On p-Adic Convergence of Perturbative Invariants of Some Rational Homology Spheres
Abstract
Description
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)
28 pages, LaTeX (the main conjecture is corrected, the analytic formula for the perturbative invariant is improved)