Loops in Reeb graphs of \(n\)-manifolds

DOI10.1007/s00454-017-9957-9zbMath1391.05144OpenAlexW2772095988MaRDI QIDQ1650793

Irina Gelbukh

Publication date: 13 July 2018

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-017-9957-9

zbMATH Keywords

Morse functionReeb graphcontour treenumber of loopsco-rank of the fundamental group

Mathematics Subject Classification ID

Paths and cycles (05C38) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Combinatorial aspects of simplicial complexes (05E45)

Related Items (10)

Criterion for a graph to admit a good orientation in terms of leaf blocks ⋮ Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds ⋮ On Reeb graphs induced from smooth functions on 3-dimensional closed manifolds with finitely many singular values ⋮ Reeb graphs of circle-valued functions: a survey and basic facts ⋮ Reeb spaces of smooth functions on manifolds II ⋮ Realization of a graph as the Reeb graph of a height function on an embedded surface ⋮ Realization of a graph as the Reeb graph of a Morse function on a manifold ⋮ Combinatorial modifications of Reeb graphs and the realization problem ⋮ A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function ⋮ ON THE MAXIMUM NUMBER OF PERIOD ANNULI FOR SECOND ORDER CONSERVATIVE EQUATIONS

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