Whirliness beyond amenability
Yannik Höll, Friedrich Martin Schneider
Abstract
Given a non-atomic standard probability space (Ω,μ), we exhibit examples of non-amenable closed topological subgroups of Aut(Ω,μ) whose natural near-action on (Ω,μ) 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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