English

Holomorphic disks and three-manifold invariants: properties and applications

Symplectic Geometry 2007-05-23 v4 Algebraic Geometry Geometric Topology

Abstract

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.

Keywords

Cite

@article{arxiv.math/0105202,
  title  = {Holomorphic disks and three-manifold invariants: properties and applications},
  author = {Peter Ozsvath and Zoltan Szabo},
  journal= {arXiv preprint arXiv:math/0105202},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T16:38:50.701Z