The higher order terms in asymptotic expansion of color Jones polynomials

Details The higher order terms in asymptotic expansion of color Jones polynomials The higher order terms in asymptotic expansion of color Jones polynomials

2011-04-03

arxiv.org/abs/1104.0403v1

Mathematics

General Topology

14 pages

Scientific paper

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.

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