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Finally I found the kind of citable original citation for the stament that I was after: added pointer to Waner 80, theorem 3.4
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which proves that the G-ANRs considered in James-Segal 78 are of the $G$-homotopy type of $G$-CW complexes.
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but I haven’t actually seen that article yet.
According to Kwasik 81, the proof of equivariant Whitehead is 5.3 in there.
In Waner80 the reference to Matumoto is confusing: Both of Matumoto’s articles are listed in the bibliography, but only the other one seems to be referred to in the text, and that other one (at least) does not state the general equivariant Whitehead theorem
Thanks! Am copying your link over also to other entries, such as G-CW complex.
(By the way, let’s maybe use more informative file names, with maybe the year or parts of the title included in the file name, in case we want to upload more than one article by a given author.)
It’s curious how Matumoto uses the condition that $G$ be compact Lie. It appears in Lemma 1.11 as a sufficient condition to imply axiom (f) in his definition 1.2 of $G$-cell complex.
(Generally, I wish the literature on equivariant homotopy theory were more up-front about which exact condition on $G$ is assumed and for which exact step in the proofs. There is a tiny ratio of discussion this gets over the importance this has for the theory.)
I guess Richard would know how to change this.
On the other hand, it makes good sense that filenames fit into one line of a file dialogue box. For uploading articles here I usually make a filename that consists of the author’s name and some abbreviation of the title such that in total (with .pdf
-suffix, apparently!) it fits below the 50 character limit.
I think the point of the filename is only to a) ensure that it’s unique and b) give sufficient hints/mnemonic for what the file might contain. It shouldn’t be too generic (to any bystandanders: don’t upload your thesis as just thesis.pdf
!) but also it need not contain full verbatim article titles.
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