The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot

Abstract: We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the fundamental group of the knot complement to the two-dimensional complex special linear group.