Holomorphic disks and topological invariants for closed three-manifolds
Symplectic Geometry
2009-09-25 v4 Differential Geometry
Geometric Topology
Abstract
The aim of this article is to introduce and study certain topological invariants for closed, oriented three-manifolds Y. These groups are relatively Z-graded Abelian groups associated to SpinC structures over Y. Given a genus g Heegaard splitting of Y, these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of the surface relative to certain totally real subspaces associated to the handlebodies.
Cite
@article{arxiv.math/0101206,
title = {Holomorphic disks and topological invariants for closed three-manifolds},
author = {Peter Ozsvath and Zoltan Szabo},
journal= {arXiv preprint arXiv:math/0101206},
year = {2009}
}
Comments
118 pages, 10 figures, to appear in Annals of Mathematics. Reorganized both this paper and its sequel: the first paper now gives the definitions for closed, oriented three-manifolds. Properties and examples are given in the second paper