Cohomology of Groups

The first three weeks of the course were not filmed (handwritten notes available upon request).  Topics included the definition of a G-CW-complex (built from cells of the form D^n \times G/H) and the definition of a weak G-homotopy equivalence of G-spaces.   (Recall a map of spaces f: X \to Y is a weak homotopy equivalence (whe) if X and Y are both empty or if for every x \in X, the induced map \pi_*(X,x) \to \pi_*(Y,f(x)) is a bijection. A whe of G-spaces is a G-map X \to Y so that for every subgroup H <G of G, the map X^H \to Y^H is a whe.)   I then outlined a proof of the G-Whitehead Theorem; a G-map Y \to Z is a whe iff for any G-CW-complex X, the map [X,Y] \to [X,Z] is bijective.