Symplectic surgeries and normal surface singularities
Symplectic Geometry
2008-12-09 v2 Geometric Topology
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.
Cite
@article{arxiv.0708.1417,
title = {Symplectic surgeries and normal surface singularities},
author = {David T. Gay and Andras I. Stipsicz},
journal= {arXiv preprint arXiv:0708.1417},
year = {2008}
}
Comments
In the main result additional hypotheses were added and the proof has been modified accordingly