Asymptotics of the Colored Jones Polynomial and the A-Polynomial

TL;DR

This paper explores the connection between the asymptotic behavior of the colored Jones polynomial and the A-polynomial for twist and torus knots, providing methods to compute the A-polynomial from polynomial asymptotics.

Contribution

It establishes a link between the asymptotics of the colored Jones polynomial and the A-polynomial, offering a new approach to compute the latter from the former.

Findings

Asymptotics of the N-colored Jones polynomial yields the potential function.

The A-polynomial can be computed from the asymptotic analysis.

Discussion includes specific cases of twist and torus knots.

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.