Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 4 (2013), 2239-2260.
The absolute gradings on embedded contact homology and Seiberg–Witten Floer cohomology
Let be a closed connected contact –manifold. In [Geom. Topol. 14 (2010) 2497–2581], Taubes defines an isomorphism between the embedded contact homology (ECH) of and its Seiberg–Witten Floer cohomology. Both the ECH of and the Seiberg–Witten Floer cohomology of admit absolute gradings by homotopy classes of oriented –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.
Algebr. Geom. Topol., Volume 13, Number 4 (2013), 2239-2260.
Received: 15 September 2012
Revised: 26 February 2013
Accepted: 3 March 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53D40: Floer homology and cohomology, symplectic aspects
Cristofaro-Gardiner, Daniel. The absolute gradings on embedded contact homology and Seiberg–Witten Floer cohomology. Algebr. Geom. Topol. 13 (2013), no. 4, 2239--2260. doi:10.2140/agt.2013.13.2239. https://projecteuclid.org/euclid.agt/1513715637