Approximate homomorphisms and sofic approximations of orbit equivalence relations

Fuente: arXiv
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Autores principales: Hayes, Ben, Elayavalli, Srivatsav Kunnawalkam
Formato: Preprint
Publicado: 2023
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author Hayes, Ben
Elayavalli, Srivatsav Kunnawalkam
author_facet Hayes, Ben
Elayavalli, Srivatsav Kunnawalkam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2306_16974
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Approximate homomorphisms and sofic approximations of orbit equivalence relations
Hayes, Ben
Elayavalli, Srivatsav Kunnawalkam
Group Theory
Dynamical Systems
Operator Algebras
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.
title Approximate homomorphisms and sofic approximations of orbit equivalence relations
topic Group Theory
Dynamical Systems
Operator Algebras
url https://arxiv.org/abs/2306.16974