Abstract
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.
Citation
Maciej Niebrzydowski. Józef H. Przytycki. "The quandle of the trefoil knot as the Dehn quandle of the torus." Osaka J. Math. 46 (3) 645 - 659, September 2009.
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