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We study the asymptotic behavior of the N-dimensional colored Jones polynomial evaluated at \(\exp (\xi /N)\) for a real number \(\xi \) greater than a certain constant. We prove that, from the asymptotic behavior, we can extract the \(\textrm{SL}(2;\mathbb {C})\) Chern–Simons invariant and the Reidemeister torsion twisted by the adjoint action both associated with a representation determined by \(\xi \) .

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On the Asymptotic Behavior of the Colored Jones Polynomial of the Figure-Eight Knot Associated With a Real Number

  • 会议论文

  • 发表日期：

    2025年

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  • Hitoshi Murakami,
  • Anh T. Tran

摘要

We study the asymptotic behavior of the N-dimensional colored Jones polynomial evaluated at \(\exp (\xi /N)\) for a real number \(\xi \) greater than a certain constant. We prove that, from the asymptotic behavior, we can extract the \(\textrm{SL}(2;\mathbb {C})\) Chern–Simons invariant and the Reidemeister torsion twisted by the adjoint action both associated with a representation determined by \(\xi \) .