Symplectic surgeries and normal surface singularities
| Autor: | David T Gay, András I Stipsicz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Surface (mathematics)
Pure mathematics 14E15 Geometric Topology (math.GT) Positive-definite matrix surface singularity Mathematics - Geometric Topology Singularity Mathematics - Symplectic Geometry FOS: Mathematics Symplectic Geometry (math.SG) Gravitational singularity Geometry and Topology Diffeomorphism Normal surface symplectic neighborhood Mathematics::Symplectic Geometry 14J17 Smoothing 57R17 Mathematics Symplectic geometry symplectic rational blow-down |
| Zdroj: | Algebr. Geom. Topol. 9, no. 4 (2009), 2203-2223 |
| ISSN: | 2203-2223 |
| Popis: | 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. In the main result additional hypotheses were added and the proof has been modified accordingly |
| Databáze: | OpenAIRE |
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