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1.
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 feedback on how best to group the questions. They are:

(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.
• CommentAuthorDL
• CommentTimeApr 12th 2011

Since all of these questions ask for references, it seems fine to ask them all in one 4-part question.
• CommentAuthorTom Church
• CommentTimeApr 12th 2011

I hope you will specify what G is.
2.
@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.