HF=HM, I : Heegaard Floer homology andSeiberg–Witten Floer homology

This is the authors' abstract. We don't add key points for this paper.

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