A Subgroup Theorem for Homological Filling Functions

TL;DR

This paper establishes a subgroup theorem for homological filling functions, showing under certain conditions that the filling function of a subgroup is bounded by that of the ambient group, with applications to hyperbolic groups.

Contribution

It provides a new algebraic result linking the homological filling functions of groups and their subgroups under specific finiteness conditions.

Findings

Homological filling function of subgroup H is bounded by that of G under certain conditions.

Contrast with examples where such bounds do not hold under weaker assumptions.

Applications include hyperbolic groups and homotopical 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 $H \leq G$ is of type $F_{n+1}$, then the $n^{th}$--homological filling function of $H$ is bounded above by that of $G$. This contrast 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.