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:
Hatcher. Algebraic Topology. Cambridge, New York, NY: Cambridge University Press, 2002. ISBN: 052179160X. (Available online.)
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).
| LEC # | TOPICS | REFERENCES |
|---|---|---|
| 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) |
