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Symplectic surgeries and
normal surface singularities
David T Gay and András I Stipsicz |
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Algebraic & Geometric Topology 9 (2009) 2203–2223
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Abstract |
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We show that every negative definite configuration of symplectic surfaces in a symplectic –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 –manifolds. |
Keywords
symplectic rational blow-down, surface singularity,
symplectic neighborhood
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Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 14E15, 14J17
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References |
Publication
Received: 9 December 2008
Revised: 25 August 2009
Accepted: 9 September 2009
Published: 27 October 2009
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Authors |
| David T Gay | |
| Department of Mathematics and
Applied Mathematics University of Cape Town Private Bag X3 Rondebosch 7701 South Africa |
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| András I Stipsicz | |
| Hungarian Academy of Sciences Renyi Institute of Mathematics Reáltanoda utca 13–15 Budapest 1053 Hungary |
Mathematics Department, Columbia
University 2990 Broadway, New York, NY 10027 USA |
| http://www.renyi.hu/~stipsicz | |
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