of graphs of groups, enhancing understanding of their algebraic structure.

Contribution

It introduces a new explicit presentation method for these groups, building on previous work and connecting them to fundamental groups of graphs of groups.

Findings

Explicit presentations for asymptotically rigid mapping class groups

Connections established between these groups and fundamental groups of graphs of groups

Enhanced understanding of the algebraic structure of these groups

Abstract

We show that several families of asymptotically rigid mapping class groups arise as explicit quotients of the fundamental group of a graph of groups, with mapping class groups as vertex and edge stabilizers. Using this description, and building on the work of Labru\`ere and Paris, we compute explicit presentations for asymptotically rigid mapping class groups of surfaces.