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A Short Proof of Affability for Certain Cantor Minimal ℤ2-Systems

Published online by Cambridge University Press:  20 November 2018

Hiroki Matui
Hiroki Matui*
Affiliation:
Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan e-mail: matui@math.s.chiba-u.ac.jp
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Abstract

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We will show that any extension of a product of two Cantor minimal $\mathbb{Z}$-systems is affable in the sense of Giordano, Putnam and Skau.

Keywords

37B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 3 , 01 September 2007 , pp. 418 - 426
Copyright
Copyright © Canadian Mathematical Society 2007

References

[GPS1] Giordano, T., Putnam, I. F., and Skau, C. F., Topological orbit equivalence and C*-crossed products. J. Reine Angew. Math. 469(1995), 51–111.Google Scholar
[GPS2] Giordano, T., Putnam, I. F., and Skau, C. F., Affable equivalence relations and orbit structure of Cantor dynamical systems. Ergodic Theory Dynam. Systems 24(2004), 441–475.Google Scholar
[GPS3] Giordano, T., Putnam, I. F., and Skau, C. F., The orbit structure of Cantor minimal ℤ2 -systems. In: Operator Algebras. Abel Symp. 1, Springer, Berlin, 2006, pp. 145–160.Google Scholar
[HPS] Herman, R. H., Putnam, I. F., and Skau, C. F., Ordered Bratteli diagrams, dimension groups and topological dynamics. Internat. J. Math. 3(1992), no. 6, 827–864.Google Scholar