On the relation between the A-polynomial and the Jones polynomial
Quantum Algebra
2007-05-23 v1 Geometric Topology
Abstract
In previous joint work with Frohman and Lofaro a noncommutative generalization of the A-polynomial of a knot was introduced, consisting of a finitely generated ideal of polynomials (the noncommutative A-ideal) in the quantum plane. The present paper shows that the noncommutative A-ideal of a knot, together with finitely many of its colored Jones polynomials determines all other colored Jones polynomials. Also, for particular knots, such as the unknot and the trefoil, the noncommutative A-ideal completely determines all colored Jones polynomials.
Keywords
Cite
@article{arxiv.math/0004158,
title = {On the relation between the A-polynomial and the Jones polynomial},
author = {Razvan Gelca},
journal= {arXiv preprint arXiv:math/0004158},
year = {2007}
}
Comments
LATEX, 6 pages