On symplectic fillings of small Seifert $3$-manifolds

Abstract

In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic filling is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding weighted homogeneous complex surface singularity.

28 pages, 32 figures; Section 3 is added, Revised argument in Section 4

References in corpus (1)

• Comparing star surgery to rational blow-down

Cited by in corpus (3)

• Some applications of Menke's JSJ decomposition for symplectic fillings
• Symplectic fillings of virtually overtwisted contact structures on lens spaces
• Hypersurface singularities and virtually overtwisted contact structures