## Holomorphic disks and three-manifold invariants: properties and applications

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@MISC{Ozsváth_holomorphicdisks,

author = {Peter Ozsváth and Zoltán Szabó},

title = {Holomorphic disks and three-manifold invariants: properties and applications},

year = {}

}

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### Abstract

̂HF(Y, s),and HFred(Y, s) associated to closed, oriented three-manifolds Y equipped with a Spin c 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. 1.