Close cohomologous Morse forms with compact leaves

@article{Gelbukh2013CloseCM,
  title={Close cohomologous Morse forms with compact leaves},
  author={Irina Gelbukh},
  journal={Czechoslovak Mathematical Journal},
  year={2013},
  volume={63},
  pages={515-528}
}
  • Irina Gelbukh
  • Published 2013
  • Mathematics
  • Czechoslovak Mathematical Journal
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… Expand

Figures from this paper

References

SHOWING 1-10 OF 18 REFERENCES
1-formes fermées singulières et groupe fondamental
Ranks of collinear Morse forms
Topology of closed one-forms
Morse theory of harmonic forms
SMOOTH REGULAR NEIGHBORHOODS
Graduate Texts in Mathematics
...
1
2
...