Andrew Kricker, University of Toronto, January 20, 2003
Title: Finite type invariants of cyclic branched covers
Abstract:
Given a knot in an integer homology sphere, one can construct
a family of closed 3-manifolds (parametrized by the positive integers),
namely the cyclic branched coverings of the knot. In this paper we give
a formula for the Casson-Walker invariants of these 3-manifolds in
terms of residues of a rational function (which measures the 2-loop
part of the Kontsevich integral of a knot) and the signature function
of the knot. Our main result actually computes the LMO invariant of
cyclic branched covers in terms of a rational invariant of the knot and
its signature function.