Co-induction and invariant random subgroups

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Standard

Co-induction and invariant random subgroups. / Kechris, Alexander S.; Quorning, Vibeke.

In: Groups, Geometry, and Dynamics, Vol. 13, No. 4, 2019, p. 1151-1193.

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

Harvard

Kechris, AS & Quorning, V 2019, 'Co-induction and invariant random subgroups', Groups, Geometry, and Dynamics, vol. 13, no. 4, pp. 1151-1193. https://doi.org/10.4171/GGD/517

APA

Kechris, A. S., & Quorning, V. (2019). Co-induction and invariant random subgroups. Groups, Geometry, and Dynamics, 13(4), 1151-1193. https://doi.org/10.4171/GGD/517

Vancouver

Kechris AS, Quorning V. Co-induction and invariant random subgroups. Groups, Geometry, and Dynamics. 2019;13(4):1151-1193. https://doi.org/10.4171/GGD/517

Author

Kechris, Alexander S. ; Quorning, Vibeke. / Co-induction and invariant random subgroups. In: Groups, Geometry, and Dynamics. 2019 ; Vol. 13, No. 4. pp. 1151-1193.

Bibtex

@article{53788f6b4392449bb71683fd62ac79f7,
title = "Co-induction and invariant random subgroups",
abstract = "In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of F2 which are all invariant and weakly mixing with respect to the action of Aut(F2). Moreover, for amenable groups Γ ≤ Δ, we obtain that the standard co-induction operation from the space of weak equivalence classes of Δ to the space of weak equivalence classes of Δ is continuous if and only if [Δ : Γ] < ∞ or coreΔ(Γ) is trivial. For general groups we obtain that the co-induction operation is not continuous when [Δ : Γ] = ∞. This answers a question raised by Burton and Kechris in [17]. Independently such an answer was also obtained, using a different method, by Bernshteyn in [8].",
keywords = "Co-induction, Invariant random subgroups, Small cancellation, Weak mixing",
author = "Kechris, {Alexander S.} and Vibeke Quorning",
year = "2019",
doi = "10.4171/GGD/517",
language = "English",
volume = "13",
pages = "1151--1193",
journal = "Groups, Geometry, and Dynamics",
issn = "1661-7207",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - Co-induction and invariant random subgroups

AU - Kechris, Alexander S.

AU - Quorning, Vibeke

PY - 2019

Y1 - 2019

N2 - In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of F2 which are all invariant and weakly mixing with respect to the action of Aut(F2). Moreover, for amenable groups Γ ≤ Δ, we obtain that the standard co-induction operation from the space of weak equivalence classes of Δ to the space of weak equivalence classes of Δ is continuous if and only if [Δ : Γ] < ∞ or coreΔ(Γ) is trivial. For general groups we obtain that the co-induction operation is not continuous when [Δ : Γ] = ∞. This answers a question raised by Burton and Kechris in [17]. Independently such an answer was also obtained, using a different method, by Bernshteyn in [8].

AB - In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of F2 which are all invariant and weakly mixing with respect to the action of Aut(F2). Moreover, for amenable groups Γ ≤ Δ, we obtain that the standard co-induction operation from the space of weak equivalence classes of Δ to the space of weak equivalence classes of Δ is continuous if and only if [Δ : Γ] < ∞ or coreΔ(Γ) is trivial. For general groups we obtain that the co-induction operation is not continuous when [Δ : Γ] = ∞. This answers a question raised by Burton and Kechris in [17]. Independently such an answer was also obtained, using a different method, by Bernshteyn in [8].

KW - Co-induction

KW - Invariant random subgroups

KW - Small cancellation

KW - Weak mixing

UR - http://www.scopus.com/inward/record.url?scp=85077284680&partnerID=8YFLogxK

U2 - 10.4171/GGD/517

DO - 10.4171/GGD/517

M3 - Journal article

AN - SCOPUS:85077284680

VL - 13

SP - 1151

EP - 1193

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

SN - 1661-7207

IS - 4

ER -

ID: 238960277