Symplectic surgeries and normal surface singularities

David T. Gay, András I. Stipsicz

Research output: Contribution to journalArticle

10 Citations (Scopus)


We show that every negative definite configuration of symplectic surfaces in a symplectic 4-manifold has a strongly symplectically convex neighborhood. We use this to show that if a negative definite configuration satisfies an additional negativity condition at each surface in the configuration and if the complex singularity with resolution diffeomorphic to a neighborhood of the configuration has a smoothing, then the configuration can be symplectically replaced by the smoothing of the singularity. This generalizes the symplectic rational blowdown procedure used in recent constructions of small exotic 4-manifolds.

Original languageEnglish
Pages (from-to)2203-2223
Number of pages21
JournalAlgebraic and Geometric Topology
Issue number4
Publication statusPublished - 2009


  • Surface singularity
  • Symplectic neighborhood
  • Symplectic rational blow-down

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'Symplectic surgeries and normal surface singularities'. Together they form a unique fingerprint.

  • Cite this