Stable decompositions and rigidity for products of countable equivalence relations
Dynamical Systems
2022-09-22 v2 Logic
Operator Algebras
Abstract
We show that the stabilization of any countable ergodic p.m.p. equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.
Keywords
Cite
@article{arxiv.2102.13216,
title = {Stable decompositions and rigidity for products of countable equivalence relations},
author = {Pieter Spaas},
journal= {arXiv preprint arXiv:2102.13216},
year = {2022}
}
Comments
v2. Corrected a gap in the proof of Lemma 4.4 (result unchanged) and some inaccuracies; improved exposition. To appear in Transactions of the AMS