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.