Timeline for In $(\mathbb{R}^4,\omega_{std})$ is positive symplectic area enough to guarantee a pseudoholomorphic disc representative?
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| Sep 5, 2016 at 12:08 | comment | added | Nikolaki | The h-principle that I refer to is for curves inside $\mathbb{R}^4$, for which there obviously is no homotopy obstruction. The disc constructed would in the end intersect the torus in a very chaotic way, but at least the boundary will be controlled (and on the torus inside the right class). This is all we need. | |
| Sep 4, 2016 at 7:51 | comment | added | Yaniv Ganor | 1) Maybe I am missing something, but to use the h-principle here, shouldn't the curve on $S^1\times S^1$ and the sought curve on $aS^1 \times b S^1$ be of the same class in H^1? i.e let's say I want to get a curve of class (1,-1) on $aS^1 \times b S^1$ (for a > b, so area is still positive). Then I start with something of class $(1,-1) \in H^1(S^1 \times S^1)$, but this class bounds no holomorphic discs. (zero area) | |
| Aug 31, 2016 at 20:16 | history | answered | Nikolaki | CC BY-SA 3.0 |