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.
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