On the AJ conjecture for knots
Geometric Topology
2014-01-28 v4 Quantum Algebra
Abstract
We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of two-bridge knots and pretzel knots. This extends the result of the first author in [Le06] where he established the AJ conjecture for a large class of two-bridge knots, including all twist knots. Along the way, we explicitly calculate the universal character ring of the knot group of the (-2,3,2n+1)-pretzel knot and show that it is reduced for all integers n.
Cite
@article{arxiv.1111.5258,
title = {On the AJ conjecture for knots},
author = {Thang T. Q. Le and Anh T. Tran},
journal= {arXiv preprint arXiv:1111.5258},
year = {2014}
}