Realization of a graph as the Reeb graph of a Morse function on a manifold

DOI10.12775/TMNA.2018.029zbMath1425.58022arXiv1805.06727MaRDI QIDQ1741801

Łukasz Patryk Michalak

Publication date: 7 May 2019

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

Full work available at URL: https://arxiv.org/abs/1805.06727

zbMATH Keywords

critical pointMorse functionReeb graph

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Relations of low-dimensional topology with graph theory (57M15) Topological invariants on manifolds (58K65) Critical points and critical submanifolds in differential topology (57R70) Critical points of functions and mappings on manifolds (58K05)

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 ⋮ Stable Bi-Maps on Surfaces and Their Graphs ⋮ 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 ⋮ 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

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

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