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Groupes Moyennables, Dimension Topologique Moyenne et sous-décalages

Amenable Groups, mean Topological Dimension and Subshifts

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Abstract

Let G be an infinite countable residually finite amenable group. In this paper we construct a continuous action of G on a compact metrisable space X such that the dynamical system (X, G) cannot be embedded in the G-shift on [0,1]G. This result generalizes a construction due to E. Lindenstrauss and B. Weiss (Mean topological dimension, Israel J. Math. 115 (2000), 1–24) for \(G = \mathbb{Z}\).

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  1. Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Fabrice Krieger

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  1. Fabrice Krieger
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Correspondence to Fabrice Krieger.

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Krieger, F. Groupes Moyennables, Dimension Topologique Moyenne et sous-décalages. Geom Dedicata 122, 15–31 (2006). https://doi.org/10.1007/s10711-006-9071-2

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  • DOI: https://doi.org/10.1007/s10711-006-9071-2

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