{"paper":{"title":"Actions of finite groups and smooth functions on surfaces","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Bohdan Feshchenko","submitted_at":"2016-10-04T21:56:34Z","abstract_excerpt":"Let $f:M\\to \\mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a connected component of some critical level of $f$, and $\\mathcal{E}_V$ be its atom. Let also $\\mathcal{S}(f)$ be a stabilizer of the function $f$ under the right action of the group of diffeomorphisms $\\mathrm{Diff}(M)$ on the space of smooth functions on $M,$ and $\\mathcal{S}_V(f) = \\{h\\in\\mathcal{S}(f)\\,| h(V) = V\\}.$ The group $\\mathcal{S}_V(f)$ acts on the set $\\pi_0\\partial \\mathcal{E}_V$ of connected components of the boundary of $\\mathcal{E}_V.$ Therefore we have a homomorphism $\\phi:\\mathcal{S}(f)\\to \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01219","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"}