On the automorphism group of foliations with geometric transverse structures
Meersseman, Laurent (Université Angers. SFR Mathstic)
Nicolau i Reig, Marcel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ribón, Javier (Universidade Federal Fluminense. Instituto de Matemática e Estatística)

Date:	2022
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.
Grants:	Agencia Estatal de Investigación PGC2018-095998-B-I00 Ministerio de Economía y Competitividad MTM2016-77642-C2-1-P Ministerio de Economía y Competitividad MTM2015-66165-P
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Automorphic groups
Published in:	Mathematische Zeitschrift, ISSN 1432-1823

Adreça alternativa: https://link.springer.com/article/10.1007%2Fs00209-021-02952-y
DOI: 10.1007/s00209-021-02952-y

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