A version of the volume conjecture

We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special linear group of degree two over complex numbers. We also confirm the conjecture for the figure-eight knot and torus knots. This version is different from S. Gukov's because of a choice of polarization.Comment: 5 pages, added more comment

6j-symbols, hyperbolic structures and the Volume Conjecture

We compute the asymptotical growth rate of a large family of $U_q(sl_2)$ $6j$-symbols and we interpret our results in geometric terms by relating them to volumes of hyperbolic truncated tetrahedra. We address a question which is strictly related with S.Gukov's generalized volume conjecture and deals with the case of hyperbolic links in connected sums of $S^2\times S^1$. We answer this question for the infinite family of fundamental shadow links.Comment: 17 pages, 3 figures. Published on Geometry & Topology 11 (2007

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

Intrinsic Spin Hall Effect

A brief review is given on the spin Hall effect, where an external electric field induces a transverse spin current. It has been recognized over 30 years that such effect occurs due to impurities in the presence of spin-orbit coupling. Meanwhile, it was proposed recently that there is also an intrinsic contribution for this effect. We explain the mechanism for this intrinsic spin Hall effect. We also discuss recent experimental observations of the spin Hall effect.Comment: 13 pages, 3 figures, to appear in Advances in Solid State Physics, Vol 45(2005), edited by B. Kramer, changes in Sections 3 and 4.