{"paper":{"title":"Realization of a graph as the Reeb graph of a Morse function on a manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"{\\L}ukasz Patryk Michalak","submitted_at":"2018-05-17T12:36:45Z","abstract_excerpt":"We investigate the problem of the realization of a given graph as the Reeb graph $\\mathcal{R}(f)$ of a smooth function $f\\colon M\\rightarrow \\mathbb{R}$ with finitely many critical points, where $M$ is a closed manifold. We show that for any $n\\geq2$ and any graph $\\Gamma$ admitting the so called good orientation there exist an $n$-manifold $M$ and a Morse function $f\\colon M\\rightarrow \\mathbb{R} $ such that its Reeb graph $\\mathcal{R}(f)$ is isomorphic to $\\Gamma$, extending previous results of Sharko and Masumoto-Saeki. We prove that Reeb graphs of simple Morse functions maximize the number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06727","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"}