An introduction to the volume conjecture and its generalizations
arXiv:0802.0039
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 (9)
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- A Link Invariant from Quantum Dilogarithm
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Cited by in corpus (13)
- Analytic Continuation Of Chern-Simons Theory
- Colored Kauffman Homology and Super-A-polynomials
- A short overview of the "Topological recursion"
- Localization for Wilson Loops in Chern-Simons Theory
- The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot
- A cabling formula for the colored Jones polynomial
- On the formulae for the colored HOMFLY polynomials
- Representations and the colored Jones polynomial of a torus knot
- On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real number
- The twisted Reidemeister torsion of an iterated torus knot
- On the Volume Conjecture for Cables of Knots
- An Introduction to A-polynomials and their Mahler Measures
- The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot