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

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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 $M\phantom{\rule{-0.17em}{0ex}}$.

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