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

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 Seiberg-Witten Floer cohomology. Both the ECH of Y and the Sei...

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Bibliographic Details
Published inarXiv.org
Main Author Cristofaro-Gardiner, Daniel
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.03.2013
Subjects
Homology
Isomorphism
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Summary: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 Seiberg-Witten Floer cohomology. Both the ECH of Y and the Seiberg-Witten Floer cohomology of Y admit absolute gradings by homotopy classes of oriented two-plane fields. We show that Taubes' isomorphism preserves these gradings. To do this, we prove another result relating the expected dimension of any component of the Seiberg-Witten moduli space over a completed connected symplectic cobordism to the ECH index of a corresponding homology class.
ISSN:2331-8422