Gromov's measure equivalence and rigidity of higher rank lattices
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- October 1999
- DOI:
- 10.48550/arXiv.math/9911262
- arXiv:
- arXiv:math/9911262
- Bibcode:
- 1999math.....11262F
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Differential Geometry
- E-Print:
- 23 pages, published version