Timeline for When is a manifold a tangent bundle?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2012 at 10:19 | comment | added | johndoe | for what it's worth, another necessary condition is orientability. | |
| Aug 31, 2012 at 9:48 | comment | added | Marco Golla | @OP: as for some necessary condition, you also need a symplectic structure with lots of Lagrangian sections. @Mariano: among other examples, exotic spheres qualify (see mathoverflow.net/questions/31690/… ). | |
| Aug 31, 2012 at 9:09 | history | edited | Benoît Kloeckner |
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| Aug 30, 2012 at 4:22 | comment | added | Chris Gerig | Haha sorry I read it so quickly that I saw "connected". | |
| Aug 30, 2012 at 4:10 | comment | added | Ian Agol | @ Chris: contractible manifolds have trivial tangent bundles (that's basically why I assumed contractibility). | |
| Aug 30, 2012 at 3:37 | comment | added | Chris Gerig | Wait, "the tangent bundle is trivializable" isn't a general statement, right? We're implicitly assuming our $M_i$ are 3-manifolds (as the explicit example is)? | |
| Aug 29, 2012 at 17:40 | answer | added | Igor Belegradek | timeline score: 9 | |
| Aug 29, 2012 at 17:36 | comment | added | Paul Reynolds | It might be worth Googling "almost tangent structure" and looking at some of those papers, for a different perspective. | |
| Aug 29, 2012 at 17:29 | answer | added | Ryan Budney | timeline score: 5 | |
| Aug 29, 2012 at 17:24 | comment | added | Ian Agol | @ Mariano: Yes, for example there are contractible manifolds $M_1, M_2$ which are not homeomorphic, but $M_1 \times \mathbb{R} \cong M_2\times \mathbb{R}$. So $TM_1\cong TM_2$ since the tangent bundle is trivializable. E.g. $\mathbb{R}^3$ and the Whitehead manifold. | |
| Aug 29, 2012 at 17:05 | comment | added | Mariano Suárez-Álvarez | Can a manifold be a tangent bundle in two different ways? | |
| Aug 29, 2012 at 16:50 | history | asked | Jon Cohen | CC BY-SA 3.0 |