Timeline for Examples of non-diffeomorphic smooth manifolds with diffeomorphic tangent bundle
Current License: CC BY-SA 2.5
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| Jul 14, 2010 at 21:15 | comment | added | Igor Belegradek | Thanks for the edit. I should have included this argument but run out of steam, and since the questioner looks at the case of high codimension the method you described is much more appropriate than the surgery-theoretic approach of (3). Also for the benefit of the questioner I wish to point out that one does not really need $k=n$. It suffices to assume that k is above metastable range so that Haefliger's embedding theorem applies to make $f$ an embedding, and of course one wants to have $k>2$ to run the h-cobordism argument you mention. | |
| Jul 14, 2010 at 14:44 | history | edited | Tom Goodwillie | CC BY-SA 2.5 |
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| Jul 13, 2010 at 14:40 | comment | added | user47274 | Thank you, it was a general question, so any answer is actually a good answer. However, it would be interesting to know examples of closed (compact without boundary) manifolds (maybe even orientable) | |
| Jul 13, 2010 at 14:04 | history | answered | Tom Goodwillie | CC BY-SA 2.5 |