Suspensions of Bernoulli shifts

Details Suspensions of Bernoulli shifts Suspensions of Bernoulli shifts

2012-04-24

arxiv.org/abs/1204.5376v1

Mathematics

Dynamical Systems

15 pages

Scientific paper

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.

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