Algebraic & Geometric Topology 9 (2009) 2203–2223

DOI: 10.2140/agt.2009.9.2203

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.

Keywords

symplectic rational blow-down, surface singularity, symplectic neighborhood

Mathematical Subject Classification

Primary: 57R17

Secondary: 14E15, 14J17

References

Publication

Received: 9 December 2008
Revised: 25 August 2009
Accepted: 9 September 2009
Published: 27 October 2009

Authors