Opis

• Tytuł:
  Realization of a graph as the Reeb graph of a height function on an embedded surface
• Twórca:
  Gelbukh, Irina
• Opis:
  We show that for a given finite graph $G$ without loop edges and isolated vertices, there exists an embedding of a closed orientable surface in $\mathbb{R}^3$ such that the Reeb graph of the associated height function has the structure of $G$. In particular, this gives a positive answer to the corresponding question posed by Masumoto and Saeki in 2011. We also give a criterion for a given surface to admit such a realization of a given graph, and study the problem in the class of Morse functions and in the class of round Morse-Bott functions. In the case of realization up to homeomorphism, the height function can be chosen Morse-Bott; we estimate from below the number of its critical circles and the number of its isolated critical points in terms of the graph structure.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Irina Gelbukh
• Data:
  2023.01.25
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 61, No 2 (June 2023); 591 - 610;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/42231/34564 ;https://apcz.umk.pl/TMNA/article/view/42231/34565
• Temat i słowa kluczowe:
  {Reeb graph;
  height function;
  Morse-Bott function;
  orientable surface;
  embedding;
  Primary: 57R40, 53A05;
  Secondary: 58K05, 57R45
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/42231
• Dostawca danych:
  Akademicka Platforma Czasopism
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