{"paper":{"title":"Topology of spaces of smooth functions and gradient-like flows with prescribed singularities on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Elena A. Kudryavtseva","submitted_at":"2021-06-06T03:09:12Z","abstract_excerpt":"By a gradient-like flow on a closed orientable surface $M$, we mean a closed 1-form $\\beta$ defined on $M$ punctured at a finite set of points (sources and sinks of $\\beta$) such that there exists a Morse function $f$ on $M$, called an energy function of $\\beta$, whose critical points coincide with equilibria of $\\beta$, and the pair $(f,\\beta)$ has a canonical form near each critical point of $f$. Let $\\mathcal{B}=\\mathcal{B}(\\beta_0)$ be the space of all gradient-like flows on $M$ having the same types of local singularities as a flow $\\beta_0$, and $\\mathcal{F}=\\mathcal{F}(f_0)$ the space o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03017","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.03017/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}