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 ${\mathrm{Spin}}^c$ structure. Given a Heegaard splitting of $Y=U_{0}\cup_{\Sigma}U_{1}$, 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 $U_{1}$.