LEC #  TOPICS  KEY DATES 

Basic Homotopy Theory  
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  Problem set 1 due 
7  Cofibration Sequences and Coexactness  
8  Weak Equivalences and Whitehead’s Theorems  
9  Homotopy Long Exact Sequence and Homotopy Fibers  
The Homotopy Theory of CW Complexes  
10  Serre Fibrations and Relative Lifting  
11  Connectivity and Approximation  
12  Cellular Approximation, Obstruction Theory  Problem set 2 due 
13  Hurewicz, Moore, Eilenberg, Mac Lane, and Whitehead  
14  Representability of Cohomology  
15  Obstruction Theory  
Vector Bundles and Principal Bundles  
16  Vector Bundles  
17  Principal Bundles, Associated Bundles  
18  Iinvariance of Bun_{G}, and GCW Complexes  Problem set 3 due 
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  
22  Why Spectral Sequences?  
23  The Spectral Sequence of a Filtered Complex  
24  Serre Spectral Sequence  Problem set 4 due 
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  Problem set 5 due 
30  Serre Classes  
31  Mod C Hurewicz and Whitehead Theorems  
32  Freudenthal, James, and Bousfield  
Characteristic Classes, Steenrod Operations, and Cobordism  
33  Chern Classes, StiefelWhitney Classes, and the LerayHirsch 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  Problem set 6 due 
37  Steenrod Operations  
38  Cobordism  
39  Hopf Algebras  
40  Applications of Cobordism 
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