D. Kotschick: Geometry of Manifolds I

(Differentialgeometrie I, in englischer Sprache)

• Time and place: Mo, Th 11-13, room E 47
• Recitation classes: Mo 16-18, room E 47
• Contents: This is the first half of a full-year course on differentiable manifolds. We shall introduce the basic concepts used in modern geometry and topology: manifolds, bundles, Lie groups; differential forms, distributions and integrability conditions; connections, curvature; homotopy, homology and cohomology groups; characteristic classes. Further topics will be chosen from both Riemannian and symplectic geometry, and from differential and algebraic topology.
• 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 familiarity wih linear algebra, multivariable calculus and point set topology. The exact level and speed of the course will be tailored to those in the audience and their previous training.
• Main text: L. Conlon: Differentiable Manifolds  --- A first course. Birkhäuser Verlag 1993.

Further Reading: J. W. Milnor: Topology from the differentiable viewpoint. Princeton University Press.
M. H. Freedman and F. Luo: Selected Applications of Geometry to Low-Dimensional Topology. Amer. Math. Soc.
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.
P. Pedersen: Riemannian Geometry. Springer Verlag 1998.