A generalization of topological Rokhlin dimension and an embedding result

2023/11/09 by Wei, Sihan, He, Zhuofeng
#37B05 #46L05 #46L35 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2311.05721

Abstract

We generalize Gabor's notion of topological Rokhlin dimension of ℤ^k-actions on compact metric space to a class of general discrete countable amenable group actions which involves the approximate subgroup structure. Then with this generalization, we conclude the finiteness of topological Rokhlin dimension, amenability dimension, dynamic asymptotic dimension and also of the nuclear dimension of the crossed product. An embedding result is also obtained, regarding those systems with mean dimension less that m/2 and with a finite-dimensional free factor.

Related

• Rokhlin dimension and C*-dynamics
• Mean topological dimension of induced amenable group actions
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• Comparison radius and mean topological dimension: Rokhlin property, comparison of open sets, and subhomogeneous C*-algebras
• Long thin covers and nuclear dimension