TY - JOUR
T1 - Holomorphic disks and three-manifold invariants
T2 - Properties and applications
AU - Ozsváth, Peter
AU - Szabó, Zoltán
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2004/5
Y1 - 2004/5
N2 - In [27], 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.
AB - In [27], 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.
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U2 - 10.4007/annals.2004.159.1159
DO - 10.4007/annals.2004.159.1159
M3 - Article
AN - SCOPUS:14544307318
SN - 0003-486X
VL - 159
SP - 1159
EP - 1245
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 3
ER -