# On the geometry and bounded cohomology of racks and quandles

Source: [On the geometry and bounded cohomology of racks and quandles](<https://www.sota2.com/research/paper/68fa5be31e209131ce9cc4da>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:09.609Z

Authors: Jarek K\\k{e}dra

Published: 2023-02-06T13:15:59.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2302.02760>)

[PDF](<https://arxiv.org/pdf/2302.02760.pdf>)