An introduction to the volume conjecture and its generalizations

Abstract

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

References in corpus (4)

• Quantum Knot Invariant for Torus Link and Modular Forms
• An analytic version of the Melvin-Morton-Rozansky Conjecture
• On the volume conjecture for small angles
• Colored Jones polynomials with polynomial growth

Cited by in corpus (1)

• A cabling formula for the colored Jones polynomial