# Embedded contact homology and Seiberg–Witten Floer cohomology II

@article{Taubes2008EmbeddedCH, title={Embedded contact homology and Seiberg–Witten Floer cohomology II}, author={Clifford H. Taubes}, journal={Geometry \& Topology}, year={2008}, volume={14}, pages={2497-2581} }

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 given contact 1‐form. These respective homology/cohomology theories carry additional structure; this sequel proves that the isomorphism that is constructed in the first four papers is compatible with this extra structure.

## 98 Citations

Periodic Floer homology and Seiberg-Witten Floer cohomology

- Mathematics
- 2009

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 Floer…

The absolute gradings on embedded contact homology and Seiberg-Witten Floer cohomology

- Mathematics
- 2012

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…

Embedded contact homology and its applications

- Mathematics
- 2010

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…

The absolute gradings on embedded contact homology and Seiberg –

- Mathematics
- 2013

Let Y be a closed connected contact 3–manifold. In [14], Taubes defines an isomorphism between the embedded contact homology (ECH) of Y and its Seiberg–Witten Floer cohomology. Both the ECH of Y and…

Embedded contact homology and open book decompositions

- Mathematics
- 2010

This is the first of a series of papers devoted to proving the equivalence of Heegaard Floer homology and embedded contact homology (abbreviated ECH). In this paper we prove that, given a closed,…

Correction to a lemma in Embedded Contact Homology and Seiberg-Witten Floer Homology IV

- Mathematics
- 2018

This note corrects an erroneous statement in Lemma 3.8 of the author's paper Embedded Contact Homology and Seiberg-Witten Floer Homology IV which was published in Volume 14 of Geometry and Topology…

HF=HM, I : Heegaard Floer homology and
Seiberg–Witten Floer homology

- MathematicsGeometry & Topology
- 2020

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…

LECTURES ON THE EQUIVALENCE OF HEEGAARD FLOER AND SEIBERG–WITTEN FLOER HOMOLOGIES

- Mathematics
- 2013

This article gives a detailed account of the lectures delivered by the author on the construction, in joint work with Yi-Jen Lee and Clifford H. Taubes, of isomorphisms between Heegaard Floer and…

An exposition of the equivalence of Heegaard
Floer homology and embedded contact homology

- Mathematics
- 2020

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…

Seiberg-Witten Floer homotopy contact invariant

- Mathematics
- 2020

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer-Mrowka-Ozv\'ath-Szab\'o. Moreover, we prove a gluing formula relating our invariant with the first author's…

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