HF=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.