Symplectic surgeries and normal surface singularities

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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

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Symplectic Geometry, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/209783

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0708.1417
 http://arxiv.org/abs/0708.1417

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arXiv