The Colored Jones Polynomial and the A-Polynomial of Knots
Geometric Topology
2007-05-23 v4 Quantum Algebra
Abstract
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knots are established.
Keywords
Cite
@article{arxiv.math/0407521,
title = {The Colored Jones Polynomial and the A-Polynomial of Knots},
author = {Thang T. Q. Le},
journal= {arXiv preprint arXiv:math/0407521},
year = {2007}
}
Comments
Typos and minor mistakes corrected. To appear in Advances in Mathematics