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arXiv · 2201.03150

Relative entropy dimensions for amenable group actions

Zubiao Xiao·Zhengyu Yin
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Abstract

We study the topological complexities of relative entropy zero extensions acted by countableinfinite amenable groups. Firstly, for a given Folner sequence $\{F_n\}_{n=0}^\infty$, we define respectively the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity. Meanwhile, we investigate the relations among them. Secondly, we introduce the notion of a relative dimension set. Moreover, using it, we discuss the disjointness between the relative entropy zero extensions which generalizes the results of Dou, Huang and Park[Trans. Amer. Math. Soc. 363(2) (2011), 659-680].

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Zubiao Xiao, Zhengyu Yin. 2022-01-10. Relative entropy dimensions for amenable group actions. https://arxiv.org/abs/2201.03150

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