Orbit equivalence for Cantor minimal ℤd-systems

By Thierry Giordano, H. Matui, I. Putnam, Christian F. Skau. 2009

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Graph algebras and orbit equivalence (2014, background): “4] to minimal Zd -actions on the Cantor set [6].”
Homology and topological full groups of étale groupoids on totally disconnected spaces (2009, background): “As described in [11], we can construct an étale principal groupoid (i.”
Continuous orbit equivalence rigidity (2015, background): “There is also a weaker notion of (topological) orbit equivalence which has been studied intensively for Z-actions on the Cantor set in the remarkable papers [11, 9, 10].”
Some remarks on topological full groups of Cantor minimal systems II (2004, background): “This classification was later extended to cover all minimal actions of finitely generated abelian groups on Cantor sets [4].”
Topological full groups of one-sided shifts of finite type (2012, background): “AF groupoids have played a crucial role in the study of orbit equivalence for minimal Z -actions ([16]).”
Dynamical Systems on Spectral Metric Spaces (2010, background): “For instance, if C is the Cantor set and if φ is a minimal homeomorphism of C, then, modulo isomorphism, the algebra C(C) oφ Z only gives the Z-actions orbit equivalent to φ [32, 33].”