Asymptotics of the Colored Jones Polynomial and the A-Polynomial

Abstract

We reveal a relationship between the colored Jones polynomial and the A-polynomial for twist knots. We demonstrate that an asymptotics of the $N$-colored Jones polynomial in large $N$ gives the potential function, and that the A-polynomial can be computed. Also discussed is a case of torus knots.

16 pages, 4 figures

References in corpus (8)

• Chern-Simons Theory and Topological Strings
• On the characteristic and deformation varieties of a knot
• Quantum Knot Invariant for Torus Link and Modular Forms
• q-series and L-functions related to half-derivatives of the Andrews--Gordon identity
• Difference equation of the colored Jones polynomial for torus knot
• On the Quantum Invariant for the Brieskorn Homology Spheres
• The colored Jones polynomial and the A-polynomial for twist knots
• Mahler measure of the colored Jones polynomial and the volume conjecture

Cited by in corpus (4)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Super-A-polynomials for Twist Knots
• SU(2)/SL(2) knot invariants and KS monodromies
• The colored Jones polynomial and Kontsevich-Zagier series for double twist knots