Non-abelian free groups admit non-essentially free actions on rooted trees

2007/07/06 by Miklós Abért, Miklos Abert, Abert, Miklos +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Geometric and Algebraic Topology #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.0707.0970

arxiv created 2007/07/18 · arxiv updated 2009/12/01

Abstract

We show that every countable non-abelian free group Γ admits a spherically transitive action on a rooted tree T such that the action of Γ on the boundary of T is not essentially free. This reproves a result of Bergeron and Gaboriau. The existence of such an action answers a question of Grigorchuk, Nekrashevich and Sushchanskii.

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