Locally Nilpotent Groups and Hyperfinite Equivalence Relations
Logic
2013-10-22 v2 Dynamical Systems
Abstract
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 machinery.
Cite
@article{arxiv.1308.5853,
title = {Locally Nilpotent Groups and Hyperfinite Equivalence Relations},
author = {Scott Schneider and Brandon Seward},
journal= {arXiv preprint arXiv:1308.5853},
year = {2013}
}