Dehn functions of coabelian subgroups of direct products of groups

TL;DR

This paper introduces new methods to accurately compute Dehn functions for coabelian subgroups of direct product groups, extending previous work and applying to various complex group structures.

Contribution

It develops novel techniques for calculating Dehn functions of coabelian subgroups, generalizing prior results and enabling applications to diverse group classes.

Findings

New methods for precise Dehn function computation

Generalization of previous results in geometric group theory

Applications to free groups, Artin groups, and groups with finiteness properties

Abstract

We develop new methods for computing the precise Dehn functions of coabelian subgroups of direct products of groups, that is, subgroups which arise as kernels of homomorphisms from the direct product onto a free abelian group. These improve and generalise previous results by Carter and Forester on Dehn functions of level sets in products of simply connected cube complexes, by Bridson on Dehn functions of cocyclic groups and by Dison on Dehn functions of coabelian groups. We then provide several applications of our methods to subgroups of direct products of free groups, to groups with interesting geometric finiteness properties and to subgroups of direct products of right-angled Artin groups.