Tuesday and Thursday 12:30:-1:50, room TBA .
Overview of the courseMorse theory is the study of the profound relationship between the topology of a space and the behavior of the functions defined on it. It is an extremely powerful tool which plays an important role in many areas of geometry and topology. In this course we will first discuss the basic machinery of Morse theory starting with the material described in Milnor's classic text. We will then discuss the modern formulation of these ideas due to Thom, Smale, Witten and Floer. This goes under the name of Morse homology, and is the (finite-dimensional) model of Floer homology.
PrerequisitesThe prerequisites for this class are basic differential topology and algebraic topology at the level of Guillemin and Pollack's book Differential Topology and Vassiliev's book Introduction to Topology. If you have taken Math 518 you should be well equipped for this class.
Reference (recommended)"Morse Theory" by J.W. Milnor, Annals of Math. Studies, vol. 51, Princeton University Press, 1963.
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