| 1 |
Category Theory |
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| 2 |
Compactly Generated Spaces |
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| 3 |
Pointed Spaces and Homotopy Groups |
Assignment 1 due |
| 4 |
Simple Computations, the Action of the Fundamental Groupoid |
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| 5 |
Cofibrations, Well Pointedness, Weak Equivalences, Relative Homotopy |
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| 6 |
Pushouts and Pullbacks, the Homotopy Fiber |
Assignment 2 due |
| 7 |
Cofibers |
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| 8 |
Puppe Sequences |
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| 9 |
Fibrations |
Assignment 3 due 1 day after Lec #9 |
| 10 |
Hopf Fibrations, Whitehead Theorem |
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| 11 |
Help! Whitehead Theorem and Cellular Approximation |
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| 12 |
Homotopy Excision |
Assignment 4 due |
| 13 |
The Hurewicz Homomorphism |
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| 14 |
Proof of Hurewicz |
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| 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 |
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| 23-28 |
The Serre Spectral Sequence |
Assignment 8 due in Lec #23
Assignment 9 due in Lec #27 |
| 29 |
Line Bundles |
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| 30 |
Induced Maps between Classifying Spaces, H*(BU(n)) |
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| 31 |
Completion of a Deferred Proof, Whitney Sum, and Chern Classes |
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| 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 |