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2009 Symplectic surgeries and normal surface singularities
David T Gay, András I Stipsicz
Algebr. Geom. Topol. 9(4): 2203-2223 (2009). 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.

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David T Gay. András I Stipsicz. "Symplectic surgeries and normal surface singularities." Algebr. Geom. Topol. 9 (4) 2203 - 2223, 2009. https://doi.org/10.2140/agt.2009.9.2203

Information

Received: 9 December 2008; Revised: 25 August 2009; Accepted: 9 September 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1193.57014
MathSciNet: MR2558309
Digital Object Identifier: 10.2140/agt.2009.9.2203

Subjects:
Primary: 57R17
Secondary: 14E15, 14J17

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 4 • 2009
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