The quandle of the trefoil knot as the Dehn quandle of the torus

Maciej Niebrzydowski; Jozef H. Przytycki

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arXiv · 0805.2743

The quandle of the trefoil knot as the Dehn quandle of the torus

Maciej Niebrzydowski·Jozef H. Przytycki

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Abstract

We prove that the fundamental quandle of the trefoil knot is isomorphic to the projective primitive subquandle of transvections of the symplectic space $\Z \oplus \Z$. 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.

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BibTeX RIS

Maciej Niebrzydowski, Jozef H. Przytycki. 2008-05-18. The quandle of the trefoil knot as the Dehn quandle of the torus. https://arxiv.org/abs/0805.2743

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