Pure Mathematics Topic D: Algebraic Topology

Course notes for Pure Mathematics Topic D 2019. There were 30 lectures.

Topic outline

1. What is algebraic topology
2. Review of topological spaces
3. Homotopy
4. Covering spaces
5. Fundamental group/groupoid
6. The Seifert-van Kampen theorem
7. Classification of covering spaces
8. Higher homotopy groups
9. Complexes, cohomology
10. Combinatorial surfaces, geometric realisation
11. Delta-sets and their cohomology
12. Long exact sequences from short exact sequences of complexes
13. Relative and reduced cohomology
14. Calculational tools for cohomology
15. Comparison of Delta-set and singular cohomology
16. The Eilenberg–Steenrod theorem