Timeline for How to recognize a vector bundle?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2020 at 19:32 | answer | added | Ben MacAdam | timeline score: 1 | |
| Nov 28, 2020 at 17:34 | answer | added | Gael Meigniez | timeline score: 2 | |
| Aug 31, 2020 at 19:21 | comment | added | Sebastian Goette | There also is the Soul Theorem in Riemannian geometry | |
| Aug 22, 2020 at 12:35 | history | edited | user163840 | CC BY-SA 4.0 |
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| Aug 22, 2020 at 6:35 | comment | added | Ryan Budney | Fibre-bundles are a little easier to identify. Under "reasonable circumstances" assuming manifolds everywhere, all you need is some compactness and the map being a submersion. This is just a careful application of the implicit function theorem. | |
| Aug 22, 2020 at 6:17 | history | edited | user163840 | CC BY-SA 4.0 |
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| Aug 22, 2020 at 5:37 | history | edited | user163840 | CC BY-SA 4.0 |
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| Aug 22, 2020 at 5:23 | comment | added | Ryan Budney | I doubt you will find a satisfactory answer in the literature in much generality, but if $E$ is a simply-connected manifold that has $B$ (a manifold) as a deformation-retract, then it is a vector bundle under some reasonable conditions, by the minimal handle theorem -- closely related to the h-cobordism theorem. A theorem of this sort appears in Kosinski's "Differential Topology" textbook. | |
| Aug 22, 2020 at 5:19 | review | First posts | |||
| Aug 22, 2020 at 9:10 | |||||
| Aug 22, 2020 at 5:17 | history | asked | user163840 | CC BY-SA 4.0 |