{"paper":{"title":"Special framed Morse functions on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Elena A. Kudryavtseva","submitted_at":"2011-06-15T22:53:18Z","abstract_excerpt":"Let $M$ be a smooth closed orientable surface. Let $F$ be the space of Morse functions on $M$, and $\\mathbb{F}^1$ the space of framed Morse functions, both endowed with $C^\\infty$-topology. The space $\\mathbb{F}^0$ of special framed Morse functions is defined. We prove that the inclusion mapping $\\mathbb{F}^0\\hookrightarrow\\mathbb{F}^1$ is a homotopy equivalence. In the case when at least $\\chi(M)+1$ critical points of each function of $F$ are labeled, homotopy equivalences $\\mathbb{\\widetilde K}\\sim\\widetilde{\\cal M}$ and $F\\sim\\mathbb{F}^0\\sim{\\mathscr D}^0\\times\\mathbb{\\widetilde K}$ are pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3116","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"}