Embedded contact homology and Seiberg–Witten Floer cohomology V

Abstract

This is a sequel to four earlier papers by the author that construct an isomorphism between the embedded contact homology and Seiberg–Witten Floer cohomology of a compact $3$–manifold with a given contact $1$–form. These respective homology/cohomology theories carry additional structure; this sequel proves that the isomorphism that is constructed in the first four papers is compatible with this extra structure.