Course Content

Homework assignments

1. Assignment 1, due 23 January 2023.
2. Assignment 2, due 28 February 2023.
3. Assignment 3, due 17 March 2023.
4. Assignment 4, due 30 March 2023.
5. Assignment 5, optional.

Exams

• Sample exam.

Calendar

All Chapter references are to Allen Hatcher, Algebraic Topology, 2001.

• Week 1 (January 10 and 12): Idea of spaces up to homotopy. The homotopy category of spaces. Hatcher Chapter 0.
• Week 2 (January 17 and 19): The fundamental group. Functoriality and applications. Hatcher Chapter 1.1.
• Week 3 (January 24 and 26): Van Kampen's Theorem. Hatcher Chapter 1.2.
• Week 4 (January 31 and February 2): Covering spaces. Hatcher Chapter 1.3. Lectures by Prof. Dorette Pronk.
• Week 5 (February 7 and 9): Covering spaces. Hatcher Chapter 1.3.
• Week 6 (February 14 and 16): Homology. Simplicial sets. Chain complexes. Hatcher Chapter 2.1.
  February 14: Robert Morissette, Simplicial approximation (Hatcher 2.C).
• Week 7 (February 21 and 23): February break.
• Week 8 (February 28 and March 2): Homology. Long exact sequence. Hatcher Chapter 2.2.
  February 28: Adrien Delazzer Meunier, Graphs and free groups (Hatcher 1.A).
• Week 9 (March 7 and 9): Cohomology. Ext groups. Universal coefficient theorem. Hatcher Chapter 3.1.
• Week 10 (March 14 and 16): Cup product. Kunneth formula. Computations. Hatcher Chapter 3.2.
  March 16: Ruizhi Liu, Local coefficients (Hatcher 3.H).
• Week 11 (March 21 and 23): Higher homotopy groups. Hatcher Chapter 4.1.
  March 21: Daniel Teixeira, H-spaces and Hopf algebras (Hatcher 3.C).
• Week 12 (March 28 and 30): Freudenthal suspension theorem. Hurewicz theorem. Hatcher Chapter 4.2.
  March 28: Thiago de Holleben, Minimal cell structures (Hatcher 4.C).
• Week 13 (April 4 and 6): Eilenberg--MacLane spaces. Whitehead brackets. Postnikov towers. Hatcher Chapter 4.3.
  April 6: Vaughn Menchions, The Hopf invariant (Hatcher 4.B).