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Mean topological dimension for actions of discrete amenable groups

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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 $[0,\infty]$.
    Mathematics Subject Classification: Primary: 37B05, 37B10; Secondary: 43A07, 20F19, 20E26.


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