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

Cristofaro-Gardiner, Daniel¹

¹Mathematics Department, University of California, Berkeley, 970 Evans Hall, Berkeley, CA 94720, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2239-2260

Résumé

Let Y be a closed connected contact 3–manifold. In [Geom. Topol. 14 (2010) 2497–2581], 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 2–plane fields. We show that Taubes’ isomorphism preserves these gradings, which implies that the absolute grading on ECH is a topological invariant. 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.

Détail

DOI : 10.2140/agt.2013.13.2239

Classification : 53D40
Keywords: embedded contact homology, Seiberg–Witten theory, absolute gradings

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