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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Quandle cohomology is a Quillen cohomology


Author: Markus Szymik
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
Published electronically: October 24, 2018
MathSciNet review: 3937311
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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).


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Markus Szymik
Affiliation: Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: markus.szymik@ntnu.no

DOI: https://doi.org/10.1090/tran/7616
Keywords: Racks, quandles, Quillen homology, transitivity, flat base change
Received by editor(s): January 17, 2017
Received by editor(s) in revised form: January 25, 2018
Published electronically: October 24, 2018
Article copyright: © Copyright 2018 American Mathematical Society