1. On dense totipotent free subgroups in full groups
- Author
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Carderi, Alessandro, Gaboriau, Damien, Le Maître, François, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon), CNRS,Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 281869850 (RTG 2229), ANR-14-CE25-0004,GAMME,Groupes, Actions, Métriques, Mesures et théorie Ergodique(2014), ANR-17-CE40-0026,AGRUME,Actions de groupes et théorie des modèles(2017), ANR-19-CE40-0008,AODynG,Algèbres d'Opérateurs et Dynamique des Groupes(2019), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-19-CE40-0008,AODynG,Algèbres d'Opérateurs et Dynamique des Groupes, and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS) more...
- Subjects
IRS ,[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] ,non-free actions ,Group Theory (math.GR) ,Dynamical Systems (math.DS) ,Measurable group actions ,transitive actions of countable groups ,[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] ,37A20, 37B05, 22F50, 22F10 ,ergodic equivalence relations ,MSC: 37A20, 22F50, 22F10, 37B05 ,orbit equivalence ,FOS: Mathematics ,free groups ,Mathematics - Dynamical Systems ,Mathematics - Group Theory ,space of subgroups - Abstract
We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated points. We introduce the class of totipotent ergodic p.m.p. actions of Gamma: those for which almost every point-stabilizer has dense conjugacy class in the perfect kernel. Equivalently, the support of the associated IRS is as large as possible, namely it is equal to the whole perfect kernel. We prove that every ergodic p.m.p. equivalence relation R of cost $, Comment: 22 pages. A figure added as well as a few extra details in the proof of the main theorem. Some small typos corrected. To appear in Geometry & Topology more...
- Published
- 2021