## Quandle cohomology is a Quillen cohomology

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- by Markus Szymik PDF
- Trans. Amer. Math. Soc.
**371**(2019), 5823-5839 Request permission

## Abstract:

Racks and quandles are fundamental algebraic structures related to the topology of knots, braids, and the Yang–Baxter equation. We show that the cohomology groups usually associated with racks and quandles agree with the Quillen cohomology groups for the algebraic theories of racks and quandles, respectively. This makes available the entire range of tools that comes with a Quillen homology theory, such as long exact sequences (transitivity) and excision isomorphisms (flat base change).## References

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## Additional Information

**Markus Szymik**- Affiliation: Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, 7491 Trondheim, Norway
- MR Author ID: 816144
- Email: markus.szymik@ntnu.no
- Received by editor(s): January 17, 2017
- Received by editor(s) in revised form: January 25, 2018
- Published electronically: October 24, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**371**(2019), 5823-5839 - MSC (2010): Primary 18G50, 57M27; Secondary 18C10, 20N02, 55U35
- DOI: https://doi.org/10.1090/tran/7616
- MathSciNet review: 3937311