Yu.Burman

Topology, term 1

Course syllabus

1. $\pi_n$ is a group
2. $\pi_n$ is homotopy invariant
3. For $n \ge 2$, the group $\pi_n$ is Abelian.
4. Feldbau lemma
5. Covering homotopy theorem
6. The homotopy sequence of a fibration is exact
7. Existence and universality of a simply connected covering
8. Classification of coverings
9. Fundamental group of a wedge of circles
10. Sphere is orientable
11. Euler's formula for embedded graphs
12. $\pi_n(S^n) = \Integer$
13. How to calculate a fundamental group using cellular decomposition