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Mar 8, 2010 at 19:34 history edited Somnath Basu CC BY-SA 2.5
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Mar 8, 2010 at 18:19 comment added algori Somnath -- unfortunately, this doesn't seem to work, see comments to the posting and in particular page 2 of the paper sju.edu/~smith/pdf_files/factor3.pdf mentioned by Igor.
Mar 8, 2010 at 0:35 comment added algori Somnath -- I think there is a potential problem when you want to take the $(n+5)$ skeleton of the pullback of $P$. $P$ does not come equipped with a preferred CW-structure. Ok, let us assume that there is a way to pick one so that $P\to K(\mathbf{Z},3)$ is a locally trivial fibration (this seems plausible but has to be proven), but then, depending on which one we pick, the skeleta of the pullback of $P$ may or may not be fibered locally trivially over $M$.
Mar 7, 2010 at 22:22 history answered Somnath Basu CC BY-SA 2.5