Timeline for Symplectic principal bundles
Current License: CC BY-SA 4.0
17 events
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| S Jul 4, 2022 at 9:02 | history | bounty ended | CommunityBot | ||
| S Jul 4, 2022 at 9:02 | history | notice removed | CommunityBot | ||
| Jun 26, 2022 at 7:49 | history | edited | YCor | CC BY-SA 4.0 |
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| S Jun 26, 2022 at 7:10 | history | bounty started | Praphulla Koushik | ||
| S Jun 26, 2022 at 7:10 | history | notice added | Praphulla Koushik | Draw attention | |
| May 21, 2022 at 12:21 | comment | added | Praphulla Koushik | Is the notion of "Symplectic Principal bundles" a standard one? I could not find anything in google search.. | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Oct 25, 2017 at 9:25 | comment | added | user21574 | I think(if I remember correcctly) you may try for such Poisson structure $\pi=\sum_{i,j,k,l}X_i\frac{\partial}{\partial X_j}\wedge \frac{\partial}{\partial X_k}\wedge \frac{\partial}{\partial X_l}$ where $X_i$ means rotation in direction $X_i$-axis on $S^3$, (I remember the proof of such Poisson structure took 3 lecture of Ctirad Klimcik) | |
| Oct 25, 2017 at 9:10 | comment | added | Ali Taghavi | @HassanJolany Thanks for your comment. Regarding the first of your comment, I think there is an easier Poison structure for $S^2$ since it is a symplectic manifold with its volume form. But I am not sure that this is equivalent to the poison structure which you explained. I was not aware of such structure, I will read the linked and references you provided. But I wonder whether the Lie bracket on S^3 which I suggested in the question, gives an alternative poison structure on S^3. | |
| Oct 25, 2017 at 8:42 | comment | added | user21574 | $S^2$ is coadjoint orbit, hence it has Kirillov-Kostant-Souriau symplectic structure , and every symplectic manifold has Poisson structure, see staff.www.ltu.se/~norbert/home_journal/electronic/93art5.pdf . Also $S^3\cong SU(2)$, you can find in p.13 a Poisson structure on $SU(2)$, mat.univie.ac.at/~michor/lie-pois.pdf | |
| Oct 25, 2017 at 7:42 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 25, 2017 at 4:35 | history | edited | Ali Taghavi |
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| Oct 25, 2017 at 4:28 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 25, 2017 at 4:19 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 24, 2017 at 6:09 | comment | added | Ali Taghavi | @HassanJolany Thank you for your very helpful comment and very interesting link. | |
| Oct 23, 2017 at 13:28 | comment | added | user21574 | The answer of 1. is yes see section 1.1 of François Lalonde, Dusa McDuff , Symplectic structures on fiber bundles sciencedirect.com/science/article/pii/S0040938301000209 | |
| Oct 23, 2017 at 9:50 | history | asked | Ali Taghavi | CC BY-SA 3.0 |