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arXiv · 1307.4321

Bounds on Embeddings of Rational Homology Balls in Symplectic 4-manifolds

Tatyana Khodorovskiy
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Abstract

The rational homology balls $B_n$ appeared in Fintushel and Stern's rational blow-down construction [FS2]. Later, Symington [Sy1], defined this operation in the symplectic category. In [Kh2], the author defined the inverse procedure, the symplectic rational blow-up. In this paper, we study the obstructions to symplectically rationally blowing up a symplectic 4-manifold, i.e. the obstructions to symplectically embedding the rational homology balls $B_n$ into a symplectic 4-manifold. We prove a theorem and give additional examples which suggest that in order to symplectically embed the rational homology balls $B_n$, for high n, a symplectic 4-manifold must at least have a high enough $c_1^2$ as well.

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Tatyana Khodorovskiy. 2013-07-16. Bounds on Embeddings of Rational Homology Balls in Symplectic 4-manifolds. https://arxiv.org/abs/1307.4321

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