Symplectic forms and surfaces of negative square

Abstract

We introduce an analogue of the inflation technique of Lalonde--McDuff, allowing us to obtain new symplectic forms from symplectic surfaces of negative self-intersection in symplectic 4-manifolds. We consider the implications of this construction for the symplectic cones of Käahler surfaces, proving along the way a result which can be used to simplify the intersections of distinct pseudo-holomorphic curves via a perturbation.