Embedded contact homology of prequantization bundles

DOI10.4310/JSG.2023.V21.N6.A1arXiv2007.13883MaRDI QIDQ6345963

Jo Nelson, Morgan Weiler

Publication date: 27 July 2020

Abstract: The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. We extend this result by computing the Z-grading on the chain complex, permitting a finer understanding of this isomorphism and a stability result for ECH. We fill in a number of technical details, including the Morse-Bott direct limit argument and the classification of certain J-holomorphic buildings. The former requires the isomorphism between filtered Seiberg-Witten Floer cohomology and filtered ECH as established by Hutchings-Taubes. The latter requires the work on higher asymptotics of pseudoholomorphic curves by Cristofaro-Gardiner--Hutchings--Zhang to obtain the writhe bounds necessary to appeal to an intersection theory argument of Hutchings-Nelson.

Mathematics Subject Classification ID

Manifolds and cell complexes (57-XX) Differential geometry (53-XX)

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