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$\mathrm{HF}=\mathrm{HM}$,
III: Holomorphic curves and the differential for the
ech/Heegaard Floer correspondence
Çağatay Kutluhan, Yi-Jen Lee and Clifford Henry Taubes |
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Geometry & Topology 24 (2020) 3013–3218
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DOI: 10.2140/gt.2020.24.3013
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Abstract |
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This is the third 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 the relationship between the differential on the embedded contact homology chain complex and the differential on the Heegaard Floer chain complex. The paper also describes the relationship between the various canonical endomorphisms that act on the homology groups of these two complexes. |
Keywords
Seiberg–Witten Floer homology, Heegaard Floer homology
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Mathematical Subject Classification 2010
Primary: 53D42
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References |
Publication
Received: 17 February 2012
Revised: 14 September 2016
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 | |
| Institute of Mathematical
Sciences 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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