Published September 2020 | Published + Accepted Version
Journal Article Open
Kazhdan groups have cost 1
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.
Additional Information© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Received: 26 October 2018 / Accepted: 16 February 2020 / Published online: 2 April 2020. Open access funding provided by Alfréd Rényi Institute of Mathematics. We are grateful to Miklós Abért for many helpful discussions, to MFO, Oberwolfach, where this work was conceived, and to Damien Gaboriau and Russ Lyons for comments on the manuscript. We also thank the anonymous referees for their thorough reading and helpful comments. The work of GP was supported by the ERC Consolidator Grant 772466 "NOISE", and by the Hungarian National Research, Development and Innovation Office, NKFIH Grant K109684.
Accepted Version - 1810.11015.pdf