Invariant random subgroups of the free group

By Lewis Bowen. 2012

59 citations recorded by the source corpus.

Let $G$ be a locally compact group. A random closed subgroup with conjugation-invariant law is called an {\em 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-Zimmer which show that there are no non-obvious IRS's of higher rank semisimple Lie groups with property (T).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6903c7cd90d667f8b6a2d998c7d239e4221d6b77

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In Geometry and Topology

1. D. Creutz
2. J. Peterson
3. Adrian Ioana
4. S. Vaes
5. Sorin Popa
6. Cyril Houdayer
7. I. Chifan
8. Thomas Sinclair

In Mathematical Physics

1. D. Creutz
2. J. Peterson
3. Adrian Ioana
4. S. Vaes
5. Sorin Popa
6. Thomas Sinclair
7. Cyril Houdayer
8. I. Chifan

Citations in the corpus

• On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, unknown): “We refer the reader to [6], [29], [112], [61], [62] for other recent works that make use of this notion.”
• Stabilizers of Ergodic Actions of Lattices and Commensurators (2013, background): “ck [AS93] Section 4). Bergeron and Gaboriau [BG04] observed that invariant random subgroups behave similarly to normal subgroups and this topic has attracted much recent attention: [ABB+11], [AGV14], [Bow12], [GS12], [Gri11], [Ver11], [Ver12]. Our work, like that of Stuck and Zimmer, rules out the e”