Seiberg - Witten Invariants and Surface Singularities Iii ( Splicings and Cyclic Covers )

We verify the conjecture formulated in [31] for suspension singularities of type g(x, y, z) = f(x, y) + z, where f is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg-Witten invariant of the linkM of g, associated with the canonical spin structure, equals −σ(F )/8, where σ(F ) is the signature of the Milnor fiber of g. In order to do this, we prove general splicing formulae for the CassonWalker invariant and for the sign refined Reidemeister-Turaev torsion (in particular, for the modified Seiberg-Witten invariant too). These provide results for some cyclic covers as well. As a by-product, we compute all the relevant invariants of M in terms of the Newton pairs of f and the integer n.