The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of periodic orbits, and whose differential counts certain embedded pseudoholomorphic curves in cross the mapping torus. It is conjectured to recover the Seiberg-Witten Floer homology of the mapping torus for most spin-c structures, and is related to a variant of contact homology. In this paper we compute the periodic Floer homology of some Dehn twists.
"The periodic Floer homology of a Dehn twist." Algebr. Geom. Topol. 5 (1) 301 - 354, 2005. https://doi.org/10.2140/agt.2005.5.301