Stavros Garoufalidis and Nathan Habegger
Abstract: Using elementary counting methods, we calculate the universal invariant (well-known as the LMO invariant) of a 3-manifold M, satisfying H_1(M,Z)=Z, in terms of the Alexander polynomial of M. We show that +1 surgery on a knot in the 3-sphere induces an injective map from finite type invariants of integral homology 3-spheres to finite type invariants of knots. We also show that weight systems of degree 2m on knots, obtained by applying finite type 3m invariants of integral homology 3-spheres, lie in the algebra of Alexander-Conway weight systems, thus answering the questions raised in \cite{Ga}.
Key words: Finite type invariants of knots and 3-manifolds, Alexander polynomial.
Notes: 10 pages plus references.