Original Article

Geometric & Functional Analysis GAFA

, Volume 13, Issue 3, pp 643-670

First online:

Property (T) and Kazhdan constants for discrete groups

  • Andrzej ŻukAffiliated withUnité de Mathématiques Pures et Appliquées, CNRS, Ecole Normale Supérieure de Lyon Email author 

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Let Γ be a group generated by a finite set S. We give a sufficient condition for Γ to have Kazhdan's property (T). This condition is easy to check and gives Kazhdan constants. We give examples of groups to which this method applies. We prove that in some setting generic presentations define groups which satisfy this condition and thus have property (T). Moreover we prove that small changes in the presentation of a group satisfying this condition do not change the fact that the group has property (T).


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