The Borel complexity of von Neumann equivalence
| Autor: | Inessa Moroz, Asger Törnquist |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Logic Discrete group Group measure space factors 010102 general mathematics 0102 computer and information sciences Ergodic theory Free probability 01 natural sciences Global theory of measure preserving actions Mathematics::Logic Conjugacy class 010201 computation theory & mathematics Free group Equivalence relation Polish space 0101 mathematics Equivalence (measure theory) Mathematics Probability measure |
| Zdroj: | Moroz, I & Törnquist, A 2021, ' The Borel complexity of von Neumann equivalence ', Annals of Pure and Applied Logic, vol. 172, no. 5, 102913 . https://doi.org/10.1016/j.apal.2020.102913 |
| DOI: | 10.1016/j.apal.2020.102913 |
| Popis: | We prove that for a countable discrete group Γ containing a copy of the free group F n , for some 2 ≤ n ≤ ∞ , as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free probability measure preserving actions of Γ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving Γ-actions. As a consequence we obtain that the isomorphism relations in the spaces of separably acting factors of type II 1 , II ∞ and III λ , 0 ≤ λ ≤ 1 , are analytic and not Borel when these spaces are given the Effros Borel structure. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|