On the automorphism group of foliations with geometric transverse structures

Laurent Meersseman, Marcel Nicolau Reig*, Javier Ribón

*Corresponding author for this work

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Abstract

We study the structure of some groups of diffeomorphisms preserving a foliation. We give an example of a 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.

Original languageEnglish
Number of pages28
JournalMathematische Zeitschrift (Print)
Issue number2
Early online date22 Jan 2022
DOIs
Publication statusE-pub ahead of print - 22 Jan 2022

Keywords

  • DIFFEOMORPHISMS
  • THEOREM
  • DEFORMATIONS
  • MANIFOLDS
  • CIRCLE

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