
TL;DR
This paper proves that all countably infinite groups with Kazhdan's property (T) have cost 1, resolving a significant open question in the field of geometric group theory.
Contribution
It establishes that Kazhdan groups have cost 1, advancing understanding of their measure-theoretic properties and answering a longstanding question.
Findings
Kazhdan groups have cost 1
Addresses a key open question in group theory
Progress towards fixed price 1 remains open
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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