Holomorphic disks and topological invariants for closed three-manifolds

Abstract

The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spinc structure. Given a Heegaard splitting of Y = U0∑⊃ 1, these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product ∑ of relative to certain totally real subspaces associated to U0 and U1.