The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot

Abstract

We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the fundamental group of the knot complement to the two-dimensional complex special linear group.

35 pages, 4 figures

References in corpus (5)

• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• Skein-theoretical derivation of some formulas of Habiro
• SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
• An introduction to the volume conjecture and its generalizations
• Representations and the colored Jones polynomial of a torus knot

Cited by in corpus (10)

• Reidemeister torsion, hyperbolic three-manifolds, and character varieties
• Asymptotics of some quantum invariants of the Whitehead chains
• On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real number
• Volume conjecture, geometric decomposition and deformation of hyperbolic structures
• Asymptotic Behavior of Colored HOMFLY Polynomial of Figure Eight Knot
• The colored Jones polynomial of the figure-eight knot and a quantum modularity
• The twisted Reidemeister torsion of an iterated torus knot
• The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot
• The asymptotic behaviors of the colored Jones polynomials of the figure eight-knot, and an affine representation
• Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot