{"paper":{"title":"One-dimensional foliations on topological manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS","math.GN"],"primary_cat":"math.GT","authors_text":"Eugene Polulyakh, Sergiy Maksymenko","submitted_at":"2016-10-03T16:15:11Z","abstract_excerpt":"Let $X$ be an $(n+1)$-dimensional manifold, $\\Delta$ be a one-dimensional foliation on $X$, and $p: X \\to X / \\Delta$ be a quotient map. We will say that a leaf $\\omega$ of $\\Delta$ is special whenever the space of leaves $X / \\Delta$ is not Hausdorff at $\\omega$. We present necessary and sufficient conditions for the map $p: X \\to X / \\Delta$ to be a locally trivial fibration under assumptions that all leaves of $\\Delta$ are non-compact and the family of all special leaves of $\\Delta$ is locally finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00615","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"}