Groups, Geometry, and Dynamics


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Volume 10, Issue 3, 2016, pp. 867–883
DOI: 10.4171/GGD/369

Published online: 2016-09-16

A subgroup theorem for homological filling functions

Richard Gaelan Hanlon[1] and Eduardo Martínez Pedroza[2]

(1) Memorial University of Newfoundland, St. John's, Canada
(2) Memorial University of Newfoundland, St. John's, Canada

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.

Keywords: Filling functions, isoperimetric functions, Dehn functions, hyperbolic groups, finiteness properties

Hanlon Richard Gaelan, Martínez Pedroza Eduardo: A subgroup theorem for homological filling functions. Groups Geom. Dyn. 10 (2016), 867-883. doi: 10.4171/GGD/369