Difference equation of the colored Jones polynomial for torus knot

Details Difference equation of the colored Jones polynomial for torus knot Difference equation of the colored Jones polynomial for torus knot

2004-03-14

arxiv.org/abs/math/0403224v1

Int. J. Math. 15, 959--965 (2004)

Mathematics

Geometric Topology

7 pages

Scientific paper

10.1142/S0129167X04002582

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}.

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