English

Property (T) and the Furstenberg Entropy of Nonsingular Actions

Group Theory 2016-03-15 v2 Dynamical Systems

Abstract

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

Keywords

Cite

@article{arxiv.1406.4488,
  title  = {Property (T) and the Furstenberg Entropy of Nonsingular Actions},
  author = {Lewis Bowen and Yair Hartman and Omer Tamuz},
  journal= {arXiv preprint arXiv:1406.4488},
  year   = {2016}
}

Comments

10 pages