{"paper":{"title":"Homotopy properties of smooth functions on the M\\\"obius band","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Iryna Kuznietsova, Sergiy Maksymenko","submitted_at":"2019-01-11T09:46:18Z","abstract_excerpt":"Let $B$ be a M\\\"obius band and $f:B \\to \\mathbb{R}$ be a Morse map taking a constant value on $\\partial B$, and $\\mathcal{S}(f,\\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\\partial B$ and preserving $f$ in the sense that $f\\circ h = f$. Under certain assumptions on $f$ we compute the group $\\pi_0\\mathcal{S}(f,\\partial B)$ of isotopy classes of such diffeomorphisms. In fact, those computations hold for functions $f:B\\to\\mathbb{R}$ whose germs at critical points are smoothly equivalent to homogeneous polynomials $\\mathbb{R}^2\\to\\mathbb{R}$ without multiple factors.\n  Togethe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03528","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"}