Suspensions of Bernoulli shifts
  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. 
Alvaro Lozano-Rojo and Olga Lukina
math.DS