HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence

Abstract

This is the second 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 this auxilliary manifold, its geometry, and the relationship between the generators of the embedded contact homology chain complex and those of the Heegaard Floer chain complex. The pseudoholomorphic curves that define the differential on the embedded contact homology chain complex are also described here as a first step to relate the differential on the latter complex with that on the Heegaard Floer complex.

Various typos corrected

References in corpus (4)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• Pseudoholomorphic punctured spheres in R x (S^1 x S^2) : Properties and existence

Cited by in corpus (15)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence
• Connected sums and involutive knot Floer homology
• Embedded contact homology and open book decompositions
• A contact invariant in sutured monopole homology
• On the monopole Lefschetz number of finite order diffeomorphisms
• On the equivalence of contact invariants in sutured Floer homology theories
• Equivariant Seiberg-Witten-Floer cohomology
• A survey of the homology cobordism group
• Brieskorn spheres, cyclic group actions and the Milnor conjecture
• Seiberg-Witten Floer Spectra and Contact Structures
• Formal Contact Categories
• Taut foliations from knot diagrams
• Knot Floer homology and the fundamental group of $(1,1)$ knots