Approximate homomorphisms and sofic approximations of orbit equivalence relations
Group Theory
2024-11-20 v2 Dynamical Systems
Operator Algebras
Abstract
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence relation is uniquely determined by the invariant random subgroup of the approximate homomorphism. We record applications of this result to recover various known stability and conjugacy characterizations for almost homomorphisms of amenable groups.
Cite
@article{arxiv.2306.16974,
title = {Approximate homomorphisms and sofic approximations of orbit equivalence relations},
author = {Ben Hayes and Srivatsav Kunnawalkam Elayavalli},
journal= {arXiv preprint arXiv:2306.16974},
year = {2024}
}
Comments
22 pages, no figures. To appear in Ergodic Theory and Dynamical Systems