Dehn functions of subgroups of right-angled Artin groups

TL;DR

This paper constructs specific right-angled Artin groups with subgroups exhibiting polynomially growing monodromy automorphisms, leading to finitely presented subgroups with Dehn functions growing as a higher polynomial, revealing new geometric properties.

Contribution

It demonstrates the existence of right-angled Artin groups with subgroups having polynomially growing monodromy automorphisms and corresponding Dehn functions, advancing understanding of their geometric complexity.

Findings

Existence of right-angled Artin groups with free-by-cyclic subgroups with automorphisms growing as n^k

Construction of finitely presented subgroups with Dehn functions growing as n^{k+2}

New examples illustrating diverse Dehn function growth rates in right-angled Artin groups

Abstract

We show that for each positive integer $k$ there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as $n^k$. As a consequence we produce examples of right-angled Artin groups containing finitely presented subgroups whose Dehn functions grow as $n^{k+2}$.