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Subgroups of $\operatorname{Diff}^{\infty}_+ (\mathbb S^1)$ acting transitively on $4$-tuples


Author: Julio C. Rebelo
Journal: Trans. Amer. Math. Soc. 356 (2004), 4543-4557
MSC (2000): Primary 37B05, 22E65
DOI: https://doi.org/10.1090/S0002-9947-04-03466-X
Published electronically: March 12, 2004
MathSciNet review: 2067133
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Abstract: We consider subgroups of $C^{\infty}$-diffeomorphisms of the circle $\mathbb S^1$which act transitively on $4$-tuples of points. We show, in particular, that these subgroups are dense in the group of homeomorphisms of $\mathbb S^1$. A stronger result concerning $C^{\infty}$-approximations is obtained as well. The techniques employed in this paper rely on Lie algebra ideas and they also provide partial generalizations to the differentiable case of some results previously established in the analytic category.


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Additional Information

Julio C. Rebelo
Affiliation: Pontificia Universidade Catolica do Rio de Janeiro PUC-Rio, Rua Marques de São Vicente 225 - Gavea, Rio de Janeiro, RJ CEP 22453-900, Brazil
Address at time of publication: Institute for Mathematical Sciences, State University of New York at Stony Brook, Stony Brook, New York 11794-3660
Email: jrebelo@mat.puc-rio.br, jrebelo@math.sunysb.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03466-X
Keywords: Groups, vector fields, Lie algebras
Received by editor(s): July 3, 2002
Received by editor(s) in revised form: July 1, 2003
Published electronically: March 12, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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