A topological characterization of symplectic fillings of Seifert 3-manifolds (2207.12663v3)

Abstract: In this paper, we investigate a relation between rational blowdown surgery and minimal symplectic fillings of a given Seifert 3-manifold with a canonical contact structure. Consequently, we determine a necessary and sufficient condition for a minimal symplectic filling of a Seifert 3-manifold satisfying certain conditions to be obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding weighted homogeneous surface singularity. Furthermore, as an application of the main results, we prove that every minimal symplectic filling of a large family of Seifert 3-manifolds with a canonical contact structure is in fact realized as a Milnor fiber of the corresponding weighted homogeneous surface singularity in the Appendix.