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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Vydané v:Research in the mathematical sciences Ročník 11; číslo 2
Hlavný autor: Saeki, Osamu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.06.2024
Predmet:
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
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Popis
Shrnutí: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