On the automorphism group of foliations with geometric transverse structure

Laurent Meersseman; Marcel Nicolau; Javier Ribon

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arXiv · 1810.07244

On the automorphism group of foliations with geometric transverse structure

Laurent Meersseman·Marcel Nicolau·Javier Ribon

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Abstract

Motivated by questions of deformations/moduli in foliation theory, we investigate the structure of some groups of diffeomorphisms preserving a foliation. We give an example of a $C^\infty$ foliation whose diffeomorphism group is not a Lie group in any reasonable sense. On the positive side, we prove that the automorphism group of a transversely holomorphic foliation or a riemannian foliation is a strong ILH Lie goup in the sense of Omori.

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Laurent Meersseman, Marcel Nicolau, Javier Ribon. 2018-10-16. On the automorphism group of foliations with geometric transverse structure. https://arxiv.org/abs/1810.07244

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