Augustin Banyaga, Committee Chair/Co-Chair Ping Xu, Committee Member Sergei Tabachnikov, Committee Member Abhay Vasant Ashtekar, Committee Member Nigel David Higson, Committee Member
Floer homology for a symplectic manifold is defined by choosing a generic function and almost complex structure. It is easy to see that if two functions generate the same isotopy of the manifold, the homology groups constructed are the same. In the thesis, I extend the choices available to include certain isotopies of the manifold. This gives a way of proving that the Seidel representation is topologically rigid, in the sense that if two Hamiltonian loops of diffeomorphisms are homotopic through loops of arbitrary diffeomorphisms, then the image of the classes of these loops under Seidel's map agree.