Orbit equivalence for Cantor minimal Z^2-systems
By Thierry Giordano, H. Matui, I. Putnam, Christian F. Skau. 2006
90 citations recorded by the source corpus.
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.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/25c117be9c417727b4db11297dd8c070a46012be
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In Mathematical Physics
- G'abor Szab'o
- W. Winter
- Toke Meier Carlsen
- H. Matui
- Nathan Brownlowe
- Michael F. Whittaker
- David Kerr
- Stuart White
Citations in the corpus
- Graph algebras and orbit equivalence (2014, methodology): “In general there is no direct method of checking whether two Cantor minimal systems are orbit equivalent.”
- Homology and topological full groups of étale groupoids on totally disconnected spaces (2009, background): “Then K is an elementary subgroupoid of G (see [6, 10]).”
- Classifying crossed product C*-algebras (2013, background): “Even Z d -actions on Cantor sets are notoriously difficult to handle in this respect (but cf. [7, 8]).”
- The Rokhlin dimension of topological ℤm‐actions (2013, background): “and Skau undertook a deep study on topological orbit equivalence of Cantor minimal Zm-actions in [4] and [5].”