Timeline for Fiber bundle orientability vs manifold orientability
Current License: CC BY-SA 4.0
8 events
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| Apr 22, 2022 at 23:45 | comment | added | Ryan Budney | Right, the structure of the argument is the same. After some linear algebra, it boils down to the statement $ab=c$, if two of the three symbols are positive, then the other one is. The key issue is when you think of the frame bundle of the total space, you can homotope the frame to be of the form "frame for the fiber, frame for the base". | |
| Apr 22, 2022 at 23:28 | comment | added | Ian Gershon Teixeira | @RyanBudney I respect your opinion I'll delete the question if you want. But just to be clear you're saying that this two out of three theorem for fiber bundles is (from your perspective) obviously true? | |
| Apr 22, 2022 at 23:12 | comment | added | Ryan Budney | @DanielAsimov: he's talking about the clutching maps being orientation preserving. i.e. the bundle corresponds to a map to the classifying space of the orientation-preserving automorphisms of the fiber. | |
| Apr 22, 2022 at 22:51 | history | edited | Ian Gershon Teixeira | CC BY-SA 4.0 |
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| Apr 22, 2022 at 21:13 | comment | added | Daniel Asimov | How is "orientable as a fibre bundle" defined as distinct from the total space's being an orientable manifold? | |
| Apr 22, 2022 at 18:52 | review | Close votes | |||
| Apr 27, 2022 at 3:03 | |||||
| Apr 22, 2022 at 18:42 | comment | added | Ryan Budney | Generally a question not getting an answer at MSE isn't a reason to post it here. Most arguments that you can use for the tangent bundle work for arbitrary bundles. I would suggest the argument using lifts of loops in the base to paths in the frame bundle. | |
| Apr 22, 2022 at 15:39 | history | asked | Ian Gershon Teixeira | CC BY-SA 4.0 |