Witten's Invariants of Rational Homology Spheres at Prime Values of $K$ and Trivial Connection Contribution

Details Witten's Invariants of Rational Homology Spheres at Prime Values of $K$ and Trivial Connection Contribution Witten's Invariants of Rational Homology Spheres at Prime Values of $K$ and Trivial Connection Contribution

1995-04-22

arxiv.org/abs/q-alg/9504015v2

Mathematics

Quantum Algebra

32 pages, no figures, LaTeX

Scientific paper

10.1007/BF02099715

We establish a relation between the coefficients of asymptotic expansion of trivial connection contribution to Witten's invariant of rational homology spheres and the invariants that T.~Ohtsuki extracted from Witten's invariant at prime values of $K$. We also rederive the properties of prime $K$ invariants discovered by H.~Murakami and T.~Ohtsuki. We do this by using the bounds on Taylor series expansion of the Jones polynomial of algebraically split links, studied in our previous paper. These bounds are enough to prove that Ohtsuki's invariants are of finite type. The relation between Ohtsuki's invariants and trivial connection contribution is verified explicitly for lens spaces and Seifert manifolds.

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