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arXiv · 1406.4488

Property (T) and the Furstenberg Entropy of Nonsingular Actions

Lewis Bowen·Yair Hartman·Omer Tamuz
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Abstract

We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure $\mu$ on a countable group $G$, A. Nevo showed that a necessary condition for $G$ to have property (T) is that the Furstenberg $\mu$-entropy values of the ergodic, properly nonsingular $G$-actions are bounded away from zero. We show that this is also a sufficient condition.

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Lewis Bowen, Yair Hartman, Omer Tamuz. 2014-06-17. Property (T) and the Furstenberg Entropy of Nonsingular Actions. https://doi.org/10.1090/proc%2F12685

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