This article is cited in 12 papers

Kazhdan Constants of Hyperbolic Groups

D. V. Osin

Budget and Treasury Academy, Ministry of Finance of the Russian Federation

Abstract: 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.

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

UDC: 517.986+512.54

Received: 11.12.2001

DOI: 10.4213/faa218

 English version: Functional Analysis and Its Applications, 2002, 36:4, 290–297

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