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January, 2003 Periodic leaves for diffeomorphisms preserving codimension one foliations
Suely DRUCK, Sebastião FIRMO
J. Math. Soc. Japan 55(1): 13-37 (January, 2003). DOI: 10.2969/jmsj/1196890839

Abstract

We consider the group of diffeomorphisms of a compact manifold M which preserve a codimension one foliation F on M. For the C2 case if F has compact leaves with nontrivial holonomy then at least one of these leaves is periodic. Our main result is proved in the context of diffeomorphisms which preserve commutative actions of finitely generated groups on [0,1]. Applying this result to foliations almost without holonomy we prove the periodicity of all compact leaves with nontrivial holonomy. We also study the codimension one foliation preserving diffeomorphisms that are C2 close to the identity.

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Suely DRUCK. Sebastião FIRMO. "Periodic leaves for diffeomorphisms preserving codimension one foliations." J. Math. Soc. Japan 55 (1) 13 - 37, January, 2003. https://doi.org/10.2969/jmsj/1196890839

Information

Published: January, 2003
First available in Project Euclid: 5 December 2007

zbMATH: 1027.37014
MathSciNet: MR1939182
Digital Object Identifier: 10.2969/jmsj/1196890839

Subjects:
Primary: 57R30

Keywords: codimension one foliation , commutativity , periodic leaf

Rights: Copyright © 2003 Mathematical Society of Japan

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Vol.55 • No. 1 • January, 2003
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