The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial

Razvan Gelca; Jeremy Sain

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arXiv · math/0201100

The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial

Razvan Gelca·Jeremy Sain

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Abstract

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.

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Razvan Gelca, Jeremy Sain. 2002-01-11. The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial. https://arxiv.org/abs/math/0201100

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