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On ergodic foliations

Published online by Cambridge University Press:  19 September 2008

Kyewon Park
Kyewon Park
Affiliation:
Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA
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Abstract

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We define an ergodic ℤ-foliation and show that it can be realized as a quotient space of the ‘covering space’. The covering space has two actions, T and S, where T is a ℤ-action, S is a map of order two, and S and T skew-commute; that is, STS = T−1. We study the isometry between two foliations via the isomorphism between two bigger group actions in the covering spaces. Properties of an ergodic foliation are studied in a way similar to the study of an ergodic action. We construct a counterexample of a K-automorphism to show that, unlike Bernoulli automorphisms, ℤ-actions do not completely determine ℤ-foliations.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 437 - 457
Copyright
Copyright © Cambridge University Press 1988

References

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