Dehn functions and finiteness properties of subgroups of perturbed right-angled Artin groups

TL;DR

This paper introduces perturbed right-angled Artin groups, constructing CAT(0) groups with finitely presented subgroups that have diverse finiteness properties and Dehn functions, expanding understanding of geometric group theory.

Contribution

It defines a new class of groups by gluing Bieri double groups into right-angled Artin groups and explores their finiteness properties and Dehn functions.

Findings

Existence of CAT(0) groups with finitely presented subgroups not of type FP_3

Construction of subgroups with exponential Dehn functions

Construction of subgroups with polynomial Dehn functions of prescribed degree

Abstract

We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups containing finitely presented subgroups which are not of type $\mathrm{FP}_3$, and have exponential, or polynomial Dehn functions of prescribed degree.