Suspensions of Bernoulli shifts

Abstract

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 realized 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.

Keywords:

• Bernoulli shift
• pseudogroup of transformations
• Gromov–Hausdorff space
• expansive dynamics