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Uniformly quasi-isometric foliations

Published online by Cambridge University Press:  19 September 2008

Mark Kellum
Mark Kellum
Affiliation:
Ecole Normale Supérieure de Lyon, 69364 Lyon, France and University of Maryland, College Park, Maryland, USA
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Abstract

Consider the natural action of 1-jets of the holonomy pseudogroup H on the transverse tangent bundle of a C1 compact foliated manifold (M, ℱ). If these 1-jets act in an equicontinuous way then it is possible to use a C1 ‘Ellis semi-group’ technique, as applied to a neighborhood of the identity in H, to produce a sheaf of compact local transformation groups whose orbits are the topological closures of leaves of ℱ. This action on the transverse manifold to ℱ then decomposes M into a union of minimal sets. These minimal sets we show to be C1 embedded submanifolds of M and the action of H on them is locally transitive.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 1 , March 1993 , pp. 101 - 122
Copyright
Copyright © Cambridge University Press 1993

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