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$\mathrm{HF}=\mathrm{HM}$,
II: Reeb orbits and holomorphic curves for the ech/Heegaard
Floer correspondence
Çağatay Kutluhan, Yi-Jen Lee and Clifford Henry Taubes |
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Geometry & Topology 24 (2020) 2855–3012
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DOI: 10.2140/gt.2020.24.2855
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Abstract |
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This is the second of five papers that construct an isomorphism between the Seiberg–Witten Floer homology and the Heegaard Floer homology of a given compact, oriented –manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an auxiliary manifold to the Heegaard Floer homology on the original. This paper describes this auxiliary manifold, its geometry and the relationship between the generators of the embedded contact homology chain complex and those of the Heegaard Floer chain complex. The pseudoholomorphic curves that define the differential on the embedded contact homology chain complex are also described here as a first step to relate the differential on the latter complex with that on the Heegaard Floer complex. |
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Keywords
Seiberg–Witten Floer homology, Heegaard Floer homology
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Mathematical Subject Classification 2010
Primary: 53C07, 53C15
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References |
Publication
Received: 17 February 2012
Revised: 3 November 2015
Accepted: 23 April 2018
Published: 29 December 2020
Proposed: Tomasz Mrowka
Seconded: András I Stipsicz, Bruce Kleiner
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Authors |
| Çağatay Kutluhan | |
| Department of Mathematics University at Buffalo Buffalo, NY United States |
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| Yi-Jen Lee | |
| Department of Mathematics The Chinese University of Hong Kong Shatin, NT Hong Kong |
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| Clifford Henry Taubes | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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