The Trivial Connection Contribution to Witten's Invariant and Finite Type Invariants of Rational Homology Spheres
Abstract
Description
We derive an analog of Melvin-Morton bound on the power series expansion of Jones polynomial of algebraically split links and boundary links. This allows us to produce a simple formula for the trivial connection contribution to Witten's invariant of rational homology spheres. We show that the n-th term in the 1/K expansion of the logarithm of this contribution is a finite type invariant of Ohtsuki order 3n and of at most Garoufalidis order n. This result is a manifold counterpart of the statement that n-th derivative of the Jones polynomial is Vassiliev's invariant of order n.
38 pages, 6 figures, LaTeX. Some results about loop corrections to invariants of manifolds as Vassiliev invariants of knots are added to subsection 2.2
38 pages, 6 figures, LaTeX. Some results about loop corrections to invariants of manifolds as Vassiliev invariants of knots are added to subsection 2.2