HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology

Abstract

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups of M.

25 pages. This version includes a minor revision to Theorem 3.3

References in corpus (3)

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

Cited by in corpus (62)

• 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
• Instantons and odd Khovanov homology
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• A combinatorial spanning tree model for knot Floer homology
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• 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
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• Graph cobordisms and Heegaard Floer homology
• A tour of bordered Floer theory
• An absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields
• Instanton Floer homology, sutures, and Heegaard diagrams
• On the Frøyshov invariant and monopole Lefschetz number
• On the monopole Lefschetz number of finite order diffeomorphisms
• Bordered Floer homology and incompressible surfaces
• On the equivalence of contact invariants in sutured Floer homology theories
• Duality and mapping tori in Heegaard Floer homology
• Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds
• An infinite-rank summand of the homology cobordism group
• Khovanov homology and the cinquefoil
• A survey of the homology cobordism group
• The combinatorics of Morse theory with boundary
• HF = ECH via open book decompositions: a summary
• An enhanced Euler characteristic of sutured instanton homology
• Equivariant Seiberg-Witten-Floer cohomology
• The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds
• Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
• Combinatorial embedded contact homology for toric contact manifolds
• Instanton Floer homology, sutures, and Euler characteristics
• On contact type hypersurfaces in 4-space
• Knots in lattice homology
• Heegaard Floer Homology and Triple Cup Products
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• Cobordism maps in embedded contact homology
• Dimensionally-reduced sutured Floer homology as a string homology
• Manolescu correction terms and knots in the three-sphere
• Localization in Khovanov homology
• Algebraic torsion via Heegaard Floer homology
• Monopoles and foliations without holonomy-invariant transverse measure
• Monopoles, twisted integral homology, and Hirsch algebras
• Brieskorn spheres, cyclic group actions and the Milnor conjecture
• Reeb periodic orbits after a bypass attachment
• On finite energy monopoles on $\mathbb{C}\times \Sigma$
• On the Pin(2)-equivariant monopole Floer homology of plumbed 3-manifolds
• Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg-Witten invariants of 3-manifolds
• Seiberg-Witten Floer Spectra and Contact Structures
• Exotic Dehn twists on sums of two contact 3-manifolds
• Formal Contact Categories
• Indefinite Stein fillings and Pin(2)-monopole Floer homology
• Seiberg-Witten Floer homotopy contact invariant
• A monopole invariant for families of contact structures
• Non-formality in $\mathrm{Pin}(2)$-monopole Floer homology
• Foliations, contact structures and their interactions in dimension three
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology
• Closed geodesics and Frøyshov invariants of hyperbolic three-manifolds
• Admissible transverse surgery does not preserve tightness
• Floer homology and right-veering monodromy
• Knot Floer homology and the fundamental group of $(1,1)$ knots
• Taut foliations from knot diagrams