相关论文: Embedded contact homology and open book decomposit…

We sketch the proof of the equivalence between the hat versions of Heegaard Floer homology and embedded contact homology. The key point is to express these two Floer homology theories in terms of an open book decomposition of the ambient…

Given an open book decomposition (S,h) adapted to a closed, oriented 3-manifold M, we define a chain map from a certain Heegaard Floer chain complex associated to (S,h) to a certain embedded contact homology chain complex associated to…

This paper is the sequel to "The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I" and is devoted to proving some of the technical parts of the HF=ECH isomorphism.

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 are conjecturally isomorphic to a version of Heegaard…

Given a closed oriented 3-manifold M, we establish an isomorphism between the Heegaard Floer homology group HF^+(-M) and the embedded contact homology group ECH(M). Starting from an open book decomposition (S,h) of M, we construct a chain…

This article is a survey on the authors' proof of the isomorphism between Heegaard Floer homology and embedded contact homology appeared in This article is a survey on the authors' proof of the isomorphism between Heegaard Floer homology…

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As…

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 is given as a composition of three…

We prove the equivalence of the sutured versions of Heegaard Floer homology, monopole Floer homology, and embedded contact homology. As applications we show that the knot versions of Heegaard Floer homology and embedded contact homology are…

We introduce a contact invariant in the bordered sutured Heegaard Floer homology of a three-manifold with boundary. The input for the invariant is a contact manifold $(M, \xi, \mathcal{F})$ whose convex boundary is equipped with a signed…

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…

This paper develops the analysis needed to set up a Morse-Bott version of embedded contact homology (ECH) of a contact three-manifold in certain cases. In particular we establish a correspondence between "cascades" of holomorphic curves in…

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…

We give a construction of embedded contact homology (ECH) for a contact $3$-manifold $Y$ with convex sutured boundary and a pair of Legendrians $\Lambda_+$ and $\Lambda_-$ contained in $\partial Y$ satisfying an exactness condition. The…

Let Y be a closed oriented 3-manifold with a contact form such that all Reeb orbits are nondegenerate. The embedded contact homology (ECH) index associates an integer to each relative 2-dimensional homology class of surfaces whose boundary…

Embedded contact knot homology (ECK) is a variation on Embedded contact homology (ECH), defined with respect to an open book decomposition compatible with a contact structure on some 3-manifold, M. The knot in question is given by the…

Given a contact three manifold $Y$ with a nondegenerate contact form $\lambda$, and an almost complex structure $J$ compatible with $\lambda$, its embedded contact homology $ECH(Y,\lambda)$ is defined (arXiv:1303.5789) and only depends on…

Giroux has described a correspondence between open book decompositions on a 3--manifold and contact structures. In this paper we use Heegaard Floer homology to give restrictions on contact structures which correspond to open book…

The embedded contact homology (ECH) of a 3-manifold with a contact form is a variant of Eliashberg-Givental-Hofer's symplectic field theory, which counts certain embedded J-holomorphic curves in the symplectization. We show that the ECH of…

Let Y be a closed connected contact 3-manifold. In the series of papers "Embedded contact homology and Seiberg-Witten Floer cohomology I-V", Taubes defines an isomorphism between the embedded contact homology (ECH) of Y and its…