Timeline for A Lie algebra associated to a foliation(A kind of saturation of foliations)
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 27, 2018 at 15:26 | comment | added | Ali Taghavi | Certainly by this question I was considering non trivial foliation. I revise the question. Could you please revise your answer on the first part of the question?thank you. | |
| Jun 27, 2018 at 11:01 | comment | added | Ali Taghavi | So in the first questiob i certainly do not consider the trivial foliation since in this case the question is trivial. I consider a foliation with proper dimension. In that full dimension I do not see how is your computation necessary since the matter is obvious. | |
| Jun 27, 2018 at 9:39 | history | edited | DamienC | CC BY-SA 4.0 |
made part 5 of the answer more precise
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| Jun 27, 2018 at 9:12 | comment | added | DamienC | @AliTaghavi: I don't understand your question. There are no connections in this business. Here "distribution" means 'subbundle". | |
| Jun 27, 2018 at 8:50 | history | edited | DamienC | CC BY-SA 4.0 |
Corrected a mistake in the previous version (it is $A/L$, and not $A$, which is vector fields on the leaf space). Also, re-organized the answer for clarity.
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| Jun 27, 2018 at 8:42 | comment | added | DamienC | The first line of my answer is not related to the rest of the answer. In the first line, yes, I consider the trivial foliation on $M$. | |
| Jun 27, 2018 at 8:38 | comment | added | Ali Taghavi | Are you considering a special connection on $M$ which is integrable as a distribution on $TM$ ? Could you please clarify your answer? | |
| Jun 27, 2018 at 8:30 | comment | added | Ali Taghavi | I can Not follow the first line! Are you considering the trivial foliation of $M$, as you wrote $D=TM$? Or you are considering a foliation of the (co) tangent bundle? In your answer what is a precise foliation $\mathcal{F}$ for which $A_{\mathcal{F}}=L_{\mathcal{F}}$? | |
| Jun 27, 2018 at 8:14 | comment | added | Ali Taghavi | @DamienC Thank you for your answer. i try to understand its details. | |
| Jun 27, 2018 at 8:04 | history | bounty ended | Ali Taghavi | ||
| Jun 26, 2018 at 10:44 | comment | added | Qfwfq | "Consider the cotangent space $T^{*}M$, which is a symplectic manifold. Functions on this are generated by functions on $M$ and vector fields" - I think the precise statement would be: functions polynomial along the fibers of $T^{*}M\to M$ are generated (as an $\mathbb{R}$-algebra) by functions on $M$ and vector fields. | |
| S Jun 26, 2018 at 10:30 | history | edited | DamienC | CC BY-SA 4.0 |
added 2 characters in body
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| Jun 26, 2018 at 10:26 | review | Suggested edits | |||
| S Jun 26, 2018 at 10:30 | |||||
| Jun 26, 2018 at 10:21 | history | answered | DamienC | CC BY-SA 4.0 |