# Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls

 Title: Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls Author: Khodorovskiy, Tatyana Citation: Khodorovskiy, Tatyana. 2012. Symplectic Rational Blow-Up and Embeddings of Rational Homology Balls. Doctoral dissertation, Harvard University. Full Text & Related Files: Khodorovskiy_gsas.harvard_0084L_10189.pdf (1.285Mb; PDF) Abstract: We define the symplectic rational blow-up operation, for a family of rational homology balls $$B_n$$, which appeared in Fintushel and Stern's rational blow-down construction. We do this by exhibiting a symplectic structure on a rational homology ball $$B_n$$ as a standard symplectic neighborhood of a certain 2-dimensional Lagrangian cell complex. We also 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. First, we present a couple of results which illustrate the relative ease with which these rational homology balls can be smoothly embedded into a smooth 4-manifold. Second, 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 $$c^2_1$$ as well. Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9572269 Downloads of this work: