Homological Isoperimetric Inequalities for Kernels of Free Extensions of Type $FP_2$

TL;DR

This paper introduces homological area-radius pairs to establish isoperimetric inequalities for subgroups of type FP_2 that are kernels of free extensions, extending previous methods.

Contribution

It adapts Gersten and Short's proof to the homological setting, providing new inequalities for specific subgroup classes.

Findings

Established homological isoperimetric inequalities for kernels of free extensions

Introduced homological area-radius pairs with surface diagrams

Extended existing proofs to a new homological context

Abstract

We define homological area-radius pairs with surface diagrams. Using these, we adapt a proof of Gersten and Short \cite{gersten2002} to obtain a homological isoperimetric inequality for subgroups of type $FP_2$ which appear as kernels of free extensions.