CAT(0) cube complexes and inner amenability
| Autor: | Robin Tucker-Drob, Phillip Wesolek, Bruno Duchesne |
|---|---|
| Přispěvatelé: | Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Texas] (TAMU), Texas A&M University [College Station], Binghamton University [SUNY], State University of New York (SUNY), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-14-CE25-0004,GAMME,Groupes, Actions, Métriques, Mesures et théorie Ergodique(2014) |
| Rok vydání: | 2021 |
| Předmět: |
Normal subgroup
Group Theory (math.GR) Dynamical Systems (math.DS) Characterization (mathematics) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Combinatorics 0103 physical sciences FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Dynamical Systems 0101 mathematics Invariant (mathematics) Operator Algebras (math.OA) [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] Mathematics Lemma (mathematics) Group (mathematics) 010102 general mathematics Mathematics - Operator Algebras 20E08 20E22 20F65 43A07 Free product Wreath product Idempotence 010307 mathematical physics Geometry and Topology Mathematics - Group Theory |
| Zdroj: | Groups, Geometry, and Dynamics Groups, Geometry, and Dynamics, European Mathematical Society, 2021, ⟨10.4171/GGD/601⟩ |
| ISSN: | 1661-7207 1661-7215 |
| Popis: | International audience; We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group G on a finite dimensional irreducible CAT(0) cube complex, there is a nonempty G-invariant closed convex subset such that every conjugation invariant mean on G gives full measure to the stabilizer of each point of this subset. Specializing our result to trees leads to a complete characterization of inner amenability for HNN-extensions and amalgamated free products. One novelty of the proof is that it makes use of the existence of certain idempotent conjugation-invariant means on G. We additionally obtain a complete characterization of inner amenabil-ity for permutational wreath product groups. One of the main ingredients used for this is a general lemma which we call the location lemma, which allows us to "locate" conjugation invariant means on a group G relative to a given normal subgroup N of G. We give several further applications of the location lemma beyond the aforementioned characterization of inner amenable wreath products. |
| Databáze: | OpenAIRE |
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