Holomorphic disks and three-manifold invariants: properties and applications.” Annals of Mathematics 159, no. 3 (2004): 1159–245. at Pennsylvania State U niversity on M ay 11, 2016 http://im rn.oxfordjournals.org/ D ow nloaded from The AD Filtration: Redu

In [27], we introduced Floer homology theories HF−(Y, s), HF∞(Y, s), HF+(Y, t), ĤF (Y, s),and HFred(Y, s) associated to closed, oriented three-man-ifolds Y equipped with a Spinc structures s ∈ Spinc(Y). In the present paper, we give calculations and study the properties of these invariants. The cal-culations 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. 1