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Dec 13, 2019 at 18:09 comment added John Klein Hmm... I had thought it was due to Haefliger, but now I see that Wall attributes it to Rourke and Sanderson's paper. I guess I was mistaken.
Dec 13, 2019 at 14:59 comment added Igor Belegradek I am about to put your answer to some use, and having trouble locating where Haefliger shows in "Differential embeddings of $S^n$ in $S^{n+2}$" that the square in the beginning of your answer is homotopy Cartesian. Could you point me to the right place? I see an equivalent statement in theorem 1.11 of "Block bundles III" by Rourke-Sanderson.
May 21, 2012 at 2:10 history edited John Klein CC BY-SA 3.0
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May 21, 2012 at 0:45 history edited John Klein CC BY-SA 3.0
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May 21, 2012 at 0:37 history edited John Klein CC BY-SA 3.0
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May 20, 2012 at 15:54 comment added John Klein You're welcome. My pleasure!
May 20, 2012 at 15:52 history edited John Klein CC BY-SA 3.0
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May 20, 2012 at 15:51 vote accept Igor Belegradek
May 20, 2012 at 15:51 comment added Igor Belegradek Beautiful! I do not think this is in Madsen and Milgram, but now there is definitely a reference (to your answer). Many thanks!
May 20, 2012 at 15:46 history edited John Klein CC BY-SA 3.0
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May 20, 2012 at 15:17 history edited John Klein CC BY-SA 3.0
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May 20, 2012 at 15:09 history answered John Klein CC BY-SA 3.0