Gromov’s measure equivalence and rigidity of higher rank lattices

@article{Furman1999GromovsME,
  title={Gromov’s measure equivalence and rigidity of higher rank lattices},
  author={A. Furman},
  journal={Annals of Mathematics},
  year={1999},
  volume={150},
  pages={1059-1081}
}
  • A. Furman
  • Published 1999
  • Mathematics
  • Annals of Mathematics
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. 
Rigidity in measure-theoretic group theory for amalgamated free products
Rigidity of amalgamated free products in measure equivalence theory
Measure equivalence rigidity of the mapping class group
Examples of groups that are measure equivalent to the free group
  • D. Gaboriau
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • 2005
Measure equivalence rigidity and bi-exactness of groups
...
1
2
3
4
5
...