### Abstract

The present paper deals with the correspondence between Morse functions and flows on nonorientable surfaces. It is proved that for every Morse flow with an indexing of saddle points on a nonorientable surface there is a unique Morse function, up to a fiber equivalence, such that its gradient flow is trajectory equivalent to the initial flow, and the values of the function in the saddle points are ordered according to the indexing. The algorithm for constructing the Morse function from a Morse flow with an indexing is given. Reeb graphs and 3-graphs, which assign Morse functions and the corresponding Morse flows with the number of the saddle points less than $3$ are presented.

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### Article Information

Title | Morse functions and flows on nonorientable surfaces |

Source | Methods Funct. Anal. Topology, Vol. 15 (2009), no. 3, 251-258 |

MathSciNet |
MR2567309 |

Copyright | The Author(s) 2009 (CC BY-SA) |

### Authors Information

*D. P. Lychak*

Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv University, Kyiv, Ukraine

*A. O. Prishlyak*

Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv University, Kyiv, Ukraine

### Citation Example

D. P. Lychak and A. O. Prishlyak, *Morse functions and flows on nonorientable surfaces*, Methods Funct. Anal. Topology **15**
(2009), no. 3, 251-258.

### BibTex

@article {MFAT503,
AUTHOR = {Lychak, D. P. and Prishlyak, A. O.},
TITLE = {Morse functions and flows on nonorientable surfaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {3},
PAGES = {251-258},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=503},
}

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