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Czechoslovak Mathematical Journal

, Volume 63, Issue 2, pp 515–528 | Cite as

Close cohomologous Morse forms with compact leaves

  • Irina Gelbukh
Article

Abstract

We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave γ, then any close cohomologous form has a compact leave close to γ. Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease under small perturbation of the form; moreover, for generic forms (Morse forms with each singular leaf containing a unique singularity; the set of generic forms is dense in the space of closed 1-forms) this number is locally constant.

Keywords

Morse form foliation compact leaf cohomology class 

MSC 2010

57R30 58K65 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Centro de Investigación en Computación (CIC)Instituto Politécnico Nacional (IPN)México CityMéxico

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