Reeb spaces of smooth functions on manifolds II

The Reeb space of a continuous function on a topological space is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth fun...

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Bibliographic Details
Published in:Research in the mathematical sciences Vol. 11; no. 2
Main Author: Saeki, Osamu
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2024
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
54C30
57R45
Reeb space
Reeb graph
Smooth function
Secondary 58K30
Primary 58K05
58K15
Peano continuum
57R70
ISSN:2522-0144, 2197-9847
Online Access:Get full text
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Summary:The Reeb space of a continuous function on a topological space is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth functions on closed manifolds such that they themselves or their Reeb spaces have some interesting properties.
ISSN:2522-0144
2197-9847
DOI:10.1007/s40687-024-00436-z