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.