The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial
The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial
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(2,2p 1)-环面结的非交换 A 理想决定了其琼斯多项式
DOI：
10.1142/s021821650300238x
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发表时间：
2002
影响因子：
0.5
通讯作者：
J. Sain
中科院分区：
文献类型：
--
作者：
R. Gelca;J. Sain
结的非交换 A 理想是 A 多项式的推广，使用考夫曼括号绞纱模块定义。在本文中，我们证明任何与 (2,2p + 1)-环面结具有相同非交换 A 理想的结都具有相同颜色的琼斯多项式。这是正交关系的结果，它产生用于计算结的所有彩色琼斯多项式的递归关系。
The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same noncommutative A-ideal as the (2,2p + 1)-torus knot has the same colored Jones polynomials. This is a consequence of the orthogonality relation, which yields a recursive relation for computing all colored Jones polynomials of the knot.