Using sympectic Floer homology, Seidel associated a module to each mapping class of a compact connected oriented two-manifold of genus bigger than one. We compute this module for mapping classes which do not have any pseudo-Anosov components in the sense of Thurston's theory of surface diffeomorphisms. The Nielsen-Thurston representative of such a class is shown to be monotone. The formula for the Floer homology is obtained for a topological separation of fixed points and a separation mechanism for Floer connecting orbits. As examples, we consider the geometric monodroy of isolated plane curve singularities. In this case, the formula for the Floer homology is particularly simple.
"Floer homology of algebraically finite mapping classes." J. Symplectic Geom. 1 (4) 715 - 765, March, 2003.