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8
votes
Accepted
Homotopy group action and equivariant cohomology theories
From modern perspective this is much more straightforward than the "genuine" version you described above the question. Naive $G$-spaces are just functors $BG\to \cal{S}$ among infinity categories. $G$ …
3
votes
Accepted
Equivariant cohomology of a semisimple Lie algebra
It vanishes as well. The complex of differential forms on $\mathfrak{g}$ is null homotopic through the standard null-homotopy coming from the linear homotopy to the origin. Since the $G$-action preser …