Morse functions and flows on nonorientable surfaces

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.

Full Text

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},
  MRNUMBER = {MR2567309},
       URL = {http://mfat.imath.kiev.ua/article/?id=503},
}