Timeline for When is a manifold a tangent bundle?
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| Aug 29, 2012 at 20:41 | comment | added | Ryan Budney | Hi Igor, yes it really depends on what level of generality the question is asked in. Say $M$ is compact, and $N$ is compact without boundary -- so we will head for the conclusion that $M$ is a disc bundle over $N$. This side-steps the issue of ends and puts you into pre-Siebenmann mathematics. The idea is $N$ is embedded in $M$ (as you mention) so the complement of an open tubular neighbourhood of $N$ is $M$ becomes an h or s-cobordism depending on your assumptions, so it's a product. | |
| Aug 29, 2012 at 18:13 | comment | added | Igor Belegradek | Regarding Step 1: how does being the homotopy type of $N$ forces anything? Don't you need some assumptions like those in my answer? | |
| Aug 29, 2012 at 17:29 | history | answered | Ryan Budney | CC BY-SA 3.0 |