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On the geometry and bounded cohomology of racks and quandles
Published 6 Feb 2023 in math.GR and math.QA | (2302.02760v3)
Abstract: We introduce and investigate a natural family of metrics on connected components of a rack. The metrics are closely related to certain bi-invariant metrics on the group of inner automorphisms of the rack. We also introduce a bounded cohomology of racks and quandles, relate them to the above metrics and prove a certain vanishing result for racks and quandles with amenable group of inner automorphisms.
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