Symplectic surgeries and normal surface singularities

Details Symplectic surgeries and normal surface singularities Symplectic surgeries and normal surface singularities

2007-08-10

arxiv.org/abs/0708.1417v2

Mathematics

Symplectic Geometry

In the main result additional hypotheses were added and the proof has been modified accordingly

Scientific paper

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.

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