{"paper":{"title":"Deformations of smooth function on $2$-torus whose KR-graph is a tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Bohdan Feshchenko","submitted_at":"2018-04-24T11:46:51Z","abstract_excerpt":"Let $f:T^2\\to \\mathbb{R}$ be Morse function on $2$-torus $T^2,$ and $\\mathcal{O}(f)$ be the orbit of $f$ with respect to the right action of the group of diffeomorphisms $\\mathcal{D}(T^2)$ on $C^{\\infty}(T^2)$. Let also $\\mathcal{O}_f(f,X)$ be a connected component of $\\mathcal{O}(f,X)$ which contains $f.$ In the case when Kronrod-Reeb graph of $f$ is a tree we obtain the full description of $\\pi_1\\mathcal{O}_f(f).$\n  This result also holds for more general class of smooth functions $f:T^2\\to \\mathbb{R}$ which have the following property: for each critical point $z$ of $f$ the germ $f$ of $z$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08966","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"}