D. Kotschick: Geometry of Manifolds II

(Differentialgeometrie, in englischer Sprache)

• Time and place: Mo, Th 11-13, room 132
• Recitation classes: TBA
• Contents: This semester we shall discuss connections and curvature on arbitrary vector bundles over smooth manifolds. This will lead to the Chern-Weil theory of characteristic classes on the one hand, and to Riemannian geometry (e.g. the study of geodesics) on the other.
• Syllabus
• Intended audience: This course is obligatory for all master's degree students wishing to take more advanced courses and seminars in geometry during their second year. The topics of those courses may include but are not limited to gauge theory, foliations and symplectic topology.
  Diplom- und Lehramts-Studenten die eine Einführung in die Differentialgeometrie hören wollen, sollten diese Vorlesung besuchen.
• Prerequisites: We shall assume only a basic knowledge of differentiable manifolds. It is not necessary to have attended Geometry of manifolds I, which covered more than enough background material for this course.
• Recommended Reading: L. Conlon: Differentiable Manifolds  --- A first course. Birkhäuser Verlag 1993.
  P. Pedersen: Riemannian Geometry. Springer Verlag 1998.
  R. L. Bishop and R. J. Crittenden: Geometry of Manifolds. 1964, reprinted 2001 by AMS Chelsea Publishing.
  B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry --- Methods and Applications, Vol. II and III, Springer Verlag 1990.
  F. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer Verlag 1983.
  S. Lang: Fundamentals of Differential Geometry. Springer Verlag 1999.
  J. W. Milnor and J. D. Stasheff: Characteristic Classes. Princeton University Press 1974.