Intrinsic tame filling functions are equivalent to intrinsic diameter functions

TL;DR

This paper proves that for any finitely presented group, the intrinsic tame filling function is equivalent to its intrinsic diameter function, and introduces new potential refinements of these functions.

Contribution

It establishes the equivalence between intrinsic tame filling functions and intrinsic diameter functions for finitely presented groups and proposes new related filling functions.

Findings

Intrinsic tame filling functions are quasi-isometry invariants.

Intrinsic tame filling functions are equivalent to intrinsic diameter functions.

New alternative filling functions are introduced as potential refinements.

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.