Symplectic Floer homology of area-preserving surface diffeomorphisms

The symplectic Floer homology HF*(phi) of a symplectomorphism phi: Sigma -> Sigma encodes data about the fixed points of phi using counts of holomorphic cylinders in R x M-phi, where M-phi is the mapping torus of phi. We give an algorithm to compute HF*(phi) for phi a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF*(h) for h any orientation-preserving mapping class.