DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

By Kazuhiro Hikami. 2004

61 citations recorded by the source corpus.

We prove that the N-colored Jones polynomial for the torus knot satisfies the second order difference equation, which reduces to the first order difference equation for a case of . We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for .

Subfields: Computational Mechanics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8c86e9903e9385a6e8f3dd27f05044ad75ace3f2

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In Computational Mechanics

1. Thang T. Q. Lê
2. I. Cherednik
3. Tudor Dimofte
4. Sergei Gukov
5. Kazuhiro Hikami

In Computational Theory and Mathematics

1. Tudor Dimofte
2. Thang T. Q. Lê
3. Kazuhiro Hikami
4. I. Cherednik
5. Sergei Gukov

In Geometry and Topology

1. Sergei Gukov
2. Tudor Dimofte
3. I. Cherednik
4. Kazuhiro Hikami
5. Thang T. Q. Lê
6. E. Witten
7. Pavel Putrov
8. Stavros Garoufalidis

Citations in the corpus

• Chern-Simons theory and S-duality (2011, background): “For example, for an (a, b) torus knot, the quantum Â-polynomial and its S-dual are given by28 [11, 85, 86]”
• Generalized volume conjecture and the A-polynomials: The Neumann–Zagier potential function as a classical limit of the partition function (2006, background): “This conjecture is proved for the torus knots [23] and the 2-bridge knots [35].”
• The colored Jones polynomial and the A-polynomial of Knots☆ (2004, background): “Hikami [15] verifies the conjecture for torus knots.”
• Jones polynomials of torus knots via DAHA (2011, background): “The papers [20, 27, 29, 36, 39] are basically sufficient in this section.”