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Orbit equivalence for Cantor minimal Z^2-systems

Thierry Giordano·Hiroki Matui·Ian F. Putnam·Christian F. Skau
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Abstract

We show that every minimal, free action of the group Z^2 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, Z-actions and Z^2-actions.

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Thierry Giordano, Hiroki Matui, Ian F. Putnam, Christian F. Skau. 2007-11-22. Orbit equivalence for Cantor minimal Z^2-systems. https://arxiv.org/abs/math/0609668

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