Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
| dc.creator | Liu, Chiu-Chu Melissa | |
| dc.date | 2002-10-17 | |
| dc.date | 2004-12-04 | |
| dc.date.accessioned | 2026-07-07T04:52:03Z | |
| dc.date.available | 2026-07-07T04:52:03Z | |
| dc.description | Let $(X,ω)$ be a symplectic manifold, $J$ be an $ω$-tame almost complex structure, and $L$ be a Lagrangian submanifold. The stable compactification of the moduli space of parametrized $J$-holomorphic curves in $X$ with boundary in $L$ (with prescribed topological data) is compact and Hausdorff in Gromov's $C^\infty$-topology. We construct a Kuranishi structure with corners in the sense of Fukaya and Ono. This Kuranishi structure is orientable if $L$ is spin. In the special case where the expected dimension of the moduli space is zero, and there is an $S^1$ action on the pair $(X,L)$ which preserves $J$ and acts freely on $L$, we define the Euler number for this $S^1$ equivariant pair and the prescribed topological data. We conjecture that this rational number is the one computed by localization techniques using the given $S^1$ action. | |
| dc.description | 85 pages, 20 figures; Section 3 and 4 corrected and refined; notation of the rest of the paper changed accordingly | |
| dc.identifier | https://arxiv.org/abs/math/0210257 | |
| dc.identifier | http://arxiv.org/abs/math/0210257 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65325 | |
| dc.subject | Symplectic Geometry | |
| dc.title | Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair | |
| dc.type | text |