Filling loops at infinity in the mapping class group

TL;DR

This paper investigates the Dehn function at infinity in the mapping class group, establishing a polynomial upper bound of degree four, similar to that of right-angled Artin groups, advancing understanding of geometric properties of these groups.

Contribution

It provides the first polynomial upper bound of degree four for the Dehn function at infinity in the mapping class group, aligning it with right-angled Artin groups.

Findings

Dehn function at infinity in the mapping class group is polynomial of degree four

Mapping class group shares similar geometric properties with right-angled Artin groups

Establishes a new upper bound for the Dehn function at infinity

Abstract

We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angled Artin groups.