Higher Order Stability in the Coefficients of the Colored Jones Polynomial

TL;DR

This paper investigates the higher order stability properties of the coefficients of the colored Jones polynomial, providing explicit expressions for second stable sequences and classifying knots based on their higher order stability.

Contribution

It introduces a new analysis of higher order stabilization in colored Jones polynomials and derives explicit formulas for certain classes of knots.

Findings

Derived an expression for the second stable sequence of the colored Jones polynomial.

Identified classes of knots sharing the same higher order stability.

Enhanced understanding of the stability behavior of polynomial coefficients.

Abstract

We discuss the higher order stabilization of the coefficients of the colored Jones polynomial. In particular, we find an expression for the second stable sequence of the colored Jones polynomial of a certain class of knots. We also determine which knots have the same higher order stability.