Professor Alexander Voronov
This will be an introduction to Morse theory and its generalizations. Morse theory one of many ways to define the homology of a manifold, just like de Rham, cellular, and singular homology. The nice thing about Morse theory is that it uses some analysis to study topology, easily generalizes to infinite dimensions, and works better in counting critical points of functions and stable points of diffeomorphisms on manifolds. And it is not covered by traditional courses in Manifolds and Topology and Algebraic Topology, either...
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