Higher order terms in asymptotic expansion of colored Jones polynomials (Q1756168)

The $N$-colored Jones polynomial of a link is the quantum invariant associated with the $(N + 1)$-dimensional irreducible representation of $sl(2;\mathbb{C})$. In the paper under review the author investigates the general expansion of the colored Jones polynomial which includes the volume conjecture expansion and the Melvin-Morton-Rozansky expansion. The author also gives an algorithm to calculate the higher order terms in general asymptotic expansions of the colored Jones polynomial from the point of view of the $A$-polynomial and the noncommutative $A$-polynomial. The author concludes by conjecturing that the Melvin-Morton-Rozansky expansion of the colored Jones polynomial is consistent with the asymptotic expansion corresponding to the abelian branch of the $A$-polynomial.