Representations and the colored Jones polynomial of a torus knot

Abstract

We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial. This suggests a generalization of the volume conjecture that relates the asymptotic behavior of the colored Jones polynomial of a knot to the volume of the knot complement.

18 pages, 1 figure, submitted to the Proceedings of the workshop "Chern-Simons Gauge Theory: 20 Years After"

References in corpus (6)

• Quantum Knot Invariant for Torus Link and Modular Forms
• Torus Knot and Minimal Model
• Proof of the volume conjecture for Whitehead chains
• An introduction to the volume conjecture and its generalizations
• An analytic version of the Melvin-Morton-Rozansky Conjecture
• On the volume conjecture for small angles

Cited by in corpus (5)

• Analytic Continuation Of Chern-Simons Theory
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot
• Torus knot state asymptotics
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot