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On Property (T) for Discrete Groups

In: Rigidity in Dynamics and Geometry

Author

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  • Andrzej Żuk

    (CNRS, Ecole Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées)

Abstract

We present a simple sufficient condition which enables one to prove property (T) for a discrete group from its presentation and to compute the Kazhdan constants. This condition applies to some lattices for which property (T) was known and gives a new elementary proof. Using this condition one can construct new examples of Kazhdan groups and finally prove that random groups in the sense of Gromov are infinite, hyperbolic and have property (T).

Suggested Citation

  • Andrzej Żuk, 2002. "On Property (T) for Discrete Groups," Springer Books, in: Marc Burger & Alessandra Iozzi (ed.), Rigidity in Dynamics and Geometry, pages 473-482, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04743-9_26
    DOI: 10.1007/978-3-662-04743-9_26
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