Affable equivalence relations and orbit structure of Cantor dynamical systems

By Thierry Giordano. Ergodic Theory and Dynamical Systems, 2004

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Some remarks on topological full groups of Cantor minimal systems II (2004, methodology): “Definition 2.1 ([ GPS3 , Definition 2.1, 3.1, 3.7]).”
Cantor aperiodic systems and Bratteli diagrams (2006, background): “In this section, we ge some results of [4,5] to aperiodic homeomorphisms with a finite number of minimal components.”
Aperiodic substitution systems and their Bratteli diagrams (2007, methodology): “[HPS], [GPS1], [ GPS3 ]), we give only the main steps of the construction.”
Homology and topological full groups of étale groupoids on totally disconnected spaces (2009, background): “With this correspondence, we also discuss connections between homology theory and K-theory of totally disconnected étale groupoids.”
Crossed Products of the Cantor Set by Free Minimal Actions of ℤd (2002, background): “Proof: The first statement follows easily from Lemma 3.4 of [ 18 ].”