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Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.  Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.de Rham cohomology SemesterWiSe 2020 / 21 Lecturer Marc Hoyois Type of course (Veranstaltungsart) Seminar Contents The goal of this seminar is to introduce and study de Rham cohomology, which is an invariant of smooth manifolds defined using differential forms. It is related both to analysis (via the fundamental theorem of calculus and Stokes' theorem) and algebraic topology (as de Rham cohomology turns out to be isomorphic to singular cohomology). Moreover, the ideas underlying the definition of de Rham cohomology are quite versatile and can be applied in many other geometric contexts, for example in algebraic geometry. The seminar will closely follow Chapter I of the book "Differential Forms in Algebraic Topology" by R. Bott and L. W. Tu and cover most of the results therein. The main theorem is Poincaré duality, which is a surprising symmetry in the cohomology of smooth compact manifolds. We will discuss it for both oriented and nonorientable manifolds. See the seminar webpage below for a detailed program of the seminar. Literature Raoul Bott, Loring W. Tu, "Differential Forms in Algebraic Topology", Springer 1982 Recommended previous knowledge Linear algebra, integration in several variables Time/Date Di 8-10 Location online Additional question session Time/Date: Mo 10-13 Location: online Course homepage http://www.mathematik.ur.de/hoyois/WS21/derham/index.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MV, MSem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |