Mean topological dimension for actions of discrete amenable groups

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April 2005, 13(3): 779-793. doi: 10.3934/dcds.2005.13.779

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, France, France

Received October 2004 Revised April 2005 Published May 2005

Abstract
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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 $[0,\infty]$.

Keywords: subshift of block type., Mean topological dimension, amenable group.

Mathematics Subject Classification: Primary: 37B05, 37B10; Secondary: 43A07, 20F19, 20E2.

Citation: Michel Coornaert, Fabrice Krieger. Mean topological dimension for actions of discrete amenable groups. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 779-793. doi: 10.3934/dcds.2005.13.779

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