Déformations de feuilletages. (Deformations of foliations)
type: Item
instance of: scholarly article
title: Déformations de feuilletages. (Deformations of foliations)
zbMATH Open document ID: 0703.57013
DOI: 10.1016/0040-9383(90)90009-9
published in: Topology
publication date: 1990-01-01T00:00:00Z
review text: 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 \({\mathcal F}\).
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4153488
zbMATH Keywords: holonomy groupoid
zbMATH Keywords: germs of deformations of a foliation
zbMATH Keywords: deformation of a foliation
zbMATH Keywords: germs of deformations of the fundamental groupoid
zbMATH Keywords: complete transversal
author: C. Bonatti
author: André Haefliger
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: 0040-9383(90)90009-9
OpenAlex ID: W2092724633
description: scientific article; zbMATH DE number 4153488