Timeline for Critical points on a fiber bundle
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2023 at 20:40 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
added 201 characters in body
|
| Oct 14, 2009 at 23:52 | comment | added | Theo Johnson-Freyd | Yes, perhaps I should have asked it locally. I actually do everything in trivializations, but I'm trained in physics :P Thanks for the answer! | |
| Oct 14, 2009 at 23:51 | vote | accept | Theo Johnson-Freyd | ||
| Oct 12, 2009 at 21:13 | comment | added | Chris Schommer-Pries | Ahh. No. If I had thought about this a little longer, I wouldn't have been worried about your assumption. As you can see the exact same argument shows that dp: T<sub>c</sub>C --> T<sub>p(c)</sub>B must be injective. So the only question is if it can have dimension less than B. Again, by looking at H, you can see that the tangent space to C must have dimension at least n. btw: Your question is completely local, so the fact that you have a fiber bundle is a red herring. As long as your notion of "bundle" includes local trivializations, you can reduce to the case that E is a trivial bundle. | |
| Oct 12, 2009 at 15:53 | comment | added | Theo Johnson-Freyd | Great, although I had not intended to make any assumptions about dimension on C. In the first picture, I was simply trying to motivate the question without being able to draw a picture. Does the question fail in general? | |
| Oct 12, 2009 at 15:26 | history | answered | Chris Schommer-Pries | CC BY-SA 2.5 |