Timeline for Examples of non-Kahler compact symplectic manifolds.
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2021 at 12:22 | history | edited | Stefan Kohl♦ |
edited tags
|
|
| Aug 30, 2021 at 12:22 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 22, 2012 at 3:37 | answer | added | user9154 | timeline score: 0 | |
| Sep 22, 2012 at 2:45 | answer | added | Francois Ziegler | timeline score: 5 | |
| Sep 22, 2012 at 1:15 | answer | added | Mike Usher | timeline score: 9 | |
| Sep 21, 2012 at 23:48 | answer | added | eigenbunny | timeline score: 12 | |
| Sep 21, 2012 at 23:10 | answer | added | Ian Agol | timeline score: 3 | |
| Sep 21, 2012 at 22:37 | comment | added | Tim Perutz | Mohammad: once you restrict to the simply connected case I can no longer make any such sweeping comments (and I won't attempt to answer in a comment box). I wonder what happens, though, if you embed Gompf's manifolds symplectically into some high-dimensional $\mathbb{C}P^n$ using Gromov-Tischler and then blow up this submanifold. | |
| Sep 21, 2012 at 19:23 | comment | added | Mohammad Farajzadeh-Tehrani | I see; do we know anything about closed simply connected examples? | |
| Sep 21, 2012 at 19:06 | comment | added | Tim Perutz | We also know that such statements are wildly false for Kaehler surfaces of Kodaira dimension 1 or 2, since e.g. we have only finitely many deformation classes of general type surfaces of fixed $c_1^2$ and $c_2$. Yet it might be hard to decide whether some particular symplectic manifold has a Kaehler structure. | |
| Sep 21, 2012 at 19:06 | comment | added | Tim Perutz | Though one can write down such examples, I think the idea of such a list rather misses the point. There are qualitative differences that can be hard to apply to specific examples. We know, thanks to Gompf, that arbitrary finitely presented groups appear as $\pi_1$ of symplectic 4-manifolds of symplectic Kodaira dimension 1 and also of symplectic Kodaira dimension 2. | |
| Sep 21, 2012 at 18:49 | history | asked | Mohammad Farajzadeh-Tehrani | CC BY-SA 3.0 |