The quandle of the trefoil knot as the Dehn quandle of the torus
The quandle of the trefoil knot as the Dehn quandle of the torus
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三叶结的 qudle 与环面的 Dehn qudle
DOI：
10.18910/11795
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发表时间：
2008
影响因子：
0.4
通讯作者：
J. Przytycki
中科院分区：
文献类型：
--
作者：
Maciej Niebrzydowski;J. Przytycki
我们证明了三叶纽结的基本困境与辛空间Z Z的断面的射影本原子困境同构，最后一个困境可以与Torus的Dehn Quandle和具有四个穿孔的2-球面上的弦Quandle同构.我们还证明了长三叶结的基本困境与具有一个孔和三个穿孔的2-球面上的绳索困境同构。
We prove that the fundamental quandle of the trefoil knot is isomorphic to the projective primitive subquandle of transvections of the sy mplectic space Z Z. The last quandle can be identified with the Dehn quandle of the tor us 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.