{"paper":{"title":"Structure of the fundamental groups of orbits of smooth functions on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Sergiy Maksymenko","submitted_at":"2014-08-12T03:29:34Z","abstract_excerpt":"Let $M$ be a smooth compact connected surface, $P$ be either the real line $\\mathbb{R}$ or the circle $S^1$ and $f:M\\to P$ be a Morse map. Denote by $\\mathcal{S}(f)$ and $\\mathcal{O}(f)$ the corresponding stabilizer and orbit of $f$ with respect to the right action of the group $\\mathcal{D}(M)$ of diffeomorphisms of $M$. In a series of papers the author described homotopy types of $\\mathcal{S}(f)$ and computed higher homotopy groups of $\\mathcal{O}(f)$. The present paper describes the structure of the remained fundamental group $\\pi_1 \\mathcal{O}(f)$ for the case when $M$ is orientable and dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2612","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"}