The colored Jones polynomial of a cable of the figure-eight knot

Hitoshi Murakami; Anh T. Tran

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arXiv · 2010.03698

The colored Jones polynomial of a cable of the figure-eight knot

Hitoshi Murakami·Anh T. Tran

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Abstract

We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial of a cable of the figure-eight knot, evaluated at $\exp(\xi/N)$ for a real number $\xi$. We show that if $\xi$ is sufficiently large, the colored Jones polynomial grows exponentially when $N$ goes to the infinity. Moreover the growth rate is related to the Chern-Simons invariant of the knot exterior associated with an $\mathrm{SL}(2;\mathbb{R})$ representation.

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Hitoshi Murakami, Anh T. Tran. 2020-10-08. The colored Jones polynomial of a cable of the figure-eight knot. https://arxiv.org/abs/2010.03698

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