On the asymptotic expansions of various quantum invariants II: the colored Jones polynomial of twist knots at the root of unity e^{(2π√(-1))/(N+(1)/(M))} and e^{(2π√(-1))/(N)}

2023/07/25 by Qingtao Chen, Chen, Qingtao, Shengmao Zhu +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2307.13670

openalex publication_date 2023/07/25 · openalex created_date 2023/07/27 · openalex updated_date 2026/07/28

Abstract

This is the second article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this article, following the method and results in \citeCZ23-1, we present an asymptotic expansion formula for the colored Jones polynomial of twist knot K_p with p≥ 6 at the root of unity e^{(2π√(-1))/(N+(1)/(M))} with M≥ 2. Furthermore, by taking the limit M→ +∞, we obtain an asymptotic expansion formula for the colored Jones polynomial of twist knots K_p with p≥ 6 at the root of unity e^{(2π√(-1))/(N)}.

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