On the automorphism group of foliations with geometric transverse structures
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 Riemannia...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:251494 |
| Acceso en línea: | https://ddd.uab.cat/record/251494 https://dx.doi.org/urn:doi:10.1007/s00209-021-02952-y |
| Access Level: | acceso abierto |
| Palabra clave: | Automorphic groups |
| Sumario: | 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. |
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