Journal of the Ramanujan Mathematical Society

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AF Equivalence Relations Associated to Locally Finite Groups


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1 Department of Mathematical Science, Norwegian University of Science and Technology (NTNU), N–7491 Trondheim, Norway
     

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In [5, Theorem 3.8], Giordano, Putnam and Skau showed that the ´etale equivalence relation associated to a (countable) group acting minimally and freely on the Cantor set is AF if and only if the group is locally finite. In this paper we answer what types of AF equivalence relations arise for such actions, linking them to Bratteli diagrams with the so-called equal path number property. Furthermore, we explore more general actions of locally finite groups, and we give a new and more transparent proof of a result by Krieger [9, Theorem 3.5 and Corollary 3.6] in the process.
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  • AF Equivalence Relations Associated to Locally Finite Groups

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Authors

Heidi Dahl
Department of Mathematical Science, Norwegian University of Science and Technology (NTNU), N–7491 Trondheim, Norway

Abstract


In [5, Theorem 3.8], Giordano, Putnam and Skau showed that the ´etale equivalence relation associated to a (countable) group acting minimally and freely on the Cantor set is AF if and only if the group is locally finite. In this paper we answer what types of AF equivalence relations arise for such actions, linking them to Bratteli diagrams with the so-called equal path number property. Furthermore, we explore more general actions of locally finite groups, and we give a new and more transparent proof of a result by Krieger [9, Theorem 3.5 and Corollary 3.6] in the process.