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Tame filling invariants for groups. (English) Zbl 1364.20024

Summary: 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.

MSC:

20F65 Geometric group theory
20F06 Cancellation theory of groups; application of van Kampen diagrams
20F69 Asymptotic properties of groups
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