Free products of abelian groups in mapping class groups

TL;DR

This paper constructs new examples of certain subgroups within mapping class groups, demonstrating their geometric properties and showing they are undistorted, which advances understanding of the group's structure.

Contribution

It introduces a novel family of parabolically geometrically finite subgroups in mapping class groups and proves their undistorted nature.

Findings

New examples of parabolically geometrically finite subgroups

Proof of undistorted embedding in Mod(S)

Enhances understanding of subgroup geometry in mapping class groups

Abstract

We construct a new family of examples of parabolically geometrically finite subgroups of the mapping class group in the sense of Dowdall-Durham-Leininger-Sisto and prove they are undistorted in Mod($S$).