Optimistic calculations about the Witten--Reshetikhin--Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries

Abstract

I calculate optimistically asymptotic behaviors of the WRT SU(2) invariants for the three-manifolds obtained from the figure-eight knot by p-surgeries with p=0,1,2,...,10, from which one can extract volumes and the Chern-Simons invariants of these closed manifolds. I conjecture that this also holds for general closed three-manifolds.

arXiv comment10 pages, to appear in the Proceedings of the workshop `Recent Progress toward the Volume Conjecture', International Institute for Advanced Study, March, 2000

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• Some limits of the colored Jones polynomials of the figure-eight knot
• Mahler measure of the colored Jones polynomial and the volume conjecture
• Yokota theory, the invariant trace fields of hyperbolic knots and the Borel regulator map
• Asymptotics and 6j-symbols
• Quantum invariants of three-manifolds obtained by surgeries along torus knots