Approximate homomorphisms and sofic approximations of orbit equivalence relations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917840955637760 |
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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 |