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Morse theory and the h-cobordism theorem SemesterWiSe 2024 / 25 Lecturer Stefan Friedl Type of course (Veranstaltungsart) Vorlesung German title Morsetheorie und der h-Kobordismussatz Contents I will teach a topology course in the winter term and the summer term. The following topics will be covered throughout the year: In Morse theory we will see that every closed smooth manifolds can be equipped with a handle decomposition. This can be used to give a proof of the classification of surfaces. The h-cobordism theorem shows that certain manifolds are products. The main application is the proof that every smooth homotopy sphere of dimension >5 is homeomorphic to the standard sphere. Afterwards we will develop the theory of vector bundles and characteristic classes. We will outline a proof of the Hirzebruch signature theorem and show, following Milnor, that there exist 7-dimensional homotopy spheres that are not diffeomorphic to the standard sphere. Literature lecture notes will be provided, some of the content will be inspired by the classical books of Milnor on Morse theory, characteristic classes and the h-cobordism theorem. Recommended previous knowledge basic knowledge of fundamental groups and homology, in the summer term I will require some knowledge of cohomology theory. Time/Date Tuesday+Thursday 10-12 Location M101 Registration
the time of the exercise class will be picked in the first lecture Modules BV, MV, MGAGeo ECTS 9 |