Subgroups of acting transitively on -tuples

Author:
Julio C. Rebelo

Journal:
Trans. Amer. Math. Soc. **356** (2004), 4543-4557

MSC (2000):
Primary 37B05, 22E65

Published electronically:
March 12, 2004

MathSciNet review:
2067133

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Abstract: We consider subgroups of -diffeomorphisms of the circle which act transitively on -tuples of points. We show, in particular, that these subgroups are dense in the group of homeomorphisms of . A stronger result concerning -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:
http://dx.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