This information sheet indicates how the course will be organized at pandemic code level yellow and green.
If the colour codes change during the academic year to orange or red, modifications are possible, for example to the teaching and evaluation methods.

Algebraic topology

Course Code :2000WETATO
Study domain:Mathematics
Academic year:2020-2021
Semester:2nd semester
Contact hours:60
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 2nd semester
Lecturer(s)Boris Shoykhet

3. Course contents *

1. General notion of a homotopy invariant of topological spaces.

2. CW-complexes.

3. The coverings and the fundamental group; examples of computation; Van Kampen theorem.

4. The higher homotopy groups: easy to define but hard (in general impossible) to compute.

5. The homology and cohomology groups: harder to define but computable.

6. Computation of H(S^n), degree of a map.

7. The Euler characteristic of a triangulated space, independence on triangulation, the Lefschetz fixed-pont theorem, Hopf theorem on zeroes on a vector field on a manifold.