TY - JOUR
T1 - On the automorphism group of foliations with geometric transverse structures
AU - Meersseman, Laurent
AU - Nicolau Reig, Marcel
AU - Ribón, Javier
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - DIFFEOMORPHISMS
KW - THEOREM
KW - DEFORMATIONS
KW - MANIFOLDS
KW - CIRCLE
UR - http://www.scopus.com/inward/record.url?scp=85123505433&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/6e8d59ef-6a5d-3ff8-822d-d953399144b6/
U2 - 10.1007/s00209-021-02952-y
DO - 10.1007/s00209-021-02952-y
M3 - Article
SN - 0025-5874
VL - 301
SP - 1603
EP - 1630
JO - Mathematische Zeitschrift (Print)
JF - Mathematische Zeitschrift (Print)
IS - 2
ER -