The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces

Abstract

We calculate limits of the colored Jones polynomials of the figure-eight knot and conclude that in most cases they determine the volumes and the Chern--Simons invariants of the three-manifolds obtained by Dehn surgeries along it.

17 pages

References in corpus (1)

• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial

Cited by in corpus (2)

• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Logarithmic knot invariants arising from restricted quantum groups