Stable decompositions and rigidity for products of countable equivalence relations

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Stable decompositions and rigidity for products of countable equivalence relations. / Spaas, Pieter.

In: Transactions of the American Mathematical Society, Vol. 376, No. 3, 2023, p. 1867-1894.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Spaas, P 2023, 'Stable decompositions and rigidity for products of countable equivalence relations', Transactions of the American Mathematical Society, vol. 376, no. 3, pp. 1867-1894. https://doi.org/10.1090/tran/8800

APA

Spaas, P. (2023). Stable decompositions and rigidity for products of countable equivalence relations. Transactions of the American Mathematical Society, 376(3), 1867-1894. https://doi.org/10.1090/tran/8800

Vancouver

Spaas P. Stable decompositions and rigidity for products of countable equivalence relations. Transactions of the American Mathematical Society. 2023;376(3):1867-1894. https://doi.org/10.1090/tran/8800

Author

Spaas, Pieter. / Stable decompositions and rigidity for products of countable equivalence relations. In: Transactions of the American Mathematical Society. 2023 ; Vol. 376, No. 3. pp. 1867-1894.

Bibtex

@article{4492d88209ff42d0ba84854c8e4c6a75,
title = "Stable decompositions and rigidity for products of countable equivalence relations",
abstract = "We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.",
author = "Pieter Spaas",
note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",
year = "2023",
doi = "10.1090/tran/8800",
language = "English",
volume = "376",
pages = "1867--1894",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Stable decompositions and rigidity for products of countable equivalence relations

AU - Spaas, Pieter

N1 - Publisher Copyright: © 2022 American Mathematical Society.

PY - 2023

Y1 - 2023

N2 - We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.

AB - We show that the “stabilization” of any countable ergodic probability measure preserving (p.m.p.) equivalence relation which is not Schmidt, i.e. admits no central sequences in its full group, always gives rise to a stable equivalence relation with a unique stable decomposition, providing the first non-strongly ergodic such examples. In the proof, we moreover establish a new local characterization of the Schmidt property. We also prove some new structural results for product equivalence relations and orbit equivalence relations of diagonal product actions.

UR - http://www.scopus.com/inward/record.url?scp=85149259480&partnerID=8YFLogxK

U2 - 10.1090/tran/8800

DO - 10.1090/tran/8800

M3 - Journal article

AN - SCOPUS:85149259480

VL - 376

SP - 1867

EP - 1894

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -

ID: 340688926