Déformations de feuilletages. (Deformations of foliations)
A deformation of a foliation \({\mathcal F}\) of a manifold M is a foliation \({\mathcal F}^ S\) of an open subset U of \(M\times S\) such that the leaves of \({\mathcal F}^ S\) are contained in the sets \(M\times \{s\}\) (s\(\in S)\) and \({\mathcal F}={\mathcal F}^ S| M\times \{s_ 0\}\) for some \(s_ 0\) of S. For fixed \((S,s_ 0)\), the authors find a natural 1-1 corespondence between the equivalence classes of germs of deformations of \({\mathcal F}\) and the germs of deformations of the fundamental groupoid \(\Pi_{{\mathcal F}}(T)\) of \({\mathcal F}\), T being a complete transversal of \({\mathcal F}\).
germs of deformations of the fundamental groupoid
scientific article; zbMATH DE number 4153488