Timeline for what prevents a manifold to be symplectic?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 19, 2013 at 20:47 | comment | added | Tim Perutz | (This should have come first, but anyway: welcome to MO!) | |
| Feb 19, 2013 at 20:34 | comment | added | Tim Perutz | "As far as I know this is the only known geometric obstruction": A little pedantically, there are further obstructions in 4 dimensions, beyond the Taubes constraints w.r.t. $[\omega]$ and the a.c. structure: namely, the Taubes constraints on a finite covering space w.r.t to the pullback data! | |
| Feb 19, 2013 at 17:48 | history | edited | Emmy Murphy | CC BY-SA 3.0 |
added 2 characters in body
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| Feb 19, 2013 at 17:45 | comment | added | Emmy Murphy | I should also add that in the case of open manifolds, the reduction of the structure group to $Sp(2n)$ is a necessary and sufficient condition for the existence of a symplectic structure. Furthermore, we can prescribe the homology class $[\omega]$ freely. This result is due to Gromov. However this only works if we don't specify any boundary conditions at infinity. If we require boundary conditions such as symplectic convexity, the question is far more subtle and interesting. | |
| Feb 19, 2013 at 17:32 | history | answered | Emmy Murphy | CC BY-SA 3.0 |