{"paper":{"title":"Topology of the spaces of functions with prescribed singularities on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Elena A. Kudryavtseva","submitted_at":"2016-01-11T00:00:10Z","abstract_excerpt":"Let $M$ be a smooth connected orientable closed surface and $f_0\\in C^\\infty(M)$ a function having only critical points of the $A_\\mu$-types, $\\mu\\in\\mathbb N$. Let ${\\mathcal F}={\\mathcal F}(f_0)$ be the set of functions $f\\in C^\\infty(M)$ having the same types of local singularities as those of $f_0$. We describe the homotopy type of the space $\\mathcal F$, endowed with the $C^\\infty$-topology, and its decomposition into orbits of the action of the group of \"left-right changings of coordinates\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02283","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"}