Difference equation of the colored Jones polynomial for torus knot

Kazuhiro Hikami

doi:10.1142/s0129167x04002582

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Difference equation of the colored Jones polynomial for torus knot

Kazuhiro Hikami

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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}.

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Kazuhiro Hikami. 2004-03-14. Difference equation of the colored Jones polynomial for torus knot. https://doi.org/10.1142/s0129167x04002582

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