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 language | English |
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Number of pages | 28 |
Journal | Mathematische Zeitschrift (Print) |
Issue number | 2 |
Early online date | 22 Jan 2022 |
DOIs | |
Publication status | E-pub ahead of print - 22 Jan 2022 |
Keywords
- DIFFEOMORPHISMS
- THEOREM
- DEFORMATIONS
- MANIFOLDS
- CIRCLE