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Article Dans Une Revue Mathematische Zeitschrift Année : 2022

On the automorphism group of foliations with geometric transverse structures

Marcel Nicolau
  • Fonction : Auteur
Javier Ribón
  • Fonction : Auteur

Résumé

Abstract We study the structure of some groups of diffeomorphisms preserving a foliation. We give an example of a $$C^\infty $$ C ∞ foliation whose diffeomorphism group has not a natural structure of Lie group. On the positive side, we prove that the automorphism group of a transversely holomorphic foliation or a Riemannian foliation is a strong ILH Lie group in the sense of Omori. We also investigate the relationship of the previous considerations with deformation problems in foliation theory. We show that the existence of a local moduli space for a given foliation imposes strong conditions on its automorphism group. They are not fulfilled in many cases, in particular they are not fulfilled by the foliation mentioned above.

Dates et versions

hal-03850397 , version 1 (13-11-2022)

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Citer

Laurent Meersseman, Marcel Nicolau, Javier Ribón. On the automorphism group of foliations with geometric transverse structures. Mathematische Zeitschrift, 2022, 301 (2), pp.1603-1630. ⟨10.1007/s00209-021-02952-y⟩. ⟨hal-03850397⟩
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