2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153940In 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, 2007Geometric Topology~57M27text