{"paper":{"title":"Homotopy properties of spaces of smooth functions on 2-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bogdan Feshchenko, Sergiy Maksymenko","submitted_at":"2014-01-10T12:01:52Z","abstract_excerpt":"Let $f:T^2\\to\\mathbb{R}$ be a Morse function on a 2-torus, $\\mathcal{S}(f)$ and $\\mathcal{O}(f)$ be its stabilizer and orbit with respect to the right action of the group $\\mathcal{D}(T^2)$ of diffeomorphisms of $T^2$, $\\mathcal{D}_{\\mathrm{id}}(T^2)$ be the identity path component of $\\mathcal{D}(T^2)$, and $\\mathcal{S}'(f) = \\mathcal{S}(f) \\cap \\mathcal{D}_{\\mathrm{id}}(T^2)$. We give sufficient conditions under which $$ \\pi_1\\mathcal{O}_f(f) \\ \\cong \\ \\pi_1\\mathcal{D}(T^2) \\times \\pi_0 \\mathcal{S}'(f) \\ \\equiv \\ \\mathbb{Z}^2 \\times \\pi_0 \\mathcal{S}'(f).$$ In fact this result holds for a la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2296","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"}