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 Bun_{G}, 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 |