Property (T) and the Furstenberg entropy of nonsingular actions
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- by Lewis Bowen, Yair Hartman and Omer Tamuz PDF
- Proc. Amer. Math. Soc. 144 (2016), 31-39 Request permission
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.References
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Additional Information
- Lewis Bowen
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
- MR Author ID: 671629
- Yair Hartman
- Affiliation: Department of Mathematics, Weizmann Institute of Science, 761001 Rehovot, Israel
- MR Author ID: 1001252
- Omer Tamuz
- Affiliation: Microsoft Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 898902
- Received by editor(s): June 30, 2014
- Received by editor(s) in revised form: December 1, 2014
- Published electronically: July 24, 2015
- Additional Notes: The first author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274.
The second author was supported by the European Research Council, grant 239885 - Communicated by: Nimish Shah
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 31-39
- MSC (2010): Primary 20F69, 37A40
- DOI: https://doi.org/10.1090/proc/12685
- MathSciNet review: 3415574