The Nature Of The Link Alexander Polynomial And 3-manifolds Invariants

This paper first studies Alexander polynomial derivatives and second order derivatives,when t=1with two components link, by Alexander skein relation. Meanwhile, special linksituation is generalized common situations.Secondly, this paper discusses the three dimensional manifold invariant said. Let theM Ldenote the oriented3-manifold obtained by surgery on framed link (L,f) inS3,which ispreserved by isotopy and movesK_+andK_-, gives a3-manifold invariant. On the onehand, on the basis of the Blanchet, Habegger, Masbaum, and Vogel’s three dimensionalmanifold invariant formula, this paper gives another similar three dimensional manifoldinvariant formula. On the other hand, if A is the2p (p is prime) unit root, then we can getanother three dimensional manifold calculation formula by surgerying on the cycle link.