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

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

1996-01-17

arxiv.org/abs/q-alg/9601015v2

Mathematics

Quantum Algebra

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

Scientific paper

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.

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