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

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

4 Scopus citations

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	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
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc/12685

Cite this

@article{7b33a46780fb49c2a759ce7d0e202dad,

title = "Property (T) and the furstenberg entropy of nonsingular actions",

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.",

author = "Lewis Bowen and Yair Hartman and Omer Tamuz",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2016",

month = jan,

day = "1",

doi = "10.1090/proc/12685",

language = "English",

volume = "144",

pages = "31--39",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Property (T) and the furstenberg entropy of nonsingular actions

AU - Bowen, Lewis

AU - Hartman, Yair

AU - Tamuz, Omer

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84945260278&partnerID=8YFLogxK

U2 - 10.1090/proc/12685

DO - 10.1090/proc/12685

M3 - Article

AN - SCOPUS:84945260278

SN - 0002-9939

VL - 144

SP - 31

EP - 39

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

Property (T) and the furstenberg entropy of nonsingular actions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this