Orbit equivalence for Cantor minimal Z^d-systems

Abstract

We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal dynamical systems on the Cantor set to include AF relations and Z^d-actions.

48 pages. Minor changes

Cited by in corpus (6)

• The Rokhlin dimension of topological Z^m-actions
• Tiling groupoids and Bratteli diagrams
• Transverse Laplacians for Substitution Tilings
• Arboreal Cantor actions
• Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces
• $K$-theory of two-dimensional substitution tiling spaces from $AF$-algebras