Realization of a graph as the Reeb graph of a height function on an embedded surface

DOI10.12775/tmna.2021.058OpenAlexW4318067798MaRDI QIDQ6187504

Irina Gelbukh

Publication date: 15 January 2024

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/topological-methods-in-nonlinear-analysis/volume-61/issue-2/Realization-of-a-graph-as-the-Reeb-graph-of-a/10.12775/TMNA.2021.058.full

zbMATH Keywords

embeddingorientable surfaceReeb graphheight functionMorse-Bott function

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Embeddings in differential topology (57R40) Singularities of differentiable mappings in differential topology (57R45) Critical points of functions and mappings on manifolds (58K05)

Cites Work

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• Loops in Reeb graphs of \(n\)-manifolds
• Realization of a graph as the Reeb graph of a Morse function on a manifold
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• Topological classification of simple Morse Bott functions on surfaces
• A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH
• Realization of smooth functions on surfaces as height functions
• Number of minimal components and homologically independent compact leaves for a morse form foliation
• Morse-Bott functions with two critical values on a surface
• Geometric realizations for free quotients

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