Timeline for Which curves are boundary of pseudoholomorphic curves?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2020 at 11:49 | answer | added | Klaus Niederkrüger | timeline score: 1 | |
| Jun 12, 2020 at 21:04 | history | became hot network question | |||
| Jun 12, 2020 at 20:23 | vote | accept | Overflowian | ||
| Jun 12, 2020 at 19:44 | answer | added | Robert Bryant | timeline score: 13 | |
| Jun 12, 2020 at 16:50 | comment | added | Overflowian | @ChrisGerig a question: you say in some scenarios we don't have any J-disk, do we get any improvement considering higher genus surfaces? | |
| Jun 12, 2020 at 16:33 | comment | added | Chris Gerig | There always exists a Lagrangian torus which contains a given smooth loop, and in some scenarios the moduli of J-disks with Lagrangian boundary conditions will be empty. Alternatively, if the loop is contained in a contact hypersurface for which it is a Reeb orbit, we can try to get some existence results using Gromov-Witten theory by stretching the neck of the 4-manifold along that hypersurface. These comments might be useless in practice. | |
| Jun 12, 2020 at 15:59 | comment | added | Ben McKay | There are conditions called moment conditions, if I remember correctly, that determine which real analytic closed curves are the boundaries of holomorphic curves in complex Euclidean space. But I think they are based on having global coordinates. I don't know if there is an answer to this question even for complete Kaehler manifolds. | |
| Jun 12, 2020 at 15:47 | history | edited | Overflowian | CC BY-SA 4.0 |
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| Jun 12, 2020 at 15:18 | comment | added | Ben McKay | I don't think this is known. | |
| Jun 12, 2020 at 13:04 | history | asked | Overflowian | CC BY-SA 4.0 |