We prove that generic convergent diagrams of proper smooth mappings are topologically stable. In proving global properties of diagrams we propose a generalization of the concept of singularity for diagrams, and we establish the of composite mappings.
We define the separatrices for pseudogroups of diffeomorphisms of open neighbourhoods of the origin in the complex plane and prove their existence for non solvable pseudogroups (Theorem 1). This extends a result by Shcherbakov (in [21]) accurately. Our method also applies to prove the topological rigidity theorem for generic pseudogroups attributed to Shcherbakov (dans [20]).
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