Kazhdan groups have cost 1

Authors :: Tom Hutchcroft
Gábor Pete
Apollo - University of Cambridge Repository
Hutchcroft, Thomas [0000-0003-0061-593X]
Source :: Inventiones mathematicae
Publication Year :: 2021
Publisher :: Apollo - University of Cambridge Repository, 2021.
Abstract: Funder: Alfréd Rényi Institute of Mathematics<br />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.