An introduction to the volume conjecture and its generalizations
Abstract
Description
In this paper we give an introduction to the volume conjecture and its generalizations. Especially we discuss relations of the asymptotic behaviors of the colored Jones polynomials of a knot with different parameters to representations of the fundamental group of the knot complement at the special linear group over complex numbers by taking the figure-eight knot and torus knots as examples.
27 pages, 12 figures, submitted to the Proceedings of the International Conference on Quantum Topology, Hanoi, August, 2007
27 pages, 12 figures, submitted to the Proceedings of the International Conference on Quantum Topology, Hanoi, August, 2007