Floer homology of algebraically finite mapping classes

Abstract

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.