{"paper":{"title":"Open Gromov-Witten invariants in dimension six","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Jean-Yves Welschinger (ICJ)","submitted_at":"2012-01-17T14:30:30Z","abstract_excerpt":"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 $L$, homol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3518","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}