The Alexander Polynomial and Finite Type 3-manifold Invariants
نویسنده
چکیده
Using elementary counting methods, we calculate the universal invariant (also known as the LMO invariant) of a 3-manifold M , satisfying H1(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 [Ga1].
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