Groups, Geometry, and Dynamics

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Volume 9, Issue 3, 2015, pp. 891–916
DOI: 10.4171/GGD/331

Invariant random subgroups of the free group

Lewis Bowen[1]

(1) The University of Texas at Austin, USA

Let $G$ be a locally compact group. A random closed subgroup with conjugation-invariant law is called an invariant random subgroup or IRS for short. We show that each nonabelian free group has a large “zoo” of IRS’s. This contrasts with results of Stuck and Zimmer which show that there are no non-obvious IRS’s of higher rank semisimple Lie groups with property (T).

Keywords: Invariant random subgroups, ergodic equivalence relations

Bowen Lewis: Invariant random subgroups of the free group. Groups Geom. Dyn. 9 (2015), 891-916. doi: 10.4171/GGD/331