A subgroup theorem for homological filling functions (Q329563)

Summary: 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 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.