Holomorphic disks and three-manifold invariants: Properties and applications

In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ Spin c (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.

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