Abstract
In Definition 20.4.33, we introduced the invariant Dm(X,\(\mathcal{R}\)) for an étale equivalence relation \(\mathcal{R}\) on a totally disconnected, compact Hausdorff space X, and showed in Proposition 20.4.40 that it is an orbit equivalence invariant. In this chapter, we will show that this invariant is complete for the class of AF equivalence relations. The classification up to orbit equivalence of minimal AF-equivalence relations will be a corollary of the following theorem from Putnam [78].
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Giordano, T., Kerr, D., Phillips, N.C., Toms, A. (2018). Orbit Equivalence of AF-Equivalence Relations. In: Perera, F. (eds) Crossed Products of C*-Algebras, Topological Dynamics, and Classification. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70869-0_22
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DOI: https://doi.org/10.1007/978-3-319-70869-0_22
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