Avsnittsöversikt
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Applications of the cohomology computation of RP^n: the Borsuk-Ulam and ham sandwich theorems.
The graded commutativity of the cup product in cohomolog.
Tensor products of abelian groups.
The Künneth theorem for the cohomology of a product of spaces.
Reading: Hatcher 3.2 up to p. 222
Supplemental reading: Hatcher 3.A: Derived functors of the tensor products and universal coefficients in homology; 3.B: The general Künneth formula.
Recommended preparatory reading: the definition of a manifold.