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Intrinsic Tame Filling Functions and Other Refinements of Diameter Functions

Andrew Quaisley, University of Nebraska - Lincoln


Tame filling functions are quasi-isometry invariants that are refinements of the diameter function of a group. Although tame filling functions were defined in part to provide a proper refinement of the diameter function, we show that every finite presentation of a group has an intrinsic tame filling function that is equivalent to its intrinsic diameter function. We then 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.

Subject Area


Recommended Citation

Quaisley, Andrew, "Intrinsic Tame Filling Functions and Other Refinements of Diameter Functions" (2023). ETD collection for University of Nebraska - Lincoln. AAI30426352.