Timeline for Classification of Compact Symplectic Homogeneous Spaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2014 at 9:15 | comment | added | Allen Knutson | If you don't require $G$-invariance, maybe you can also figure out whether $G_2/SU(3)$ admits a complex structure... | |
| Jan 20, 2014 at 9:13 | comment | added | Allen Knutson | If a Lie group $G$ acts transitively on a symplectic manifold $M$, then $M$ is a cover of a coadjoint orbit of a central extension of $M$. If $G$ is compact connected, then its central extensions are trivial enough and its coadjoint orbits are simply connected, so $M$ is just a coadjoint orbit of $G$, hence Kähler. Which is to say, there are no new examples if the symplectic form is $G$-invariant. | |
| Jan 19, 2014 at 19:28 | comment | added | pod146 | In general, no, it does not have to be G-invariant. However, most constructions of a symplectic form on $M$ will automatically produce such an object. | |
| Jan 19, 2014 at 19:08 | history | edited | Ricardo Andrade |
replaced deprecated tag 'geometry'; replaced tag 'symplectic-topology' with 'sg.symplectic-geometry'; added tag 'homogeneous-spaces'
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| Jan 19, 2014 at 19:07 | comment | added | Francois Ziegler | You don't require the symplectic form to be $G$-invariant, do you? | |
| Jan 19, 2014 at 19:05 | review | First posts | |||
| Jan 19, 2014 at 19:20 | |||||
| Jan 19, 2014 at 18:50 | history | asked | pod146 | CC BY-SA 3.0 |