/AlgebraicTopology2019

Course notes for Pure Mathematics Topic D 2019

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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