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