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

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.

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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.

Information

Published: September 2009
First available in Project Euclid: 26 October 2009

zbMATH: 1193.57004
MathSciNet: MR2583322

Subjects:
Primary: 57M99
Secondary: 17A99

Rights: Copyright © 2009 Osaka University and Osaka City University, Departments of Mathematics

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Vol.46 • No. 3 • September 2009
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