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

Thierry Giordano, Hiroki Matui, Ian F. Putnam, F. Christian

• 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