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

  title={HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology},
  author={Çağatay Kutluhan and Yi-Jen Lee and Clifford H. Taubes},
  journal={arXiv: Geometric Topology},
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. 
Heegaard Floer Homology and Triple Cup Products
We give a complete calculation of the infinity flavor of Heegaard Floer homology with mod 2 coefficients for all three-manifolds and torsion Spin^c structures. The computation agrees with theExpand
Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions
The proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology is sketched and expressed in terms of an open book decomposition of the ambient manifold. Expand
The equivalence of two Seiberg-Witten Floer homologies
We show that monopole Floer homology (as defined by Kronheimer and Mrowka) is isomorphic to the S^1-equivariant homology of the Seiberg-Witten Floer spectrum constructed by the second author.
Duality and mapping tori in Heegaard Floer homology
We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants ofExpand
A remark on the geography problem in Heegaard Floer homology
We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integerExpand
Algebraic torsion via Heegaard Floer homology
We outline Hutchings's prescription that produces an ECH analog of Latschev and Wendl's algebraic $k$-torsion in the context of $ech$, a variant of ECH used in a proof of the isomorphism betweenExpand
Notes on bordered Floer homology
This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard Floer homology canExpand
Floer theory and its topological applications
We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, andExpand
HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence
This is the fourth 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 isExpand
Tour of bordered Floer theory
This survey explains the formal structure and construction of bordered Floer homology and sketches how it can be used to compute some aspects of Heegaard Floer theory. Expand


Periodic Floer homology and Seiberg-Witten Floer cohomology
Various Seiberg-Witten Floer cohomologies are defined for a closed, oriented 3-manifold; and if it is the mapping torus of an area-preserving surface automorphism, it has an associated periodic FloerExpand
Embedded contact homology and Seiberg–Witten Floer cohomology II
This is a sequel to four earlier papers by the author that construct an isomorphism between the embedded contact homology and Seiberg‐Witten Floer cohomology of a compact 3‐manifold with a givenExpand
Given a three-manifold with b1 = 1 and a nontorsion spin c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodicExpand
The periodic Floer homology of a Dehn twist.
The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits,Expand
Embedded contact homology and its applications
Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology (and both areExpand
Heegaard Splittings and Seiberg-Witten monopoles
This is an expansion on my talk at the Geometry and Topology conference at McMaster University, May 2004. We outline a program to relate the Heegaard Floer homologies of Ozsvath-Szabo, andExpand
Embedded contact homology and Seiberg-Witten Floer cohomology I
This is the third of five papers whose purpose is to prove that the embedded contact homology of a compact, oriented 3–dimensional manifold with contact 1–form is isomorphic to the manifold’sExpand
Monopoles and Three-Manifolds
Preface 1. Outlines 2. The Seiberg-Witten equations and compactness 3. Hilbert manifolds and perturbations 4. Moduli spaces and transversality 5. Compactness and gluing 6. Floer homology 7.Expand
A cylindrical reformulation of Heegaard Floer homology
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold U a0;1c R, where U is the Heegaard surface, instead of Sym g .U/. We then show that the entireExpand
Holomorphic disks and topological invariants for closed three-manifolds
The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y, equipped with a Spiny structure. Given a Heegaard splitting of Y = U 0o U Σ U 1 , theseExpand