{"paper":{"title":"The foliated Lefschetz hyperplane theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\'Alvaro del Pino, David Mart\\'inez Torres, Francisco Presas","submitted_at":"2014-10-12T02:11:19Z","abstract_excerpt":"A foliation $(M,\\mathcal{F})$ is said to be $2$--calibrated if it admits a closed 2-form $\\omega$ making each leaf symplectic. By using approximately holomorphic techniques, a sequence $W_k$ of $2$--calibrated submanifolds of codimension--$2$ can be found for $(M, \\mathcal{F}, \\omega)$. Our main result says that the Lefschetz hyperplane theorem holds for the pairs $(F, F \\cap W_k)$, with $F$ any leaf of $\\mathcal{F}$. This is applied to draw important consequences on the transverse geometry of such foliations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3043","kind":"arxiv","version":2},"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"}