Self-Dual Instantons and Holomorphic Curves

Abstract

We prove new adjunction inequalities for embedded surfaces in fourmanifolds with non-negative self-intersection number using the Donaldson invariants.These formulas are completely analogous to the ones obtained by Ozsváth and Szabó [11] using the Seiberg-Witten invariants.To prove these relations, we give a fairly explicit description of the structure of the Fukaya-Floer homology of a surface times a circle.As an aside, we also relate the Floer homology of a surface times a circle with the cohomology of some symmetric products of the surface.