Dehn functions of subgroups of right-angled Artin groups

Abstract

The question of what is a possible range for the Dehn functions (a.k.a. isoperimetric spectrum) for certain classes of groups is a natural and interesting one. Due to works of many authors starting with Gromov, we know a lot about the isoperimetric spectrum for the class of all finitely presented groups. Much less is known for other natural classes of groups, such as subgroups of CAT(0) groups or of right-angled Artin groups. The isoperimetric spectrum for the subgroups of right-angled Artin groups, known so far, consists of polynomials up to degree 4 and exponential functions. We extend the knowledge of this spectrum to contain the set of all positive integers. We start by constructing a series of free-by-cyclic groups whose monodromy automorphisms grow as n^k, which admit a virtual embedding into suitable right-angled Artin groups. As a consequence we produce examples of right-angled Artin groups containing finitely presented subgroups whose Dehn functions grow as n^(k+2).