Equivalence of Geometric and Combinatorial Dehn Functions

Abstract

We prove that if a finitely presented group acts properly discontinuously, cocompactly and by isometries on a simply connected Riemannian manifold, then the Dehn function of the group and the corresponding filling function of the manifold are equivalent, in a sense described below.

Cited by in corpus (7)

• Filling inequalities for nilpotent groups
• Rigidity of high dimensional graph manifolds
• Density of isoperimetric spectra
• Scaled relators and Dehn functions for nilpotent groups
• A Combination Theorem for Relatively Hyperbolic Groups
• A spherical decomposition for Riemannian open 3-manifolds
• A polynomial isoperimetric inequality for SL(n,Z)