Symplectic surgeries and normal surface singularities

David T. Gay, András I. Stipsicz

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume9
Issue number4
DOIs
Publication statusPublished - 2009

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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