Kazhdan groups have cost 1
Group Theory
2020-04-10 v2 Dynamical Systems
Probability
Abstract
We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.
Cite
@article{arxiv.1810.11015,
title = {Kazhdan groups have cost 1},
author = {Tom Hutchcroft and Gábor Pete},
journal= {arXiv preprint arXiv:1810.11015},
year = {2020}
}
Comments
16 pages, 2 figures. V2: Minor revisions. Added additional remarks and simulations. Accepted version, to appear in Invent. Math