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.

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

References in corpus (5)

• Holomorphic disks and three-manifold invariants: properties and applications
• Heegaard splittings of compact 3-manifolds
• Holomorphic triangles and invariants for smooth four-manifolds
• Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I
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Cited by in corpus (9)

• Holomorphic disks and three-manifold invariants: properties and applications
• Seifert fibered contact three-manifolds via surgery
• Joining and gluing sutured Floer homology
• Computations of Heegaard-Floer knot homology
• Comultiplicativity of the Ozsvath-Szabo contact invariant
• Knot Floer homology of (1,1)-knots
• Symmetric products of surfaces; a unifying theme for topology and physics
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Variants of equivariant Seiberg-Witten Floer homology