%0 Electronic Article
%A Ozsváth, Peter and Szabó, Zoltán
%I Princeton University Press
%D 2004
%G English
%@ 0003-486X
%~ Staatliche Kunstsammlungen Dresden, Kunstbibliothek
%T Holomorphic Disks and Three-Manifold Invariants: Properties and Applications
%V 159
%J Annals of Mathematics
%V 159
%N 3
%P 1159-1245
%U https://www.jstor.org/stable/3597176
%X In [27], we introduced Floer homology theories$HF^{-}(Y,\germ{s})$,$HF^{\infty}(Y,\germ{s})$,$HF^{+}(Y,\germ{t})$,$\widehat{HF}(Y,\germ{s})$, and$HF_{\text{red}}(Y,\germ{s})$associated to closed, oriented three-manifolds Y equipped with a$\text{Spin}^{c}$structures$\germ{s}\in \text{Spin}^{c}(Y)$. 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$HF^{\pm}$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.

%Z https://katalog.skd.museum/Record/ai-55-aHR0cHM6Ly93d3cuanN0b3Iub3JnL3N0YWJsZS8zNTk3MTc2
%U https://katalog.skd.museum/Record/ai-55-aHR0cHM6Ly93d3cuanN0b3Iub3JnL3N0YWJsZS8zNTk3MTc2