Property (T) and the furstenberg entropy of nonsingular actions

Lewis Bowen; Yair Hartman; Omer Tamuz

doi:10.1090/proc/12685

Property (T) and the furstenberg entropy of nonsingular actions

Lewis Bowen, Yair Hartman, Omer Tamuz

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	American English
Pages (from-to)	31-39
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	1
DOIs	https://doi.org/10.1090/proc/12685
State	Published - 1 Jan 2016

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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Property (T) and the furstenberg entropy of nonsingular actions

Abstract

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