On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real nubmer

Hitoshi Murakami, Anh T. Tran

Published 2021-09-10Version 1

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 $\rm{SL}(2;\mathbb{C})$ Chern--Simons invariant and the Reidemeister torsion twisted by the adjoint action both associated with a representation determined by $\xi$.