The isotropy group of a foliation: the local case

2020/06/02 by Dominique Cerveau, Cerveau, Dominique, Alcides Lins Neto +1
Mathematics · #34M15 #37F75 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:34M15 #msc:37F75

paper · pdf · doi:10.48550/arxiv.2006.01761

29 pages

arxiv created 2020/06/02 · openalex publication_date 2020/06/02 · arxiv updated 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a holomorphic singular foliation \fa of (\Cⁿ,0) we define Iso(\fa) as the group of germs of biholomorphisms on (\Cⁿ,0) preserving \fa: Iso(\fa)=\Φ∈ Diff(\Cⁿ,0) | Φ^*(\fa)=\fa\. The normal subgroup of Iso(\fa), of biholomorphisms sending each leaf of \fa into itself, will be denoted as Fix(\fa). The corresponding groups of formal biholomorphisms will be denoted as \whIso(\fa) and \whFix(\fa), respectively. The purpose of this paper will be to study the quotients Iso(\fa)/Fix(\fa) and \whFix(\fa)/\whFix(\fa), mainly in the case of codimension one foliation.

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