On ergodic foliations
Copyright policy )On ergodic foliations
AbstractWe 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.
- Bryn Mawr College United States
group actions, K-automorphism, Bernoulli automorphisms, \({\mathbb Z}\)-action, ergodic foliation, General groups of measure-preserving transformations, Foliations in differential topology; geometric theory, Ergodic theory, covering spaces, ergodic action
group actions, K-automorphism, Bernoulli automorphisms, \({\mathbb Z}\)-action, ergodic foliation, General groups of measure-preserving transformations, Foliations in differential topology; geometric theory, Ergodic theory, covering spaces, ergodic action
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