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arXiv · 0708.1417

Symplectic surgeries and normal surface singularities

David T. Gay·Andras I. Stipsicz
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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.

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BibTeXRIS

David T. Gay, Andras I. Stipsicz. 2008-12-09. Symplectic surgeries and normal surface singularities. https://arxiv.org/abs/0708.1417

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