Fukaya Floer homology of $\Sigma \times S^1$ and applications

Abstract

We determine the Fukaya Floer homology of the three-manifold which is the product of a Riemann surface of genus $g\geq 1$ times the circle. This sets up the groundwork for finding the structure of the Donaldson invariants of four-manifolds not of simple type in the future. We give the following applications: 1) We show that every four-manifold with $b^+>1$ is of finite type. 2) Some results relevant to Donaldson invariants of connected sums along surfaces. 3) We find the invariants of the product of two Riemann surfaces both of genus greater or equal than one.