Abstract
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.
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Acknowledgements
The author would like to thank the organizers and all the participants of the 17th International Workshop on Real and Complex Singularities, held in São Carlos, Brazil, in July 2022, which was an unforgettable event and stimulated the author to write this paper. He would also like to thank the anonymous referees whose invaluable advice highly improved the exposition of the paper. The author has been supported in part by JSPS KAKENHI Grant Numbers JP22K18267, JP23H05437.
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Saeki, O. Reeb spaces of smooth functions on manifolds II. Res Math Sci 11, 24 (2024). https://doi.org/10.1007/s40687-024-00436-z
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DOI: https://doi.org/10.1007/s40687-024-00436-z