Some limits of the colored Jones polynomials of the figure-eight knot

Abstract

We will study the asymptotic behaviors of the colored Jones polynomials of the figure-eight knot. In particular we will show that for certain limits we obtain the volumes of the cone manifolds with singularities along the knot.

arXiv comment11 pages

References in corpus (4)

• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• On the volume conjecture for hyperbolic knots
• Optimistic calculations about the Witten--Reshetikhin--Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries
• The asymptotic behavior of the colored Jones function of a knot and its volume

Cited by in corpus (6)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Asymptotics of the colored Jones function of a knot
• Feynman loops and three-dimensional quantum gravity
• On the asymptotic behavior of the colored Jones polynomial of the figure-eight knot associated with a real number
• Quantum Field Theory and the Volume Conjecture
• Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot