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Global Differential Geometry (Summer Semester 2012)

Lecture: Tuesday 14:00-15:30 Z1
Thursday 11:30-13:00 Z1
Problem class: Thursday 17:30-19:00 Z1
Lecturer Prof. Dr. Wilderich Tuschmann
Office hours: by appointment - please contact me by email;
Room 1.002 Kollegiengebäude Mathematik (20.30)
Email: tuschmann@kit.edu
Problem classes Dr. Martin Herrmann
Office hours: Nach Vereinbarung
Room 1.021 Kollegiengebäude Mathematik (20.30)
Email: martin.herrmann@kit.edu


The course will cover various central themes of modern global differential geometry like

  • de Rham and Hogde theory
  • Geometric finiteness theorems
  • Geometry and topology of Riemannian manifolds with lower curvature bounds
  • Comparison geometry
  • Alexandrov spaces
  • Gromov-Hausdorff covergence

and, if time will permit, spin geometry and rudiments of Seiberg-Witten theory.


Thorough knowlegde of differentiable manifolds and first concepts of Riemannian Geometry like bundles, connections, and curvature; basics of Algebraic Topology.

Exercise Sheets

See the german page.


R. Bott & L. Tu, Differential forms in algebraic topology. Graduate Texts in Mathematics 82, Springer-Verlag, New York-Berlin (1982)

S. Gallot, D. Hulin & J. Lafontaine, Riemannian geometry. Third edition. Universitext, Springer-Verlag, Berlin (2004)

M. Gromov, Metric structures for Riemannian and non-Riemannian spaces. Birkhäuser Boston, Inc., Boston, MA (1999)

H. B. Lawson & M.-L. Michelsohn, Spin geometry. Princeton Mathematical Series 38, Princeton University Press, Princeton, NJ (1989)

J. Milnor, Morse theory. Annals of Mathematics Studies 51, Princeton University Press, Princeton, N.J. (1963)

T. Sakai, Riemannian geometry. Translations of Mathematical Monographs 149, American Mathematical Society, Providence, RI (1996)

C. Taubes, The geometry of the Seiberg-Witten invariants. Surveys in differential geometry, Vol. III (Cambridge, MA, 1996), 299 – 339, Int. Press, Boston, MA (1998)