In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of these theories and Turaev's torsion, a relationship with the minimal genus problem (Thurston norm), and surgery exact sequences. We also include some applications of these techniques to three-manifold topology.
arXiv Mathematics e-prints
- Pub Date:
- May 2001
- Mathematics - Symplectic Geometry;
- Mathematics - Algebraic Geometry;
- Mathematics - Geometric Topology
- 87 pages, 12 figures. To appear in Annals of Mathematics. Reorganized both this paper and its prequel, math.SG/0101206