Counting real pseudo-holomorphic discs and spheres in dimension four and six
| dc.creator | Cho, Cheol-Hyun | |
| dc.date | 2006-04-24 | |
| dc.date | 2006-04-25 | |
| dc.date.accessioned | 2026-07-07T07:11:12Z | |
| dc.date.available | 2026-07-07T07:11:12Z | |
| dc.description | First, we provide another proof that the signed count of the real $J$-holomorphic spheres (or $J$-holomorphic discs) passing through a generic real configuration of $k$ points is independent of the choice of the real configuration and the choice of $J$, if the dimension of the Lagrangian submanifold $L$ (fixed points set of the involution) is two or three, and also if we assume $L$ is orientable and relatively spin, and $M$ is strongly semi-positive. This theorem was first proved by Welschinger in a more general setting, and we provide more natural approach using the degree of evaluation maps from the moduli spaces of $J$-holomorphic discs. Then, we define the invariant count of discs intersecting cycles of a symplectic manifold at fixed interior marked points, and intersecting real points at the boundary under certain assumptions. The last result is new and was not proved by Welshinger's method. | |
| dc.description | 18 pages, 2 figures, typo corrected | |
| dc.identifier | https://arxiv.org/abs/math/0604501 | |
| dc.identifier | http://arxiv.org/abs/math/0604501 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111665 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53D45;14N35 | |
| dc.title | Counting real pseudo-holomorphic discs and spheres in dimension four and six | |
| dc.type | text |