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?

]]>also pointer to:

- Sören Illman, Section 2 of:
*Equivariant singular homology and cohomology for actions of compact lie groups*(doi:10.1007/BFb0070055) In: H. T. Ku, L. N. Mann, J. L. Sicks, J. C. Su (eds.),*Proceedings of the Second Conference on Compact Transformation Groups*Lecture Notes in Mathematics, vol 298. Springer 1972 (doi:10.1007/BFb0070029)

Have expanded/improved the list of attributions for the Prop. (here) that $G$-manifolds are $G$-CW complexes.

]]>added pointer to:

- Sören Illman, Section 2 of:
*Equivariant algebraic topology*, Annales de l’Institut Fourier, Tome 23 (1973) no. 2, pp. 87-91 (doi:10.5802/aif.458)

added pointer to:

- Wolfgang Lück, Sections I.1, I.2 of:
*Transformation Groups and Algebraic K-Theory*, Lecture Notes in Mathematics**1408**(Springer 1989) (doi:10.1007/BFb0083681)

added pointer to:

- Tammo tom Dieck, Sections I.1, I.2 of:
*Transformation Groups*, de Gruyter 1987 (doi:10.1515/9783110858372)

I have added pointer to

- Glen Bredon, Section I.1. of
*Equivariant cohomology theories*, Springer Lecture Notes in Mathematics Vol. 34. 1967 (doi:10.1007/BFb0082690)

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.

]]>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, 1971Takao 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…)

]]>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

]]>I added a bit about G-CW embedding into presheaves on Or(G).

]]>started *G-CW complex*.