Higher order terms in asymptotic expansion of colored Jones polynomials

$SL(2,\mathbb{C})$ Chern–Simons theory provide several methods to calculate the higher order terms in asymptotic expansion of colored Jones polynomial from the view of $A$-polynomial and noncommutative $A$-polynomial. First, we present one of those algorithms explicitly. Then through the detailed calculations, we conjecture that the Melvin–Morton–Rozansky (MMR) expansion of colored Jones polynomial is consistent with the asymptotic expansion of colored Jones polynomial in abelian branch of $A$-polynomial studied in this article.

Keywords

colored Jones polynomial, asymptotic expansion, volume conjecture, $A$-polynomial, non-commutative $A$-polynomial, AJ conjecture

2010 Mathematics Subject Classification

Primary 57M27. Secondary 57N10.

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This main part of this work was finished when the author was visiting University of California, Los Angeles in 2011. The author would like to thank the China Scholarship Council for the financial support for his visit. The author thanks Professor H. Fuji for providing him partial of the calculations in his paper. The author is grateful to the referee for valuable comments and suggestions which improved the presentation of the content.

Received 2 September 2017

Published 21 December 2018