Holomorphic disks and three-manifold invariants: Properties and applications

• 成果类型: Article
• 署名作者: Ozsváth, P; Szabó, Z
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.159.1159
• 发表日期: 2004
• 页码: 1159-1245
• 关键词: seiberg-witten invariants; instanton homology; 4-manifolds; EQUATIONS; torsion; KNOTS; sw

摘要

In [27], we introduced Floer homology theories HF- (Y, s), HFinfinity (Y, s), HF+ (Y, t), (HF) over cap (Y, s),and HFred (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spin(c) structures s is an element of 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.