The Borel complexity of von Neumann equivalence

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

The Borel complexity of von Neumann equivalence. / Moroz, Inessa; Törnquist, Asger.

I: Annals of Pure and Applied Logic, Bind 172, Nr. 5, 102913, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Moroz, I & Törnquist, A 2021, 'The Borel complexity of von Neumann equivalence', Annals of Pure and Applied Logic, bind 172, nr. 5, 102913. https://doi.org/10.1016/j.apal.2020.102913

APA

Moroz, I., & Törnquist, A. (2021). The Borel complexity of von Neumann equivalence. Annals of Pure and Applied Logic, 172(5), [102913]. https://doi.org/10.1016/j.apal.2020.102913

Vancouver

Moroz I, Törnquist A. The Borel complexity of von Neumann equivalence. Annals of Pure and Applied Logic. 2021;172(5). 102913. https://doi.org/10.1016/j.apal.2020.102913

Author

Moroz, Inessa ; Törnquist, Asger. / The Borel complexity of von Neumann equivalence. I: Annals of Pure and Applied Logic. 2021 ; Bind 172, Nr. 5.

Bibtex

@article{4a422a57e7cf458097d09434620c9148,
title = "The Borel complexity of von Neumann equivalence",
abstract = "We prove that for a countable discrete group Γ containing a copy of the free group Fn, 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 II1, II∞ and IIIλ, 0≤λ≤1, are analytic and not Borel when these spaces are given the Effros Borel structure.",
keywords = "Ergodic theory, Global theory of measure preserving actions, Group measure space factors",
author = "Inessa Moroz and Asger T{\"o}rnquist",
year = "2021",
doi = "10.1016/j.apal.2020.102913",
language = "English",
volume = "172",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier",
number = "5",

}

RIS

TY - JOUR

T1 - The Borel complexity of von Neumann equivalence

AU - Moroz, Inessa

AU - Törnquist, Asger

PY - 2021

Y1 - 2021

N2 - We prove that for a countable discrete group Γ containing a copy of the free group Fn, 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 II1, II∞ and IIIλ, 0≤λ≤1, are analytic and not Borel when these spaces are given the Effros Borel structure.

AB - We prove that for a countable discrete group Γ containing a copy of the free group Fn, 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 II1, II∞ and IIIλ, 0≤λ≤1, are analytic and not Borel when these spaces are given the Effros Borel structure.

KW - Ergodic theory

KW - Global theory of measure preserving actions

KW - Group measure space factors

UR - http://www.scopus.com/inward/record.url?scp=85095856209&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2020.102913

DO - 10.1016/j.apal.2020.102913

M3 - Journal article

AN - SCOPUS:85095856209

VL - 172

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 5

M1 - 102913

ER -

ID: 257977197