Calendar

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