Kashaev's invariant and the volume of a hyperbolic knot after Y. Yokota

I follow Y. Yokota to explain how to obtain a tetrahedron decomposition of the complement of a hyperbolic knot and compare it with the asymptotic behavior of Kashaev's link invariant using the figure-eight knot as an example.Comment: 21 pages, 21 figures, submitted to the Proceedings of "Physics and Combinatorics" Workshop, Nagoya 199

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

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.Comment: 35 pages, 4 figure