Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations
Dynamical Systems
2025-10-07 v1 Logic
Abstract
We show that the isomorphism of ergodic measure-preserving transformations is not Borel reducible to the relation induced by the conjugacy action of the full group of an ergodic measure-preserving transformation on itself. This answers a question of Le Ma\^{i}tre in the negative and gives a positive indication towards a conjecture of Sabok. In fact, we prove that the isomorphism of ergodic measure-preserving transformation is unbalanced, which answers another question of Le Ma\^{i}tre in the positive.
Cite
@article{arxiv.2510.04989,
title = {Unbalancedness of the conjugacy relation of ergodic measure-preserving transformations},
author = {Bo Peng},
journal= {arXiv preprint arXiv:2510.04989},
year = {2025}
}
Comments
7pages