The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface

@article{Gelbukh2013TheNO,
  title={The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface},
  author={Irina Gelbukh},
  journal={Rocky Mountain Journal of Mathematics},
  year={2013},
  volume={43},
  pages={1537-1552}
}
  • Irina Gelbukh
  • Published 2013
  • Mathematics
  • Rocky Mountain Journal of Mathematics
On a closed orientable surface M 2 of genus g, we consider the foliation of a weakly generic Morse form ! on M 2 and show that for such forms c(!) + m(!) = g 1 k(!), wh ere c(!) is the number of homologically independent compact leaves of the foliation, m(!) is the number of its mini- mal components, and k(!) is the total number of singularities of ! that are surrounded by a minimal component. We also give lower bounds on m(!) in terms of k(!) and the form rank rk! or the structure of ker… Expand

Figures from this paper

Structure of a Morse form foliation on a closed surface in terms of genus
Ranks of collinear Morse forms
Singular foliations for M-theory compactification

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