SYMPLECTIC RATIONAL BLOW-UP TATYANA KHODOROVSKIY

Abstract. Fintushel and Stern defined the rational blow-down con-struction [FS] for smooth 4-manifolds, where a linear plumbing config-uration of spheres Cn is replaced with a rational homology ball Bn, n ≥ 2. Subsequently, Symington [Sy] defined this procedure in the sym-plectic category, where a symplectic Cn (given by symplectic spheres) is replaced by a symplectic copy of Bn to yield a new symplectic man-ifold. As a result, a symplectic rational blow-down can be performed on a manifold whenever such a configuration of symplectic spheres can be found. In this paper, we define the inverse procedure, the rational blow-up in the symplectic category, where we present the symplectic structure of Bn as an entirely standard symplectic neighborhood of a certain Lagrangian 2-cell complex. Consequently, a symplectic rational blow-up can be performed on a manifold whenever such a Lagrangian 2-cell complex is found. 1