Floer homology
Heegaard Floer homology is an invariant due to Peter Ozsváth and Zoltán Szabó of a closed 3-manifold equipped with a spin"c" structure. It is computed using a Heegaard diagram of the space via a construction analogous to Lagrangian Floer homology. announced a proof that Heegaard Floer homology is isomorphic to Seiberg-Witten Floer homology, and announced a proof that the plus-version of Heegaard Floer homology (with reverse orientation) is isomorphic to embedded contact homology.