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Annals of Mathematics, II. Series, Vol. 150, No. 3, pp. 1059-1081, 1999
EMIS ELibM Electronic Journals Annals of Mathematics, II. Series
Vol. 150, No. 3, pp. 1059-1081 (1999)

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Gromov's measure equivalence and rigidity of higher rank lattices

Alex Furman

Review from Zentralblatt MATH:

Author's abstract: ``In this paper the notion of measure equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are measure equivalent; this is one of the motivations for this notion. The main result of this paper is ME rigidity of higher rank lattices: any countable group which is ME to a lattice in a simple Lie group $G$ of higher rank is commensurable to a lattice in $G$''.

Reviewed by S.K.Kaul

Keywords: quasi-isometry; measure equivalence; countable groups; lattices; locally compact group; rigidity

Classification (MSC2000): 22E40 37A05

Full text of the article:

Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.

© 2001 Johns Hopkins University Press
© 2001--2002 ELibM for the EMIS Electronic Edition
Metadata extracted from Zentralblatt MATH with kind permission