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September 2014 Smoothings of singularities and symplectic surgery
Heesang Park, András I. Stipsicz
J. Symplectic Geom. 12(3): 585-597 (September 2014).

Abstract

Suppose that $C$ is a connected configuration of two-dimensional symplectic submanifolds in a symplectic 4-manifold with negative definite intersection graph $\Gamma_C$. Let $(S, 0)$ be a normal surface singularity with resolution graph $\Gamma_C$ and suppose that $W_S$ is a smoothing of $(S, 0)$. We show that if we replace an appropriate neighborhood of $C$ with $W_S$, then the resulting 4-manifold admits a symplectic structure. The operation generalizes the rational blow-down operation of Fintushel-Stern, and therefore our result extends Symington's theorem about symplectic rational blow-downs.

Citation

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Heesang Park. András I. Stipsicz. "Smoothings of singularities and symplectic surgery." J. Symplectic Geom. 12 (3) 585 - 597, September 2014.

Information

Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1312.53108
MathSciNet: MR3248669

Rights: Copyright © 2014 International Press of Boston

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Vol.12 • No. 3 • September 2014
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