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arXiv · 2608.11662

Whirliness beyond amenability

Yannik Höll·Friedrich Martin Schneider
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Abstract

Given a non-atomic standard probability space $(\Omega,\mu)$, we exhibit examples of non-amenable closed topological subgroups of $\mathrm{Aut}(\Omega,\mu)$ whose natural near-action on $(\Omega,\mu)$ is whirly. This answers a 2010 question by Pestov in the negative. The argument proceeds via constructing Gaussian near-actions from topologically faithful unitary representations of non-amenable whirly Polish groups.

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Yannik Höll, Friedrich Martin Schneider. 2026-08-12. Whirliness beyond amenability. https://arxiv.org/abs/2608.11662

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