Mathematical Notes

, Volume 63, Issue 6, pp 760–763 | Cite as

Noncompact leaves of foliations of Morse forms

  • I. A. Mel'nikova
Article

Abstract

In this paper foliations determined by Morse forms on compact manifolds are considered. An inequality involving the number of connected components of the set formed by noncompact leaves, the number of homologically independent compact leaves, and the number of singular points of the corresponding Morse form is obtained.

Key words

Morse forms noncompact leaves of foliations two-dimensional manifolds 

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References

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    I. A. Mel'nikova, “Singular points of Morse forms and foliations,”Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. [Moscow Univ. Math. Bull.], No. 4, 37–40 (1996).MATHMathSciNetGoogle Scholar
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    P. Arnoux and G. Levitt, “Sur l'unique ergodicité des 1-formes fermées singulières,”Invent. Math.,84, 141–156 (1986).CrossRefMathSciNetGoogle Scholar
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    I. A. Mel'nikova,Compact Foliations of Morse Forms [in Russian], Kandidat thesis in the physico-mathematical sciences, Moscow State University, Moscow (1996).Google Scholar
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    F. Harary,Graph Theory, Addison-Wesley, Reading, Mass. (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • I. A. Mel'nikova
    • 1
  1. 1.Central Research Institute for Economics, Informatics, and Control SystemsUSSR

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