Orbit equivalence for Cantor minimal Z^2-systems
  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. 
Thierry Giordano, Hiroki Matui, Ian F. Putnam and Christian F. Skau