Week 1: University cancelled (snow)
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2/3: Introduction to the course; the syllabus; overview of algebraic topology
2/5: Brief review of homology. Construction of singular cohomology. Universal coefficients and the cup product. Reference: Hatcher, Chapter 2, 3.1 - 3.2
2/10 Free resolutions and Ext. Reference: Hatcher, 3.1
2/12 Proof of universal coefficients. Reference: Hatcher, 3.1
2/17 Relative cohomology. Long exact sequence of a pair and of a triple. Excision. Homotopy invariance. Induced homomorphisms. Cellular cohomology. Mayer-Vietoris. Reference: Hatcher, 3.1
2/19 Cup product. The cohomology ring. The Kunneth formula. Reference: Hatcher, 3.2
2/24 Graded commutativity of cup product. Reference: Hatcher, 3.2
2/26 Axioms for homology / cohomology. Proof of the Kunneth formula. Reference: Hatcher, 2.3, 3.1, 3.2
3/3 More about Hatcher 3.2. Reference: Hatcher, 3.2
3/5 Orientiations. The cap product. Poincare duality. Strategy of proof. Reference: Hatcher, 3.3
3/10 Compactly supported cohomology. Direct limits. A general statement of Poincare duality. Reference: Hatcher, 3.3
3/12 Proof of Poincare duality. Reference: Hatcher, 3.3