On p-Adic Convergence of Perturbative Invariants of Some Rational Homology Spheres

Abstract

R.~Lawrence has conjectured that for rational homology spheres, the series of Ohtsuki's invariants converges p-adicly to the SO(3) Witten-Reshetikhin-Turaev invariant. We prove this conjecture for Seifert rational homology spheres. We also derive it for manifolds constructed by a surgery on a knot in S^3. Our derivation is based on a conjecture about the colored Jones polynomial that we have formulated in our previous paper. We also present numerical examples of p-adic convergence for some simple manifolds.

28 pages, LaTeX (the main conjecture is corrected, the analytic formula for the perturbative invariant is improved)

References in corpus (3)

• A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I
• A Large k Asymptotics of Witten's Invariant of Seifert Manifolds
• Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial

Cited by in corpus (1)

• Finite type invariants of integral homology 3-spheres: A survey