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Morse theory SemesterSoSe 2022 Lecturer Ulrich Bunke Type of course (Veranstaltungsart) Seminar German title Morsetheorie Contents The goal of this seminar is to present the basic constructions of Morse theory and first applications. Interesting outcomes are (the Morse-) inequalities relating the number of critical points of a function on a manifold with the Betti numbers of the manifold, a proof of the fact that a smooth manifold has the homotopy type of a CW-complex, applications to the homotopy type of path- and loop spaces, and a way to calculate the homology of a manifold using gradient flows. Prerequisites for this seminar are the basic theory of smooth manifolds, some elements of Riemannian geometry, and some basic notions of algebraic topology. This seminar could be an interesting addition to the parallel lecture course in Differential Geometry II. The detailed plan of the seminar can be found via the link on Bunke's homepage: https://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Bunke/index.html Recommended previous knowledge Basic knowledge on manifolds. and Riemannian geometry is recommended. Time/Date Fr 10-12 Location MA102 Course homepage GRIPS (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MV, MSem, MGAGeo ECTS BSem und MSem: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16. LA-GySem: 6 LP. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 +++ weitere Details: siehe Modulkatalog +++ |