Gromov's measure equivalence and rigidity of higher rank lattices

• Autores: Alex Furman
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 150, Nº 3, 1999, págs. 1059-1081
• Idioma: inglés
• DOI: 10.2307/121062
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• Resumen

  • 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.