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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 1st 2013

started G-CW complex.

• CommentRowNumber2.
• CommentAuthorTim_Porter
• CommentTimeNov 1st 2013

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 12th 2018
• (edited Apr 12th 2018)

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

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 13th 2021
• (edited Mar 13th 2021)

• 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…)

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

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.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 13th 2021

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeJul 13th 2021

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

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeJul 13th 2021

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)
• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeSep 13th 2021
• (edited Sep 13th 2021)

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?