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$\mathrm{HF}=\mathrm{HM}$,
IV: The Seiberg–Witten Floer homology and ech
correspondence
Çağatay Kutluhan, Yi-Jen Lee and Clifford Henry Taubes |
|
Geometry & Topology 24 (2020) 3219–3469
|
Abstract |
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This is the fourth 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. The second isomorphism relates the relevant version of the embedded contact homology on the auxiliary manifold with a version of the Seiberg–Witten Floer homology on this same manifold. The third isomorphism relates the Seiberg–Witten Floer homology on the auxiliary manifold with the appropriate version of Seiberg–Witten Floer homology on the original manifold. The paper describes the second of these isomorphisms. |
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Keywords
Heegaard Floer homology, Seiberg–Witten Floer homology,
pseudoholomorphic curves
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Mathematical Subject Classification 2010
Primary: 53C07
Secondary: 52C15
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References |
Publication
Received: 17 February 2012
Revised: 16 February 2019
Accepted: 14 November 2019
Published: 6 January 2021
Proposed: Tomasz Mrowka
Seconded: Tobias H Colding, Yasha Eliashberg
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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 |
|
| Clifford Henry Taubes | |
| Department of Mathematics Harvard University Cambridge, MA United States |
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