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started G-CW complex.
I added a bit about G-CW embedding into presheaves on Or(G).
moved the section on smooth G-manifolds from “Properties” to “Examples”.
added pointer to Waner 80, who attributes this class of examples to Matumoto 71
added pointer to
Takao Matumoto, On $G$-CW complexes and a theorem of JHC Whitehead, J. Fac. Sci. Univ. Tokyo Sect. IA 18, 363-374, 1971
Takao Matumoto, Equivariant K-theory and Fredholm operators, J. Fac. Sci. Tokyo 18 (1971/72), 109-112 (pdf)
which is apparently the origin of the concept for equivariance groups being compact Lie groups.
(A minute ago I also knew the original reference for finite groups, but now I seem to have lost it…)
I have added pointer to
for the origin of the concept of G-CW complexes over finite groups.
It’s interesting that Bredon’s proposal to parametrize over the $G$-orbit category precedes the proof of the equivariant Whitehead theorem by 4 years, and the proof of Elmendorf’s theorem by 16 years, given that it’s only the combination of these two theorems which justify Bredon’s idea on deeper grounds.
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Have added a remark (here) that $G$-CW-complexes for finite groups are equivalently CW-complexes with cellular group action.
Then I have made explicit (here) – for the simple special case of finite groups $G$ – that binary products in k-spaces preserve $G$-CW complex structure.
I gather this is still true for compact Lie groups $G$, “due to” the equivariant triangulation theorem – but what’s an actual proof of this implication?
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