Seiberg-Witten invariants and surface singularities III. Splicings and cyclic covers

Abstract

We verify the conjecture formulated in math.AG/0111298 for suspension singularities of type $g(x,y,z)=f(x,y)+z^n$, where $f$ is an irreducible plane curve singularity. More precisely, we prove that the modified Seiberg-Witten invariant of the link $M$ of $g$, associated with the canonical $spi{n}^c$ structure, equals $-\sigma (F)/8$, where $\sigma (F)$ is the signature of the Milnor fiber of $g$. In order to do this, we prove general splicing formulae for the Casson-Walker 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 $n$.

Cited by in corpus (1)

• Links and analytic invariants of superisolated singularities