Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface

被引：0

作者：

Gelbukh, Irina ^{[1
]}

机构：

[1] Inst Politecn Nacl, CIC, Mexico City 07738, DF, Mexico

来源：

TOPOLOGY AND ITS APPLICATIONS | 2024年 / 341卷

关键词：

Reeb graph; Morse-Bott function; Realization problem; Surface; FINITE GRAPH; FLOWS;

D O I：

10.1016/j.topol.2023.108745

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the set of directed Reeb graphs of Morse-Bott functions on a given surface. Namely, we prove a criterion on realization of a given digraph as the directed Reeb graph of a Morse-Bott function on a given surface. (c) 2023 Elsevier B.V. All rights reserved.

引用

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页数：15

共 9 条

[1] REALIZATION OF A GRAPH AS THE REEB GRAPH OF A MORSE-BOTT OR A ROUND FUNCTION
Gelbukh, Irina
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2022, 59 (01) : 1 - 16
[2] A FINITE GRAPH IS HOMEOMORPHIC TO THE REEB GRAPH OF A MORSE-BOTT FUNCTION
Gelbukh, Irina
MATHEMATICA SLOVACA, 2021, 71 (03) : 757 - 772
[3] Reeb Graphs of Morse–Bott Functions on a Given Surface
Irina Gelbukh
Bulletin of the Iranian Mathematical Society, 2024, 50 (6)
[4] REALIZATION OF A GRAPH AS THE REEB GRAPH OF A MORSE FUNCTION ON A MANIFOLD
Michalak, Lukasz Patryk
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2018, 52 (02) : 749 - 762
[5] Morse-Bott functions with two critical values on a surface
Irina Gelbukh
Czechoslovak Mathematical Journal, 2021, 71 : 865 - 880
[6] Morse-Bott Functions with Two Critical Values on a Surface
Gelbukh, Irina
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2021, 71 (03) : 865 - 880
[7] REALIZATION OF A GRAPH AS THE REEB GRAPH OF A HEIGHT FUNCTION ON AN EMBEDDED SURFACE
Gelbukh, Irina
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2023, 61 (02) : 591 - 610
[8] A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH
Masumoto, Yasutaka
Saeki, Osamu
KYUSHU JOURNAL OF MATHEMATICS, 2011, 65 (01) : 75 - 84
[9] A finite graph is the Reeb graph of a Morse circle-valued function
Gelbukha, Irina
FILOMAT, 2023, 37 (11) : 3575 - 3590

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