Holomorphic disks and topological invariants for closed three-manifolds

The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spin(c) structure. Given a Heegaard splitting of Y = U-0 boolean ORSigma U-1, these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Sigma relative to certain totally real subspaces associated to U-0 and U-1.