Lecture 41

Hatcher, ch. 2, sec 2 (p134 - 135)

Last time I outlined how the Meier-Vietoris sequence computes H_n(S^n). Explain how this computation may be also deduced from _simplicial_ homology, just in the case of n=2 where you can be explicit. (this is easiest to do with the delta-complex structure where you glue two 2-simplices together along their common boundary).
Discuss some of the applications given in Hatcher (as time allows): the degree of a map between spheres, Theorem 2.28, and Proposition 2.29. Some of the degree discussion relies on the homotopy invariance of homology - just assume this, even though we have not proved it.