2013/07/16 by Khodorovskiy, Tatyana
#57R17 #57R40 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1307.4321
The rational homology balls Bn 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 Bn 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 Bn, for high n, a symplectic 4-manifold must at least have a high enough c12 as well.