  This is the fourth of five papers that construct an isomorphism between the
Seiberg-Witten Floer homology and the Heegaard Floer homology of a given
compact, oriented 3-manifold. The isomorphism is given as a composition of
three isomorphisms; the first of these relates a version of embedded contact
homology on an an auxillary manifold to the Heegaard Floer homology on the
original. The second isomorphism relates the relevant version of the embedded
contact homology on the auxilliary manifold with a version of the
Seiberg-Witten Floer homology on this same manifold. The third isomorphism
relates the Seiberg-Witten Floer homology on the auxilliary manifold with the
appropriate version of Seiberg-Witten Floer homology on the original manifold.
The paper describes the second of these isomorphisms.
