The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial
Geometric Topology
2007-05-23 v1 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.math/0201100,
title = {The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial},
author = {Razvan Gelca and Jeremy Sain},
journal= {arXiv preprint arXiv:math/0201100},
year = {2007}
}
Comments
15 pages, Latex, 13 figures