Mean topological dimension for actions of discrete amenable groups

Michel Coornaert; Fabrice Krieger

doi:10.3934/dcds.2005.13.779

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2005, Volume 13, Issue 3: 779-793. Doi: 10.3934/dcds.2005.13.779

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Mean topological dimension for actions of discrete amenable groups

Michel Coornaert^1, and
Fabrice Krieger^1,

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

Received: September 30, 2004

Revised: March 31, 2005

Published: March 2005

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Abstract

Let $G$ be a countable amenable group containing subgroups of arbitrarily large finite index. Given a polyhedron $P$ and a real number $\rho$ such that $0 \leq \rho \leq$dim$(P)$, we construct a closed subshift $X \subset P^G$ having mean topological dimension $\rho$. This shows in particular that mean topological dimension of compact metrisable $G$-spaces take all values in $[0,\infty]$.

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Mathematics Subject Classification: Primary: 37B05, 37B10; Secondary: 43A07, 20F19, 20E26.

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