D. Kotschick: Differenzierbare Mannigfaltigkeiten (BA/MA) / Differential Geometry (TMP)

• Time and place: Tuesday 10-12 and Wednesday 14-16 (Note change of time!), room B 006
• Exercise classes: Monday 14-16 in room B 252, Thursday 10-12 in room B 006 and Friday 12-14 in room B132. The Monday and Thursday classes will be held in English, and the Friday class in German.
• Contents: We shall introduce the basic concepts used in modern geometry: manifolds, vector bundles, Lie groups and Lie algebras; vector fields and flows; differential forms, distributions and integrability conditions; Riemannian metrics, connections, curvature.
• Lecture notes (Updated 3 February 2014.)
• Intended audience: This course is obligatory for all Bachelor/Master and all TMP students wishing to take further courses in geometry and/or topology later on. It is also suitable for those who do not want to specialize in this area, but want to learn the basics for use in physics or in other areas of mathematics.
  Modules covered by this course: WP11 Bachelor Mathematik, WP8 Master Mathematik, WP1 TMP Master, WP52 Master Wirtschaftsmathematik
  Bachelor-, Diplom- und Lehramts-Studenten die eine Einführung in die Differentialgeometrie hören wollen, sollten diese Vorlesung besuchen. (Bei Bedarf werden sowohl deutsche als auch englische Übungsgruppen angeboten.) Für Lehramtstudenten eignet sich diese Vorlesung für das Prüfungsgebiet Geometrie im Staatsexamen.
• Prerequisites: We shall assume familiarity with linear algebra, multivariable calculus and point set topology.
• Main text: L. Conlon: Differentiable Manifolds  --- A first course. Birkhäuser Verlag 1993. (The second, expanded, edition of this book does not have the subtitle "A first course'' any more; of course you can use the second edition if you like.)
  Further Reading: B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry --- Methods and Applications, Vol. II, Springer Verlag 1990.
  S. Morita: Geometry of Differential Forms. Amer. Math. Soc. 2001.
  F. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer Verlag 1983.
  S. Lang: Fundamentals of Differential Geometry. Springer Verlag 1999.



• Note about the exam: The exam for this course is just that - an exam for people who took the course. If you did not attend the course and register for it, you cannot take the exam. We will not stop you from gate crashing, but we will not grade your exam.
  There are only two valid registrations: either you signed up on the sheets I circulated in class in October and/or December, or you talked to me in person and subsequently received an email from me confirming that you are registered.
  Having successfully gate crashed the midterm does not constitute a valid registration.
  
• Makeup exam: On April 1st there will be a makeup exam for those who failed the final. This is not an April fool's joke! See here for further information.