250128 VO Differential Topology (2023W)
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Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
Classes only start at 9:00, so they are from 9:00-11:15.
Wednesday
04.10.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
11.10.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
18.10.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
25.10.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
08.11.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
15.11.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
22.11.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
29.11.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
06.12.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
13.12.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
10.01.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
17.01.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
24.01.
08:00 - 11:15
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday
31.01.
08:00 - 11:15
Seminarraum 9 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, Poincare-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 Theoryother 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 Theoryother 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
Last modified: Tu 19.03.2024 15:26