Difference equation of the colored Jones polynomial for torus knot

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}.

7 pages

References in corpus (3)

• A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I
• Skein-theoretical derivation of some formulas of Habiro
• Torus Knot and Minimal Model

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