Symplectic Rational Blow-down Along Seifert Fibered 3-Manifolds

Abstract

The rational blow-down procedure (introduced by Fintushel and Stern [4] and generalized by Park [25]) turned out to be one of the most effective operations in constructing smooth 4-manifolds with interesting topological properties, cf. [5, 26–28]. Recall that when performing the rational blow-down operation we simply replace the tubular neighbourhood of a string of 2-spheres (intersecting each other according to the linear plumbing tree with framings specified by the continued fraction coefficients of − p 2 pq−1 for some p, q relatively prime) with a rational homology disk. The success of this operation might be explained by the fact that—as Symington showed [30, 31]—it can be performed symplectically. More precisely, if the ambient 4-manifold is symplectic and the spheres are symplectic submanifolds intersecting each other orthogonally then the neighbourhood