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

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 $M$.