Yu.Burman
Topology, term 1
Course syllabus

$\pi_n$ is a group

$\pi_n$ is homotopy invariant

For $n \ge 2$, the group $\pi_n$ is Abelian.

Feldbau lemma

Covering homotopy theorem

The homotopy sequence of a fibration is exact

Existence and universality of a simply connected covering

Classification of coverings

Fundamental group of a wedge of circles

Sphere is orientable

Euler's formula for embedded graphs

$\pi_n(S^n) = \Integer$

How to calculate a fundamental group using cellular decomposition