Faithful invariant random subgroups in acylindrically hyperbolic groups

Yair Glasner; Anton Hase

doi:10.1112/blms.12817

Faithful invariant random subgroups in acylindrically hyperbolic groups

Yair Glasner, Anton Hase

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group (Formula presented.) admits a weakly mixing probability measure preserving action (Formula presented.) which is faithful but not essentially free. In other words, (Formula presented.) admits a weakly mixing nontrivial faithful IRS. We also prove that every nonelementary hyperbolic group admits a characteristic random subgroup with the same properties.

Original language	American English
Pages (from-to)	1760-1772
Number of pages	13
Journal	Bulletin of the London Mathematical Society
Volume	55
Issue number	4
DOIs	https://doi.org/10.1112/blms.12817
State	Published - 1 Aug 2023

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/blms.12817

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title = "Faithful invariant random subgroups in acylindrically hyperbolic groups",

abstract = "Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group (Formula presented.) admits a weakly mixing probability measure preserving action (Formula presented.) which is faithful but not essentially free. In other words, (Formula presented.) admits a weakly mixing nontrivial faithful IRS. We also prove that every nonelementary hyperbolic group admits a characteristic random subgroup with the same properties.",

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AB - Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group (Formula presented.) admits a weakly mixing probability measure preserving action (Formula presented.) which is faithful but not essentially free. In other words, (Formula presented.) admits a weakly mixing nontrivial faithful IRS. We also prove that every nonelementary hyperbolic group admits a characteristic random subgroup with the same properties.

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Faithful invariant random subgroups in acylindrically hyperbolic groups

Abstract

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