Differential Topology

Module MA5122

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA5122 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from SS 2013 to SS 2014.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


We will follow a direct approach to differential topology and to many of its applications without requiring and exploiting the abstract machinery of algebraic topology. The course will cover immersion, submersions and embeddings of manifolds in Euclidean space (including the basic results by Sard and Whitney), a discussion of the Euler number and winding numbers, fixed point theorems, the Borsuk-Ulam theorem and respective applications.

Learning Outcome

At the end of the module, students are able to analyse topological problems from a differentiable viewpoint and to see differential problems from a topological perspective.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2. Helpful but not essential: MA2004 Vector Analysis.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Differential Topology Wolf, M. Mittwoch, 10:15–11:45
UE 1 Differential Topology (Exercise Session) Müller-Hermes, A. Wolf, M. Montag, 14:15–15:45
Freitag, 08:30–10:00

Learning and Teaching Methods

lecture, excercise course, homeworks




- V. Guillemin, A. Pollack, Differential Topology. - J.W. Milnor, Topology from the differentiable viewpoint.

Module Exam

Description of exams and course work

Klausur oder mündliche Prüfung (abhängig von der Teilnehmerzahl)

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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