A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function

DOI10.1515/ms-2021-0018zbMath1478.58005OpenAlexW3048583996MaRDI QIDQ2054666

Irina Gelbukh

Publication date: 3 December 2021

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ms-2021-0018

zbMATH Keywords

surfaceimmersionReeb graphheight functionMorse-Bott function

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Topological invariants on manifolds (58K65) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60) Real-valued functions on manifolds (58C05)

Related Items (4)

Criterion for a graph to admit a good orientation in terms of leaf blocks ⋮ Reeb graphs of circle-valued functions: a survey and basic facts ⋮ Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface ⋮ Realization of a graph as the Reeb graph of a height function on an embedded surface

Uses Software

• MathOverflow

Cites Work

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• The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
• The co-rank conjecture for 3-manifold groups

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