Conjugacy, orbit equivalence and classification of measure-preserving group actions

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Standard

Conjugacy, orbit equivalence and classification of measure-preserving group actions. / Törnquist, Asger Dag.

I: Ergodic Theory and Dynamical Systems, Bind 29, Nr. 3, 01.06.2009, s. 1033-1049.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Törnquist, AD 2009, 'Conjugacy, orbit equivalence and classification of measure-preserving group actions', Ergodic Theory and Dynamical Systems, bind 29, nr. 3, s. 1033-1049. https://doi.org/10.1017/S0143385708080528

APA

Törnquist, A. D. (2009). Conjugacy, orbit equivalence and classification of measure-preserving group actions. Ergodic Theory and Dynamical Systems, 29(3), 1033-1049. https://doi.org/10.1017/S0143385708080528

Vancouver

Törnquist AD. Conjugacy, orbit equivalence and classification of measure-preserving group actions. Ergodic Theory and Dynamical Systems. 2009 jun. 1;29(3):1033-1049. https://doi.org/10.1017/S0143385708080528

Author

Törnquist, Asger Dag. / Conjugacy, orbit equivalence and classification of measure-preserving group actions. I: Ergodic Theory and Dynamical Systems. 2009 ; Bind 29, Nr. 3. s. 1033-1049.

Bibtex

@article{f869ab9f104842b985fa446e205ba748,
title = "Conjugacy, orbit equivalence and classification of measure-preserving group actions",
abstract = "We prove that if G is a countable discrete group with property (T) over an infinite subgroup HG which contains an infinite Abelian subgroup or is normal, then G has continuum-many orbit-inequivalent measure-preserving almost-everywhere-free ergodic actions on a standard Borel probability space. Further, we obtain that the measure-preserving almost-everywhere-free ergodic actions of such a G cannot be classified up to orbit equivalence by a reasonable assignment of countable structures as complete invariants. We also obtain a strengthening and a new proof of a non-classification result of Foreman and Weiss for conjugacy of measure-preserving ergodic almost-everywhere-free actions of discrete countable groups.",
author = "T{\"o}rnquist, {Asger Dag}",
year = "2009",
month = jun,
day = "1",
doi = "10.1017/S0143385708080528",
language = "English",
volume = "29",
pages = "1033--1049",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Conjugacy, orbit equivalence and classification of measure-preserving group actions

AU - Törnquist, Asger Dag

PY - 2009/6/1

Y1 - 2009/6/1

N2 - We prove that if G is a countable discrete group with property (T) over an infinite subgroup HG which contains an infinite Abelian subgroup or is normal, then G has continuum-many orbit-inequivalent measure-preserving almost-everywhere-free ergodic actions on a standard Borel probability space. Further, we obtain that the measure-preserving almost-everywhere-free ergodic actions of such a G cannot be classified up to orbit equivalence by a reasonable assignment of countable structures as complete invariants. We also obtain a strengthening and a new proof of a non-classification result of Foreman and Weiss for conjugacy of measure-preserving ergodic almost-everywhere-free actions of discrete countable groups.

AB - We prove that if G is a countable discrete group with property (T) over an infinite subgroup HG which contains an infinite Abelian subgroup or is normal, then G has continuum-many orbit-inequivalent measure-preserving almost-everywhere-free ergodic actions on a standard Borel probability space. Further, we obtain that the measure-preserving almost-everywhere-free ergodic actions of such a G cannot be classified up to orbit equivalence by a reasonable assignment of countable structures as complete invariants. We also obtain a strengthening and a new proof of a non-classification result of Foreman and Weiss for conjugacy of measure-preserving ergodic almost-everywhere-free actions of discrete countable groups.

UR - http://www.scopus.com/inward/record.url?scp=69949086743&partnerID=8YFLogxK

U2 - 10.1017/S0143385708080528

DO - 10.1017/S0143385708080528

M3 - Journal article

AN - SCOPUS:69949086743

VL - 29

SP - 1033

EP - 1049

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 3

ER -

ID: 61335006