Various Seiberg–Witten–Floer cohomologies are defined for a closed, oriented three-manifold; and if it is the mapping torus of an areapreserving surface automorphism, it has an associated periodic Floer homology as defined by Michael Hutchings. We construct an isomorphism between a certain version of Seiberg–Witten–Floer cohomology and the corresponding periodic Floer homology, and describe some immediate consequences.
"Periodic Floer homology and Seiberg-Witten-Floer cohomology." J. Symplectic Geom. 10 (1) 81 - 164, March 2012.