Avsnittsöversikt
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Derived functors of abelian groups with free resolutions. The fundamental lemma of homological algebra. The universal coefficient theorem in cohomology.
The definition of the cup product in cohomology with coefficients in a ring. Computation of the mod-2 cohomology of RP^n.
Reading: Hatcher 3.1, whole section. This section contains proofs of the long exact sequence, excision, Mayer-Vietoris etc. for cohomology, but these proofs are completely analogous to the homology setting, so I will skip them in class. Hatcher 3.2 up to p. 209.
Suggested exercises: 3.1.5, 8, 9; 3.2.1, 3, 7
Preparatory reading: read about tensor products and, if you have time, look at the universal coefficient theorem in homology (Hatcher 3A).