| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Category Theory | |
| 2 | Compactly Generated Spaces | |
| 3 | Pointed Spaces and Homotopy Groups | Assignment 1 due |
| 4 | Simple Computations, the Action of the Fundamental Groupoid | |
| 5 | Cofibrations, Well Pointedness, Weak Equivalences, Relative Homotopy | |
| 6 | Pushouts and Pullbacks, the Homotopy Fiber | Assignment 2 due |
| 7 | Cofibers | |
| 8 | Puppe Sequences | |
| 9 | Fibrations | Assignment 3 due 1 day after Lec #9 |
| 10 | Hopf Fibrations, Whitehead Theorem | |
| 11 | Help! Whitehead Theorem and Cellular Approximation | |
| 12 | Homotopy Excision | Assignment 4 due |
| 13 | The Hurewicz Homomorphism | |
| 14 | Proof of Hurewicz | |
| 15 | Eilenberg-Maclane Spaces | Assignment 5 due |
| 16-20 | Brown Representability Theorem; Principle G-bundles and Classifying Spaces; Existence of Classifying Spaces | Assignment 6 due in Lec #16 |
| 21 | Spectral Sequences | Assignment 7 due 1 day after Lec #21 |
| 22 | The Spectral Sequence of a Filtered Complex | |
| 23-28 | The Serre Spectral Sequence | Assignment 8 due in Lec #23 Assignment 9 due in Lec #27 |
| 29 | Line Bundles | |
| 30 | Induced Maps between Classifying Spaces, H*(BU(n)) | |
| 31 | Completion of a Deferred Proof, Whitney Sum, and Chern Classes | |
| 32 | Properties of Chern Classes, the Splitting Principle | Assignment 10 due |
| 33 | Chern Classes and Elementary Symmetric Polynomials | Assignment 11 due 5 days after Lec #33 Assignment 12 due 12 days after Lec #33 |