The quandle of the trefoil knot as the Dehn quandle of the torus
Niebrzydowski, Maciej ; Przytycki, Józef H.
Osaka J. Math., Tome 46 (2009) no. 1, p. 645-659 / Harvested from Project Euclid
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We prove that the fundamental quandle of the trefoil knot is isomorphic to the projective primitive subquandle of transvections of the symplectic space $\mathbb{Z} \oplus \mathbb{Z}$. The last quandle can be identified with the Dehn quandle of the torus and the cord quandle on a 2-sphere with four punctures. We also show that the fundamental quandle of the long trefoil knot is isomorphic to the cord quandle on a 2-sphere with a hole and three punctures.
Publié le : 2009-09-15
Classification:  57M99,  17A99 
@article{1256564199,
     author = {Niebrzydowski, Maciej and Przytycki, J\'ozef H.},
     title = {The quandle of the trefoil knot as the Dehn quandle of the torus},
     journal = {Osaka J. Math.},
     volume = {46},
     number = {1},
     year = {2009},
     pages = { 645-659},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256564199}
}

Niebrzydowski, Maciej; Przytycki, Józef H. The quandle of the trefoil knot as the Dehn quandle of the torus. Osaka J. Math., Tome 46 (2009) no. 1, pp.  645-659. http://gdmltest.u-ga.fr/item/1256564199/