Locally Nilpotent Groups and Hyperfinite Equivalence Relations
نویسندگان
چکیده
A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is hyperfinite. In this paper we show that this question has a positive answer when the acting group is locally nilpotent. This extends previous results obtained by Gao–Jackson for abelian groups and by Jackson–Kechris–Louveau for finitely generated nilpotent-by-finite groups. Our proof is based on a mixture of coarse geometric properties of locally nilpotent groups together with an adaptation of the Gao–Jackson
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