Tame filling invariants for groups

A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, is introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and extrinsic diameter functions for finitely presented groups. We show that the existence of a (finite-valued) tame filling functions implies that the group is tame combable. Bounds on both intrinsic and extrinsic tame filling functions are discussed for stackable groups, including groups with a finite complete rewriting system, Thompson's group F, and almost convex groups.