Global Differential Geometry (Sommersemester 2012)
- Dozent*in: Prof. Dr. Wilderich Tuschmann (Sprecher des Institutes)
- Veranstaltungen: Vorlesung (0153500), Übung (0153600)
- Semesterwochenstunden: 4+2
| Termine | ||
|---|---|---|
| Vorlesung: | Dienstag 14:00-15:30 | Z1 |
| Donnerstag 11:30-13:00 | Z1 | |
| Übung: | Donnerstag 17:30-19:00 | Z1 |
| Lehrende | ||
|---|---|---|
| Dozent | Prof. Dr. Wilderich Tuschmann (Sprecher des Institutes) | |
| Sprechstunde: derzeit nur nach vorheriger Vereinbarung per E-Mail | ||
| Zimmer 1.002 Kollegiengebäude Mathematik (20.30) | ||
| Email: tuschmann@kit.edu | Übungsleiter | Dr. Martin Herrmann |
| Sprechstunde: nach Vereinbarung | ||
| Zimmer 1.021 Kollegiengebäude Mathematik (20.30) | ||
| Email: martin.herrmann@kit.edu | ||
Contents
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.
Prerequisites
Thorough knowlegde of differentiable manifolds and first concepts of Riemannian Geometry like bundles, connections, and curvature; basics of Algebraic Topology.
Exercise Sheets
Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 9
Exercise sheet 10
Literaturhinweise
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)