The Rokhlin dimension of topological ℤm‐actions
By G'abor Szab'o. 2013
74 citations recorded by the source corpus.
We study the topological variant of Rokhlin dimension for topological dynamical systems (X,α,Zm) in the case, where X is assumed to have finite covering dimension. Finite Rokhlin dimension in this sense is a property that implies finite Rokhlin dimension of the induced action on C* ‐algebraic level, as was discussed in a recent paper by Hirshberg, Winter and Zacharias. In particular, it implies under these conditions that the transformation group C* ‐algebra has finite nuclear dimension. Generalizing partial results of Lindenstrauss and Gutman, we show that free Zm ‐actions on finite‐dimensional spaces satisfy a strengthened version of the so‐called marker property, which yields finite Rokhlin dimension for such actions.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2ff843a3313313c6f1a0609c385e899ae4e5d974
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In Atomic and Molecular Physics, and Optics
In Mathematical Physics
Citations in the corpus
- Almost Finiteness and the Small Boundary Property (2018, background): “8 of [41].”
- Nuclear dimension and $$\mathcal Z$$Z-stability (2014, unknown): “This leads to classification by K -theory ([44]; see [36,50] for the case of Zd actions).”
- Nuclear dimension and Z-stability of non-simple C*-algebras (2013, background): “Crossed products of the Cantor set by a free Zn action also satisfy (A1) and (A2)(a), and have been shown by Szabó to have finite nuclear dimension [33].”
- Dimension, comparison, and almost finiteness (2017, background): “and that we can also relax the hypothesis dim(X) ≤ d by merely requiring that the action have the topological small boundary property with respect to d ([42], Definition 3.”