Avsnittsöversikt
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The definition of cohomology of a chain complex, space, CW complex, or Delta-complex. Example: homology and cohomology of real projective space, the latter with coefficients in an arbitrary abelian group G.
Covariant and contravariant additive functors; left and right exact functors. Proof that Hom(-,G) is a left exact contravariant functor. Definition of Ext(A,G). Formulation of the universal coefficient theorem for cohomology.
No homework this week (because it's exam week for some). Suggested reading: Chapter III until p. 193 (up to and excluding Lemma 3.1); Chapter II.3 "Categories and Functors"
Suggested exercises: III.1.4, 6, 8, 9. Compute the (cellular) homology and cohomology of your favorite spaces (e.g. orientable and nonorientable surfaces, lens spaces, etc.)