2018-11-04T13:52:22-08:00 http://mathoverflow.tqft.net/ Lussumo Vanilla & Feed Publisher http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14094#Comment_14094 2011-04-12T15:35:41-07:00 2018-11-04T13:52:22-08:00 Kevin Walker http://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.

http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14092#Comment_14092 2011-04-12T12:37:07-07:00 2018-11-04T13:52:22-08:00 Tom Church http://mathoverflow.tqft.net/account/412/

I hope you will specify what G is.

http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14091#Comment_14091 2011-04-12T10:41:51-07:00 2018-11-04T13:52:22-08:00 DL http://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.

http://mathoverflow.tqft.net/discussion/1009/four-closely-related-questions-how-best-to-group-them/?Focus=14090#Comment_14090 2011-04-12T09:26:02-07:00 2018-11-04T13:52:22-08:00 Kevin Walker http://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.]]>