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Kevin Walker comments on "Four closely related questions -- how best to group them?" (14094)http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14094#Comment_140942011-04-12T15:35:41-07:002019-08-20T17:00:50-07:00Kevin Walkerhttp://mathoverflow.tqft.net/account/36/
@Tom Church - Yes, I plan on saying what G is (i.e. an abelian group). What I wrote above was just a abbreviated version to indicate how the questions were related.
Tom Church comments on "Four closely related questions -- how best to group them?" (14092)http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14092#Comment_140922011-04-12T12:37:07-07:002019-08-20T17:00:50-07:00Tom Churchhttp://mathoverflow.tqft.net/account/412/
I hope you will specify what G is.
DL comments on "Four closely related questions -- how best to group them?" (14091)http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14091#Comment_140912011-04-12T10:41:51-07:002019-08-20T17:00:50-07:00DLhttp://mathoverflow.tqft.net/account/276/
Since all of these questions ask for references, it seems fine to ask them all in one 4-part question.
Kevin Walker comments on "Four closely related questions -- how best to group them?" (14090)http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14090#Comment_140902011-04-12T09:26:02-07:002019-08-20T17:00:50-07:00Kevin Walkerhttp://mathoverflow.tqft.net/account/36/
I'm preparing to ask, at MO, either (a) four closely related small questions, or (b) one large four-part question, or, most likely, (c) something intermediate between (a) and (b). I'm seeking ...
(1) What's a good reference/citation for the cohomology of the Eilenberg-MacLane space $K(G, 2)$? (I'm really just interested in the degree five-or-less cohomology. Recall that $\pi_i(K(G, 2)) = G$ if $i=2$ and is trivial otherwise.)

(2) What's a good reference/citation for explicit constructions of $K(G, 2)$?

(3) The finite cell complex $X$ (details omitted here) has $\pi_2 = G$. Is there a reference for the 4- and 5-cells one needs to add to $X$ to make it into a $K(G, 2)$? (Of course one also needs to add higher cells, but I'm not interested in those.)

(4) The finite cell complex $Y$ (details omitted here; not the same as $X$ above) has $\pi_2 = G$. Is there a reference for the 4- and 5-cells one needs to add to $Y$ to make it into a $K(G, 2)$?

My first thought was to let (1) be a stand-alone question and lump (2), (3) and (4) together. But if there's a consensus here in favor of some other way of grouping them then I'm happy to follow that.]]>