Complete lecture notes (PDF - 1.4MB)
| LEC # | TOPICS |
|---|---|
|
Basic Homotopy Theory (PDF) | |
| 1 | Limits, Colimits, and Adjunctions |
| 2 | Cartesian Closure and Compactly Generated Spaces |
| 3 | Basepoints and the Homotopy Category |
| 4 | Fiber Bundles |
| 5 | Fibrations, Fundamental Groupoid |
| 6 | Cofibrations |
| 7 | Cofibration Sequences and Co-exactness |
| 8 | Weak Equivalences and Whitehead’s Theorems |
| 9 | Homotopy Long Exact Sequence and Homotopy Fibers |
|
The Homotopy Theory of CW Complexes (PDF) | |
| 10 | Serre Fibrations and Relative Lifting |
| 11 | Connectivity and Approximation |
| 12 | Cellular Approximation, Obstruction Theory |
| 13 | Hurewicz, Moore, Eilenberg, Mac Lane, and Whitehead |
| 14 | Representability of Cohomology |
| 15 | Obstruction Theory |
|
Vector Bundles and Principal Bundles (PDF) | |
| 16 | Vector Bundles |
| 17 | Principal Bundles, Associated Bundles |
| 18 | I-invariance of BunG, and G-CW Complexes |
| 19 | The Classifying Space of a Group |
| 20 | Simplicial Sets and Classifying Spaces |
| 21 | The Čech Category and Classifying Maps |
|
Spectral Sequences and Serre Classes (PDF) | |
| 22 | Why Spectral Sequences? |
| 23 | The Spectral Sequence of a Filtered Complex |
| 24 | Serre Spectral Sequence |
| 25 | Exact Couples |
| 26 | The Gysin Sequence, Edge Homomorphisms, and the Transgression |
| 27 | The Serre Exact Sequence and the Hurewicz Theorem |
| 28 | Double Complexes and the Dress Spectral Sequence |
| 29 | Cohomological Spectral Sequences |
| 30 | Serre Classes |
| 31 | Mod C Hurewicz and Whitehead Theorems |
| 32 | Freudenthal, James, and Bousfield |
|
Characteristic Classes, Steenrod Operations, and Cobordism (PDF) | |
| 33 | Chern Classes, Stiefel-Whitney Classes, and the Leray-Hirsch Theorem |
| 34 | H*(BU(n)) and the Splitting Principle |
| 35 | The Thom Class and Whitney Sum Formula |
| 36 | Closing the Chern Circle, and Pontryagin Classes |
| 37 | Steenrod Operations |
| 38 | Cobordism |
| 39 | Hopf Algebras |
| 40 | Applications of Cobordism |