A subgroup theorem for homological filling functions

Abstract

We use algebraic techniques to study homological filling functions of groups and their subgroups. If $G$ is a group admitting a finite $(n+1)$-dimensional $K(G,1)$ and $H\le G$ is of type $F_{n+1}$, then the $n$th homological filling function of $H$ is bounded above by that of $G$. This contrasts with known examples where such inequality does not hold under weaker conditions on the ambient group $G$ or the subgroup $H$. We include applications to hyperbolic groups and homotopical filling functions.