HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence

Abstract

This is the third of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an an auxillary manifold to the Heegaard Floer homology on the original. This paper describes the relationship between the differential on the embedded contact homology chain complex and the differential on the Heegaard Floer chain complex. The paper also describes the relationship between the various canonical endomorphisms that act on the homology groups of these two complexes.

various typos corrected in this new version

References in corpus (4)

• Floer homology and knot complements
• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence

Cited by in corpus (33)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• A combinatorial spanning tree model for knot Floer homology
• Connected sums and involutive knot Floer homology
• Embedded contact homology and open book decompositions
• HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence
• A contact invariant in sutured monopole homology
• Graph cobordisms and Heegaard Floer homology
• A tour of bordered Floer theory
• Instanton Floer homology, sutures, and Heegaard diagrams
• On the monopole Lefschetz number of finite order diffeomorphisms
• Bordered Floer homology and incompressible surfaces
• Duality and mapping tori in Heegaard Floer homology
• On the equivalence of contact invariants in sutured Floer homology theories
• Equivariant Seiberg-Witten-Floer cohomology
• A survey of the homology cobordism group
• Instanton Floer homology, sutures, and Euler characteristics
• Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
• Cobordism maps in embedded contact homology
• On contact type hypersurfaces in 4-space
• Dimensionally-reduced sutured Floer homology as a string homology
• Algebraic torsion via Heegaard Floer homology
• Containment problems for polytopes and spectrahedra
• Brieskorn spheres, cyclic group actions and the Milnor conjecture
• Formal Contact Categories
• Seiberg-Witten Floer homotopy contact invariant
• Seiberg-Witten Floer Spectra and Contact Structures
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology
• Admissible transverse surgery does not preserve tightness
• Knot Floer homology and the fundamental group of $(1,1)$ knots
• Taut foliations from knot diagrams
• Foliations, contact structures and their interactions in dimension three