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Classification of cocycles of generic equivalence relations

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Abstract

We study cocycles of an ergodic generic countable equivalence relation ℜ modulo meager sets. Two cocycles of ℜ are called weakly equivalent if they are cohomologous up to an element of Aut ℜ. It is proved that two nontransient cocycles with values in an arbitrary countable group are weakly equivalent if and only if their generic Mackey actions are isomorphic.

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  1. Institute for Low Temperature Physics & Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., 61103, Kharkov, Ukraine

    Vyacheslav Kulagin

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  1. Vyacheslav Kulagin
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Kulagin, V. Classification of cocycles of generic equivalence relations. Isr. J. Math. 152, 83–104 (2006). https://doi.org/10.1007/BF02771977

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  • DOI: https://doi.org/10.1007/BF02771977

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