Timeline for Which submanifolds are leaves of a foliation?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2022 at 20:55 | vote | accept | Leo Moos | ||
| Oct 20, 2022 at 17:39 | comment | added | Jason DeVito - on hiatus | @mme: Thanks! I didn't check details, but I think the compability on the boundary shouldn't be too hard using a collar. It seems that using this, one should be able to assume that near the boundary, the foliation is the obvious foliation of $\partial M\times [0,1)$. Then, of course, things glue with no problems. | |
| Oct 20, 2022 at 16:54 | history | became hot network question | |||
| Oct 20, 2022 at 16:02 | comment | added | mme | @JasonDeVito When $M$ is actually closed and $\Sigma$ is separating, this amounts to a foliation on both sides with $\partial M_i = \Sigma$ a leaf (with some smoothness compatibility conditions on the boundary, which maybe are hard to guarantee? I am not sure.) Because the two sides are compact manifolds with boundary whose boundary is a leaf, this is answered by Bill Thurston's Theorem 2(a) here. When you allow some noncompactness you have a lot more freedom. | |
| Oct 20, 2022 at 15:44 | comment | added | Jason DeVito - on hiatus | What obstructions are there for extending $\Sigma^n$ to a foliation on all of $M$ (without removing any points)? | |
| Oct 20, 2022 at 14:55 | answer | added | Robert Bryant | timeline score: 11 | |
| Oct 19, 2022 at 21:35 | history | asked | Leo Moos | CC BY-SA 4.0 |