Pushing fillings in right-angled Artin groups

Abstract

We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence functions, finding that the k-dimensional divergence of a RAAG is bounded by r^{2k+2}. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties "at infinity," are defined here as a family of quasi-isometry invariants of groups; thus, these results give new information about the QI classification of RAAGs. By pushing along the height gradient, we also show that the k-th order Dehn function of a Bestvina-Brady group is bounded by V^{(2k+2)/k}. We construct a class of RAAGs called "orthoplex groups" which show that each of these upper bounds is sharp.

The result on the Dehn function at infinity in mapping class groups has been moved to the note "Filling loops at infinity in the mapping class group."

Cited by in corpus (9)

• Top dimensional quasiflats in $CAT(0)$ cube complexes
• Quasi-isometric classification of right-angled Artin groups I: the finite out case
• Bowditch's JSJ tree and the quasi-isometry classification of certain Coxeter groups, with an appendix written jointly with Christopher Cashen
• Homological and homotopical Dehn functions are different
• Snowflake geometry in CAT(0) groups
• Lipschitz connectivity and filling invariants in solvable groups and buildings
• Dehn functions of coabelian subgroups of direct products of groups
• Divergence, thickness and hypergraph index for general Coxeter groups
• Complete classification of the Dehn functions of Bestvina-Brady groups