#### Volume 24, issue 6 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
$\mathrm{HF}=\mathrm{HM}$, 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 $M\phantom{\rule{-0.17em}{0ex}}$.

##### Keywords
Heegaard Floer homology, Seiberg–Witten Floer homology
##### Mathematical Subject Classification 2010
Primary: 53C07, 53C15
##### 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