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$\mathrm{HF}=\mathrm{HM}$, I: Heegaard Floer homology and Seiberg–Witten Floer homology

Çağatay Kutluhan, Yi-Jen Lee and Clifford Henry Taubes

Geometry & Topology 24 (2020) 2829–2854
DOI: 10.2140/gt.2020.24.2829
Abstract

Let M be a closed, connected and oriented 3–manifold. This article is the first of a five-part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg–Witten Floer homology groups of M.

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Keywords
Heegaard Floer homology, Seiberg–Witten Floer homology
Mathematical Subject Classification 2010
Primary: 53C07, 53C15
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
Authors
Çağatay Kutluhan
Department of Mathematics
University at Buffalo
Buffalo, NY
United States
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