Holomorphic disks and three-manifold invariants: properties and applications

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

2001-05-24

arxiv.org/abs/math/0105202v4

Mathematics

Symplectic Geometry

87 pages, 12 figures. To appear in Annals of Mathematics. Reorganized both this paper and its prequel, math.SG/0101206

Scientific paper

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. 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 these theories 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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