Orbit equivalence for Cantor minimal $\mathbb{Z}^{2}$-systems

• Autores: Thierry Giordano, Hiroki Matui, Ian F. Putnam, F. Christian
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 21, Nº 3, 2008, págs. 863-892
• Idioma: inglés
• DOI: 10.1090/s0894-0347-08-00595-x
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• Resumen

  • 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