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
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References
SHOWING 1-10 OF 28 REFERENCES
The Seiberg–Witten equations and the Weinstein conjecture
- Mathematics
- 2006
Let M denote a compact, oriented 3–dimensional manifold and let a denote a contact 1–form on M; thus a∧da is nowhere zero. This article proves that the vector field that generates the kernel of da…
Monopoles and Three-Manifolds
- Mathematics
- 2008
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.…
Rounding corners of polygons and the embedded contact homology of T 3
- Mathematics
- 2006
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…
Geometry of four-manifolds
- Mathematics
- 1986
1. Four-manifolds 2. Connections 3. The Fourier transform and ADHM construction 4. Yang-Mills moduli spaces 5. Topology and connections 6. Stable holomorphic bundles over Kahler surfaces 7. Excision…
Compactness results in Symplectic Field Theory
- Mathematics
- 2003
This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic…
Seiberg-Witten and Gromov invariants for symplectic 4-manifolds
- Mathematics
- 2005
1. SW => Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves 1. The Seiberg-Witten equations 2. Estimates 3. The monotonicity formula 4. The local structure of [alpha]1(0) 5.…
The embedded contact homology index revisited
- Mathematics
- 2008
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…
Coherent orientations in symplectic field theory
- Mathematics
- 2001
Abstract.We study the coherent orientations of the moduli spaces of holomorphic curves in Symplectic Field Theory, generalizing a construction due to Floer and Hofer. In particular we examine their…
The analysis of elliptic families
- Mathematics
- 1986
In this paper we specialize the results obtained in [BF1] to the case of a family of Dirac operators. We first calculate the curvature of the unitary connection on the determinant bundle which we…
An index inequality for embedded pseudoholomorphic curves in symplectizations
- Mathematics
- 2001
Abstract.Let Σ be a surface with a symplectic form, let φ be a symplectomorphism of Σ, and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic…