{"paper":{"title":"Topology of singular holomorphic foliations along a compact divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Mar\\'in, Jean-Fran\\c{c}ois Mattei","submitted_at":"2012-06-11T07:59:02Z","abstract_excerpt":"We consider a singular holomorphic foliation $\\uF$ defined near a compact curve $\\uC$ of a complex surface. Under some hypothesis on $(\\uF,\\uC)$ we prove that there exists a system of tubular neighborhoods $U$ of a curve $\\underline{\\mc D}$ containing $\\uC$ such that every leaf $L$ of $\\uF_{|(U\\setminus \\underline{\\mc D})}$ is incompressible in $U\\setminus \\underline{\\mc D}$. We also construct a representation of the fundamental group of the complementary of $\\underline{\\mc D}$ into a suitable automorphism group, which allows to state the topological classification of the germ of $(\\uF,\\uD)$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2121","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"}