Extensive amenability and an application to interval exchanges
Résumé
Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, we establish the amenability of all subgroups of the group IET of interval exchange transformations that have angular components of rational rank~${\leq 2}$. In addition, we obtain a reformulation of extensive amenability in terms of inverted orbits and use it to present a purely probabilistic proof that recurrent actions are extensively amenable. Finally, we study the triviality of the Poisson boundary for random walks on IET and show that there are subgroups $G
Domaines
Théorie des groupes [math.GR]mikael de la salle : Connectez-vous pour contacter le contributeur
https://hal.science/hal-01219528
Soumis le : jeudi 22 octobre 2015-20:09:52
Dernière modification le : mardi 30 avril 2024-15:58:17
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Identifiants
- HAL Id : hal-01219528 , version 1
- ARXIV : 1503.04977
- DOI : 10.1017/etds.2016.32
Citer
Kate Juschenko, Nicolás Matte Bon, Nicolas Monod, Mikael de La Salle. Extensive amenability and an application to interval exchanges. Ergodic Theory and Dynamical Systems, 2016, pp.1 - 25. ⟨10.1017/etds.2016.32⟩. ⟨hal-01219528⟩
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