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 |