Pure Mathematics Topic D: Algebraic Topology
Course notes for Pure Mathematics Topic D 2019. There were 30 lectures.
Topic outline
- What is algebraic topology
- Review of topological spaces
- Homotopy
- Covering spaces
- Fundamental group/groupoid
- The Seifert-van Kampen theorem
- Classification of covering spaces
- Higher homotopy groups
- Complexes, cohomology
- Combinatorial surfaces, geometric realisation
- Delta-sets and their cohomology
- Long exact sequences from short exact sequences of complexes
- Relative and reduced cohomology
- Calculational tools for cohomology
- Comparison of Delta-set and singular cohomology
- The Eilenberg–Steenrod theorem