{"paper":{"title":"Homeotopy groups of one-dimensional foliations on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG","math.GN"],"primary_cat":"math.GT","authors_text":"Eugene Polulyakh, Sergiy Maksymenko, Yuliya Soroka","submitted_at":"2017-08-01T09:21:07Z","abstract_excerpt":"Let $Z$ be a non-compact two-dimensional manifold obtained from a family of open strips $\\mathbb{R}\\times(0,1)$ with boundary intervals by gluing those strips along their boundary intervals. Every such strip has a foliation into parallel lines $\\mathbb{R}\\times t$, $t\\in(0,1)$, and boundary intervals, whence we get a foliation $\\Delta$ on all of $Z$. Many types of foliations on surfaces with leaves homeomorphic to the real line have such \"striped\" structure. That fact was discovered by W. Kaplan (1940-41) for foliations on the plane $\\mathbb{R}^2$ by level-set of pseudo-harmonic functions $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00216","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"}