In , we introduced Floer homology theories HF-(Y, s)t HF∞(Y,s), HF+(Y,t), HF(Y,s),and. HF red(Y,s) associated to closed, oriented three-manifolds Y equipped with a Spinc structures s ∈ Spinc(Y). 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 HF ± 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty