Morse theory for analytic functions on surfaces

@inproceedings{Arango2005MorseTF,
  title={Morse theory for analytic functions on surfaces},
  author={Jaime Arango and Oscar Perdomo},
  year={2005}
}
In this paper we deal with analytic functions f : S → R defined on a compact two dimensional Riemannian surface S whose critical points are semi degenerated (critical points having a non identically vanishing Hessian). To any element p of the set of semi degenerated critical points Q we assign an unique index which can take the values −1, 0 or 1, and prove that Q is made up of finitely many (critical) points with non zero index and embedded circles. Further, we generalize the famous Morse… CONTINUE READING

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