A Subgroup of a Direct Product of Free Groups whose Dehn Function has a Cubic Lower Bound

TL;DR

This paper proves that a specific finitely presented subgroup of a direct product of three free groups has a Dehn function with at least cubic growth, indicating complex geometric properties.

Contribution

It introduces a new example of a subgroup with a cubic lower bound on its Dehn function within a direct product of free groups.

Findings

Dehn function of the subgroup has at least cubic growth

Provides insight into the geometric complexity of certain subgroups

Advances understanding of isoperimetric inequalities in free group products

Abstract

We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.