SU\G(𝔸)/K·U

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Differentiable equisingularity of holomorphic foliations

Differentiable equisingularity of holomorphic foliations

We prove that a C ∞ equivalence between germs holomorphic foliations at (C 2 , 0) establishes a bijection between the sets of formal separatrices preserving equisingularity classes.As a consequence, if one of the foliations is of second type, so is the other and they are equisingular.