Topology IV.b - homotopy theory

Homework/Semi-flipped teaching. Please have a look at Section 1 of Chapter 5 about the Hurewicz homomorphism. It concerns a proposition about singular homology: it is invariant under weak homotopy equivalences. This is done by turning any weak equivalence into a cofibration and then dealing with homology of pairs, the technical details are not too enlightening. I will quickly recall the computation from the lemma and the example, they will be important (but are easy).

I will start the lecture by some leftovers about cofibrations and fibrations (Fubini tricks, comparison between fiber and homotopy fiber of a fibration). Then we will move to the statement and proof of the Hurewicz Theorem.