A version of the volume conjecture

Abstract

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.

5 pages, added more comments

References in corpus (2)

• An analytic version of the Melvin-Morton-Rozansky Conjecture
• The colored Jones polynomials and the Alexander polynomial of the figure-eight knot

Cited by in corpus (7)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• An introduction to the volume conjecture and its generalizations
• Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds
• Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
• The higher order terms in asymptotic expansion of color Jones polynomials
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot