Holomorphic disks and topological invariants for closed three-manifolds
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2001
- DOI:
- 10.48550/arXiv.math/0101206
- arXiv:
- arXiv:math/0101206
- Bibcode:
- 2001math......1206O
- Keywords:
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- Mathematics - Symplectic Geometry;
- Mathematics - Differential Geometry;
- Mathematics - Geometric Topology
- E-Print:
- 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