Lecture Notes

Lecture notes were posted after most lectures, summarizing the contents of the lecture. Sometimes these are detailed, and sometimes they give references in the following texts:

Amazon logo Hatcher. Algebraic Topology. Cambridge, New York, NY: Cambridge University Press, 2002. ISBN: 052179160X. (Available online.)

Amazon logo May. A Concise Course in Algebraic Topology. Chicago, IL: University of Chicago Press, 1999. ISBN: 0226511820 (cloth: alk. paper) and 0226511839 (pbk.: alk. paper). (PDF - 1.3 MB)

Brown, Edgar H., Jr. "Cohomology Theories." Ann. of Math 2, no. 75 (1962).

1 Category Theory (PDF)  
2 Compactly Generated Spaces (PDF)  
3 Pointed Spaces and Homotopy Groups (PDF)  
4 Simple Computations, the Action of the Fundamental Groupoid (PDF)  
5 Cofibrations, Well Pointedness, Weak Equivalences, Relative Homotopy (PDF)  
6 Pushouts and Pullbacks, the Homotopy Fiber (PDF)  
7 Cofibers (PDF)  
8 Puppe Sequences (PDF)  
9 Fibrations (PDF)  
10 Hopf Fibrations, Whitehead Theorem (PDF)  
11 Help! Whitehead Theorem and Cellular Approximation (PDF)  
12 Homotopy Excision (PDF )  
13 The Hurewicz Homomorphism (PDF)  
14 Proof of Hurewicz (PDF)  
15 Eilenberg-Maclane Spaces (PDF)  
16-20 Brown Representability Theorem; Principle G-bundles and Classifying Spaces; Existence of Classifying Spaces Brown Representability Theorem: Hatcher. Algebraic Topology. Section 4.E.

Principle G-bundles and Classifying Spaces: May. A Concise Course in Algebraic Topology. Chapter 23, section 8.

Existence of Classifying Spaces: Brown, Edgar H., Jr. "Cohomology Theories." Ann of Math 2, no. 75 (1962): 467-484. Section 5, application 1.
21 Spectral Sequences (PDF)  
22 The Spectral Sequence of a Filtered Complex (PDF)  
23-28 The Serre Spectral Sequence Hatcher. "Spectral Sequence Notes." Chapter 1.
29 Line Bundles (PDF)  
30 Induced Maps Between Classifying Spaces, H*(BU(n)) (PDF)  
31 Completion of a Deferred Proof, Whitney Sum, and Chern Classes (PDF)  
32 Properties of Chern Classes, the Splitting Principle (PDF)  
33 Chern Classes and Elementary Symmetric Polynomials (PDF)