Simple singularities and topology of symplectically filling 4-manifold

Abstract.

Topological restrictions of symplectically filling 4-manifolds of links around simple singularities are studied by using the Seiberg-Witten monopole equations. In particular, the intersection form of minimal symplectically filling 4-manifolds of the singularity of type E ₈ is determined. Moreover, for the case of simply elliptic singularities, similar restrictions are obtained. In the proof, a vanishing theorem of the Seiberg-Witten invariant is discussed.