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arXiv · 2410.01447

On inner-amenability and boundary actions

Jacopo Bassi
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Abstract

Let $\Gamma$ be a discrete countable group. One result in this work is that if $\Gamma$ is ICC inner-amenable non-amenable then it cannot satisfy the (AO)-property, answering a question posed by C. Anantharaman-Delaroche. A generalization of this phenomenon is also considered. It is also proved that if $\Gamma$ is a "sufficiently large" discrete subgroup of a product of locally compact second countable bi-exact groups, then it cannot be inner-amenable. Both these results generalize the well-known fact that ICC non-amenable inner-amenable discrete countable groups cannot be bi-exact.

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Jacopo Bassi. 2024-10-02. On inner-amenability and boundary actions. https://arxiv.org/abs/2410.01447

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