Intrinsic tame filling functions are equivalent to intrinsic diameter functions

Abstract

Intrinsic tame filling functions are quasi-isometry invariants that are refinements of the intrinsic diameter function of a group. The main purpose of this paper is to show that every finite presentation of a group has an intrinsic tame filling function that is equivalent to its intrinsic diameter function. We also introduce some alternative filling functions — based on concepts similar to those used to define intrinsic tame filling functions — that are potential proper refinements of the intrinsic diameter function.