1999/11/01 by Alex Furman · 5 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Advanced Topics in Algebra #Mathematics #Equivalence (formal languages) #Rigidity (electromagnetism) #Rank (graph theory) #Measure (data warehouse) #Pure mathematics #Combinatorics #Data mining
paper · doi:10.2307/121062
openalex publication_date 1999/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/16
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.