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Differential Forms 2

CIT413033Elective Modules5 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn how differential forms are applied in algebraic and differential topology as well as in differential geometry. In the end you will be able to apply and interrelate concepts such as de-Rham cohomology, Poincaré duality, Mayer-Vietoris, the Künneth formula, fixed-point and degree theory as well as basics on fiber bundles, characteristic classes, Lie groups and Riemannian manifolds.

What you will be able to do

  • Application of differential forms to compute de-Rham cohomology groups
  • Understanding and using Poincaré duality, Mayer-Vietoris sequences and the Künneth formula
  • Application of degree and fixed-point theory
  • Basic knowledge on fiber bundles and characteristic classes
  • Insights into Lie groups and Riemannian manifolds
  • Interlinking topological, geometric, algebraic and analytic methods

What the module consists of

  • VorlesungVermittlung der Inhalte durch Vortrag, Beispiele und Diskussionen
  • Übung (alle zwei Wochen)Vertiefung der Inhalte durch Aufgabenblätter und Lösungen; Selbstüberprüfung des Lernfortschritts

Teaching method

  • VorlesungPräsentation der Inhalte mit demonstrativen Beispielen und Diskussion, Anregung zur eigenständigen Analyse und Literaturarbeit
  • ÜbungenErmöglichen der Vertiefung durch Aufgaben und Lösungen, regelmäßige Selbstkontrolle
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Official page in TUMonline · Details are not binding.