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On the cost of generating an equivalence relation

Published online by Cambridge University Press:  14 October 2010

Gilbert Levitt
Affiliation:
Laboratoire de Topologie et Géométrie, URA CNRS 1408, Université Toulouse III, 31062 Toulouse Cedex, France ([email protected])

Abstract

Given a measure-preserving equivalence relation R with countable classes, we study relations between the properties of R and metric invariants. We give applications to pseudogroups of measure-preserving homeomorphisms.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

[Ad]Adams, S.. Trees and amenable equivalence relations. Ergod. Th. & Dynam. Sys. 10 (1990), 114.CrossRefGoogle Scholar
[CFW]Connes, A., Feldman, J. and Weiss, B.. An amenable equivalence relation is generated by a single transformation. Ergod. Th. & Dynam. Sys. 1 (1981), 431450.CrossRefGoogle Scholar
[FM]Feldman, J. and Moore, C.. Ergodic equivalence relations, cohomology and von Neumann algebras. I Trans. Amer. Math. Soc. 234 (1977), 289324.CrossRefGoogle Scholar
[Ga]Gaboriau, D.. Dynamique des systèmes d'isométries et actions de groupes sur les arbres réels. Thèse, Toulouse 1993.Google Scholar
[Gh]Ghys, E.. Topologie des feuilles génériques. Ann. Math. 141 (1995), 387422.CrossRefGoogle Scholar
[GL]Gaboriau, D. and Levitt, G.. The rank of actions on ℝ-trees. Ann. Sc. ENS (to appear).Google Scholar
[GLP1]Gaboriau, D., Levitt, G. and Paulin, F.. Pseudogroups of isometries of ℝ and Rips' theorem on free actions on ℝ-trees. Isr. J. Math. 87 (1994), 403428.CrossRefGoogle Scholar
[GLP2]Gaboriau, D., Levitt, G. and Paulin, F.. Pseudogroups of isometries of ℝ: reconstruction of free actions on ℝ-trees. Ergod. Th. & Dynam. Sys. 15 (1995), 633652.CrossRefGoogle Scholar
[Ha]Haefliger, A.. Groupoï des d'holonomie et classifiants. Structures Transverses des Feuilletages. Astérisque 116 (1984), 7097.Google Scholar
[Le1]Levitt, G.. 1-formes fermées singulières et groupe fondamental. Inv. Math. 88 (1987), 635667.CrossRefGoogle Scholar
[Le2]Levitt, G.. La dynamique des pseudogroupes de rotations. Inv. Math. 113 (1993), 633670.CrossRefGoogle Scholar
[Sa]Salem, E.. Riemannian foliations and pseudogroups of isometries. Appendix D in Molino, P., ed, Riemannian Foliations, Progress in Math. 73 (1988).Google Scholar