250110 VO Differential Topology (2025W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Wednesday 01.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 07.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 08.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 14.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 15.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 21.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 22.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 28.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 29.10. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 04.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 05.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 11.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 12.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 18.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 19.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 25.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 26.11. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 02.12. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 03.12. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 09.12. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 10.12. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 16.12. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 17.12. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 07.01. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 13.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 14.01. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 20.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 21.01. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
- Tuesday 27.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 28.01. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
This course will be a basic introduction to differential topology, with an eye toward Morse theory. Topics include smooth manifolds and the tangent bundle, Sard's Lemma, Transversality, the Brower fixed point Theorem, Euler number, Poincaré-Hopf theorem, and Morse theory.
Assessment and permitted materials
Written or oral exam after the end of the course.
Minimum requirements and assessment criteria
Basic prerequisites are the concepts of multivariable calculus, including differential forms, vector fields, and implicit function theorem, as well as preferably the definitions of differentiable manifolds and tangent spaces.
In particular, the course is also suitable for advanced bachelor students.
In particular, the course is also suitable for advanced bachelor students.
Examination topics
The contents of the course.
Reading list
the course is based on the books:
-J. Milnor: Topology from the Differentiable Viewpoint
and
J. Milnor: Morse Theory
other useful books include:
-V. Guillemin, A. Pollack Differential Topology
-M. Hirsch Differential Topology
-T. Bröcker, K. Jänich Einführung in die Differentialtopologie
-A. Kosinski Differential Manifolds
-J. Lee Introduction to smooth manifolds
-J. Milnor: Topology from the Differentiable Viewpoint
and
J. Milnor: Morse Theory
other useful books include:
-V. Guillemin, A. Pollack Differential Topology
-M. Hirsch Differential Topology
-T. Bröcker, K. Jänich Einführung in die Differentialtopologie
-A. Kosinski Differential Manifolds
-J. Lee Introduction to smooth manifolds
Association in the course directory
MGEV; ML2; MEL
Last modified: Th 26.03.2026 11:27