2012/04/24 by Álvaro Lozano Rojo, Alvaro Lozano-Rojo, Lozano-Rojo, Alvaro +2
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS
paper · pdf · doi:10.48550/arxiv.1204.5376
Minor corrections. Accepted to: Dynamical Systems. An International Journal
openalex publication_date 2012/04/24 · arxiv created 2013/07/21 · arxiv updated 2013/07/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We show that for a given finitely generated group, its Bernoulli shift space can be equivariantly embedded as a subset of a space of pointed trees with Gromov-Hausdorff metric and natural partial action of a free group. Since the latter can be realised as a transverse space of a foliated space with leaves Riemannian manifolds, this embedding allows us to obtain a suspension of such Bernoulli shift. By a similar argument we show that the space of pointed trees is universal for compactly generated expansive pseudogroups of transformations.