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Article Dans Une Revue Mathematische Annalen Année : 2013

Open Gromov-Witten invariants in dimension six

Résumé

Let $L$ be a closed orientable Lagrangian submanifold of a closed symplectic six-manifold $(X , \omega)$. We assume that the first homology group $H_1 (L ; A)$ with coefficients in a commutative ring $A$ injects into the group $H_1 (X ; A)$ and that $X$ contains no Maslov zero pseudo-holomorphic disc with boundary on $L$. Then, we prove that for every generic choice of a tame almost-complex structure $J$ on $X$, every relative homology class $d \in H_2 (X , L ; \Z)$ and adequate number of incidence conditions in $L$ or $X$, the weighted number of $J$-holomorphic discs with boundary on $L$, homologous to $d$, and either irreducible or reducible disconnected, which satisfy the conditions, does not depend on the generic choice of $J$, provided that at least one incidence condition lies in $L$. These numbers thus define open Gromov-Witten invariants in dimension six, taking values in the ring $A$.
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Dates et versions

hal-00660667 , version 1 (17-01-2012)

Identifiants

Citer

Jean-Yves Welschinger. Open Gromov-Witten invariants in dimension six. Mathematische Annalen, 2013, 356 (3), pp.1163-1182. ⟨10.1007/s00208-012-0883-0⟩. ⟨hal-00660667⟩
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