The word and Riemannian metrics on lattices of semisimple groups

Lubotzky, Alexander ; Mozes, Shahar ; Raghunathan, M. S. (2000) The word and Riemannian metrics on lattices of semisimple groups Publications Mathématiques de L'IHÉS, 91 (1). pp. 5-53. ISSN 0073-8301

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Official URL: http://www.springerlink.com/content/m1j543827026r0...

Related URL: http://dx.doi.org/10.1007/BF02698740

Abstract

Let G be a semisimple Lie group of rank ≥ 2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with respect to some finite set of generators. Confirming a conjecture of D. Kazhdan (cf. Gromov [Gr2]) we show that these metrics are Lipschitz equivalent. It is shown that a cyclic subgroup of Γ is virtually unipotent if and only if it has exponential growth with respect to the generators of Γ.

Item Type:Article
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ID Code:39056
Deposited On:06 May 2011 11:11
Last Modified:17 May 2016 21:39

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