English

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