PreprintCC BY 4.0arXiv
Mean dimension and radius of comparison
Abstract
Consider a minimal and free topological dynamical system $(X, Γ)$, where Γ is a discrete amenable group. Assume $(X, Γ)$ has the uniform Rokhlin property (URP) and the Cuntz comparison of open sets (COS), then it is shown that rc(C(X) rtimes Γ) = 1/2 mdim(X, Γ). The same statement also holds for unital simple AH algebras with diagonal maps. The arguments in both cases are based on the recent preprint of OpenAI dealing with ℤ-actions and the topological ideas used in that paper.
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BibTeX
@misc{elliott2026mean,
title = {{Mean dimension and radius of comparison}},
author = {George A. Elliott and Zhuang Niu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11143},
eprint = {2610.11143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mean dimension and radius of comparison
AU - George A. Elliott
AU - Zhuang Niu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11143
UR - https://arxiv.org/abs/2610.11143
AB - Consider a minimal and free topological dynamical system $(X, Γ)$, where Γ is a discrete amenable group. Assume $(X, Γ)$ has the uniform Rokhlin property (URP) and the Cuntz comparison of open sets (COS), then it is shown that rc(C(X) rtimes Γ) = 1/2 mdim(X, Γ). The same statement also holds for unital simple AH algebras with diagonal maps. The arguments in both cases are based on the recent preprint of OpenAI dealing with ℤ-actions and the topological ideas used in that paper.
ER -