The higher order terms in asymptotic expansion of color Jones polynomials

Abstract

Color Jones polynomial is one of the most important quantum invariants in knot theory. Finding the geometric information from the color Jones polynomial is an interesting topic. In this paper, we study the general expansion of color Jones polynomial which includes the volume conjecture expansion and the Melvin-Morton-Rozansky (MMR) expansion as two special cases. Following the recent works on SL(2,C) Chern-Simons theory, we present an algorithm to calculate the higher order terms in general asymptotic expansion of color Jones polynomial from the view of A-polynomial and noncommutative A-polynomial. Moreover, we conjecture that the MMR expansion corresponding to the abelian branch of A-polynomial. Lastly, we give some examples to illustrate how to calculate the higher order terms. These results support our conjecture.

14 pages

References in corpus (5)

• On the characteristic and deformation varieties of a knot
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• An analytic version of the Melvin-Morton-Rozansky Conjecture
• The colored Jones polynomial and the A-polynomial for twist knots
• The $A$-polynomial of the $(-2,3,3+2n)$ pretzel knots