Algebraic topology

Course Code :2000WETATO
Study domain:Mathematics
Academic year:2017-2018
Semester:1st semester
Contact hours:60
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 1st 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.