Timeline for A Lie algebra associated to a foliation(A kind of saturation of foliations)
Current License: CC BY-SA 4.0
19 events
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| Jun 27, 2018 at 13:10 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| S Jun 27, 2018 at 8:04 | history | bounty ended | Ali Taghavi | ||
| S Jun 27, 2018 at 8:04 | history | notice removed | Ali Taghavi | ||
| Jun 26, 2018 at 10:53 | comment | added | Qfwfq | As for the added question, I don't think it's possible to have such a $U$ that is not the whole of $M$, just because all the definitions involved are sheaf theoretic, hence "local", and all foliations (regular and of the same codimension), on manifolds of the same dimension, locally look the same. | |
| Jun 26, 2018 at 10:21 | answer | added | DamienC | timeline score: 2 | |
| Jun 26, 2018 at 7:22 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| S Jun 22, 2018 at 12:47 | history | bounty started | Ali Taghavi | ||
| S Jun 22, 2018 at 12:47 | history | notice added | Ali Taghavi | Draw attention | |
| Jun 19, 2018 at 21:07 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 20:47 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 20:29 | comment | added | Ali Taghavi | @BertramArnold Thanks for your comment. So we do not get a new foliation. That is the second and third question has negative answer. But what about the first auestion? I revise the question by adding a questlon in the last part of the post. | |
| Jun 19, 2018 at 14:00 | comment | added | Bertram Arnold | Except for trivial cases $A_{\mathcal F}$ will not be (sections of a) subbundle since it is not closed under multiplication by $C^\infty(M)$. By Frobenius's theorem you can find local charts such that $D = \langle \partial_1,\dots,\partial_k\rangle$. Then $A_{\mathcal F} = \{f_i(x)\partial_i\mid \partial_i f_j = 0\text{ for }i\le k < j\}$ which is not closed under multiplication by $x_{k+1}$ unless $k = 0$ (or $k=n$, in which case this function doesn't exist). | |
| Jun 19, 2018 at 13:59 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 13:20 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 13:14 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 13:08 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 12:59 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 12:40 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 19, 2018 at 12:29 | history | asked | Ali Taghavi | CC BY-SA 4.0 |