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| Main Authors: | , |
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| Format: | Preprint |
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2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2007.13883 |
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| _version_ | 1866914803320094720 |
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| author | Nelson, Jo Weiler, Morgan |
| author_facet | Nelson, Jo Weiler, Morgan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_13883 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Embedded contact homology of prequantization bundles Nelson, Jo Weiler, Morgan Symplectic Geometry 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. |
| title | Embedded contact homology of prequantization bundles |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2007.13883 |