The quandle of the trefoil knot as the Dehn quandle of the torus. (English) Zbl 1193.57004
A quandle is an algebraic structure consisting of a set with a self-distributive right-invertible binary operation under which every element is idempotent. In this paper, the authors define an isomorphism between the fundamental quandle of the trefoil knot and the Dehn quandle of the torus. The quandle of the long trefoil is considered in terms of cord quandles, and an additional isomorphism between the fundamental quandle of the trefoil knot and a cord quandle on the 4-punctured 2-sphere is given.
Reviewer: Sam Nelson (Claremont)
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57M99 | General low-dimensional topology |
| 17A99 | General nonassociative rings |
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