Topology IV.b - homotopy theory

Homework/Semi-flipped teaching. I will assume that you know how to construct an Eilenberg-Mac Lane space (this will be presented during the exercise session, it's an exercise from Sheet 12), and also that the basic properties of pointed homotopy classes into a K(A, n): Proposition 3.2 that cofiber sequences are sent to exact sequences of abelian groups, Proposition 3.3 about the suspension isomorphism, and Proposition 3.4 about the wedge axiom. They correspond to the exercise about maps into K(Z, n) from Sheet 12, the proofs are short and identical. I will start, after your questions of course, with Lemma 3.6 and the comparison of [X, K(A, n)] with ordinary cohomology with coefficients in A.