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Bibliographic Details
Main Authors: Abert, Miklos, Elek, Gabor
Format: Preprint
Published: 2011
Subjects:
Online Access:https://arxiv.org/abs/1108.2147
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author Abert, Miklos
Elek, Gabor
author_facet Abert, Miklos
Elek, Gabor
contents We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve this by employing symbolic dynamics and an ultraproduct construction which also facilitates the extension of our results to unitary representations. As a byproduct, we show that the weak equivalence class of every free non-amenable action contains an action that satisfies the measurable von Neumann problem.
format Preprint
id arxiv_https___arxiv_org_abs_1108_2147
institution arXiv
publishDate 2011
record_format arxiv
spellingShingle The Space of Actions, Partition Metric and Combinatorial Rigidity
Abert, Miklos
Elek, Gabor
Functional Analysis
Group Theory
37A15
We introduce a natural pseudometric on the space of actions of d-generated groups. In this pseudometric, the zero classes correspond to the weak equivalence classes defined by Kechris, and the metric identification is compact. We achieve this by employing symbolic dynamics and an ultraproduct construction which also facilitates the extension of our results to unitary representations. As a byproduct, we show that the weak equivalence class of every free non-amenable action contains an action that satisfies the measurable von Neumann problem.
title The Space of Actions, Partition Metric and Combinatorial Rigidity
topic Functional Analysis
Group Theory
37A15
url https://arxiv.org/abs/1108.2147