Journal of Symplectic Geometry

Volume 1 (2001)

Number 4

Floer homology of algebraically finite mapping classes

Pages: 715 – 765



Ralf Gautschi


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.

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