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# Journal of Symplectic Geometry

## Volume 1 (2001)

### Number 4

### Floer homology of algebraically finite mapping classes

Pages: 715 – 765

DOI: http://dx.doi.org/10.4310/JSG.2001.v1.n4.a4

#### Author

#### 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.