Difference equation of the colored Jones polynomial for torus knot
Geometric Topology
2007-05-23 v1
Abstract
We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}. We show that the A-polynomial of the torus knot can be derived from this difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for T_{2,2m+1}.
Keywords
Cite
@article{arxiv.math/0403224,
title = {Difference equation of the colored Jones polynomial for torus knot},
author = {Kazuhiro Hikami},
journal= {arXiv preprint arXiv:math/0403224},
year = {2007}
}
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7 pages