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Jun 12, 2018 at 16:37 history edited Neil Strickland CC BY-SA 4.0
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Apr 17, 2012 at 19:56 comment added berl13 Thank you, for making this precise. The proof of Neil Strickland works of course in any case.
Apr 17, 2012 at 15:30 history edited Neil Strickland CC BY-SA 3.0
Minor corrections
Apr 17, 2012 at 15:28 comment added Neil Strickland @Charles: perhaps. Then of course the correct statement is that $\mathbb{Z}\times BU$ is the group completion of $\coprod_nBU(n)$. If, as in the question, we take the colimit rather than the coproduct of the spaces $BU(n)$, we get $BU$, which is already group-complete.
Apr 17, 2012 at 15:22 comment added Charles Rezk I suppose the questioner intends "Quillen's plus construction" in the sense of "group completion", rather than the correct sense of "construction that kills a perfect subgroup of the fundamental group without changing the homology".
Apr 17, 2012 at 14:43 history answered Neil Strickland CC BY-SA 3.0