Stable decompositions and rigidity for products of countable equivalence relations

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....

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Spaas, Pieter
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.09.2022
Subjects
Decomposition
Equivalence
Ergodic processes
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422