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arXiv · 1708.02468

On universal minimal proximal flows of topological groups

Xiongping Dai·Eli Glasner
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Abstract

In this paper, we show that the action of a characteristically simple, non-extremely amenable (non-strongly amenable, non-amenable) group on its universal minimal (minimal proximal, minimal strongly proximal) flow is effective. We present necessary and sufficient conditions, for the action of a topological group with trivial center on its universal minimal proximal flow, to be effective. A theorem of Furstenberg about the isomorphism of the universal minimal proximal flows of a discrete group and its subgroups of finite index ([Theorem~II.4.4]) is strengthened. Finally, for a pair of groups $H < G$ the same method is applied in order to extend the action of $H$ on its universal minimal proximal flow to an action of its commensurator group $\mathrm{Comm}_G(H)$.

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Xiongping Dai, Eli Glasner. 2017-08-08. On universal minimal proximal flows of topological groups. https://arxiv.org/abs/1708.02468

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