Presentations of Dehn quandles

Abstract

The paper gives two approaches to write explicit presentations for the class of Dehn quandles using presentations of their underlying groups. The first approach gives finite presentations for Dehn quandles of a class of Garside groups and Gaussian groups. The second approach is for general Dehn quandles when the centralisers of generators of their underlying groups are known. Several examples including Dehn quandles of spherical Artin groups, surface groups and mapping class groups of orientable surfaces are given to illustrate the results.

arXiv comment32 pages

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• On structure groups of set-theoretic solutions to the Yang-Baxter equation
• Yang-Baxter deformations of quandles and racks
• The Birman-Hilden theory
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Cited by in corpus (1)

• Finiteness of canonical quotients of Dehn quandles of surfaces