Higher Dehn functions of Bestvina-Brady groups

Abstract

The k-dimensional Dehn function of a group captures the difficulty of filling k-spheres by (k+1)-balls in a complex that models the group. I will talk about a method for modifying fillings of spheres in the complex associated with a right-angled Artin group. This can be used to obtain sharp bounds on the higher Dehn functions of certain subgroups called Bestvina-Brady groups. Similar ideas lead to estimates on higher divergence functions in right-angled Artin groups. This is joint work with Aaron Abrams, Noel Brady, Moon Duchin, and Robert Young.