Orbit equivalence for Cantor minimal -systems

Authors:
Thierry Giordano, Hiroki Matui, Ian F. Putnam and Christian F. Skau

Journal:
J. Amer. Math. Soc. **21** (2008), 863-892

MSC (2000):
Primary 37B99; Secondary 37B50, 37A20

DOI:
https://doi.org/10.1090/S0894-0347-08-00595-X

Published electronically:
January 22, 2008

MathSciNet review:
2393431

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every minimal, free action of the group on the Cantor set is orbit equivalent to an AF-relation. As a consequence, this extends the classification of minimal systems on the Cantor set up to orbit equivalence to include AF-relations, -actions and -actions.

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Additional Information

**Thierry Giordano**

Affiliation:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, Canada K1N 6N5

**Hiroki Matui**

Affiliation:
Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

**Ian F. Putnam**

Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4

**Christian F. Skau**

Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway

DOI:
https://doi.org/10.1090/S0894-0347-08-00595-X

Received by editor(s):
September 22, 2006

Published electronically:
January 22, 2008

Additional Notes:
The first author was supported in part by a grant from NSERC, Canada

The second author was supported in part by a grant from the Japan Society for the Promotion of Science

The third author was supported in part by a grant from NSERC, Canada

The last author was supported in part by the Norwegian Research Council

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.