Kazhdan Constants of Hyperbolic Groups

D. V. Osin

Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 46-54.

Résumé

Let $H$ be an infinite hyperbolic group with Kazhdan property $(T)$ and let $\varkappa(H,X)$ denote the Kazhdan constant of $H$ with respect to a generating set $X$. We prove that $\inf_{X}\varkappa(H,X)=0$, where the infimum is taken over all finite generating sets of $H$. In particular, this gives an answer to a Lubotzky question.

Détail

Keywords: Kazhdan property (T), hyperbolic group, left regular representation
Mots-clés : amenable group.

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