Kazhdan groups have cost 1

2018/10/25 by Hutchcroft, Tom, Pete, Gábor · 4 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.11015

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.

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• Vanishing uniqueness thresholds in Voronoi percolation on products
• Higher property T and below-rank phenomena of lattices
• Products of Infinite Countable Groups Have Fixed Price One

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