Cocycle and orbit superrigidity for lattices in SL(n,R) acting on homogeneous spaces

Details Cocycle and orbit superrigidity for lattices in SL(n,R) acting on homogeneous spaces Cocycle and orbit superrigidity for lattices in SL(n,R) acting on homogeneous spaces

2008-10-20

arxiv.org/abs/0810.3630v1

In Geometry, rigidity, and group actions, Eds. B. Farb and D. Fisher. The University of Chicago Press, 2011, pp. 419-451

Mathematics

Operator Algebras

Scientific paper

We prove cocycle and orbit equivalence superrigidity for lattices in SL(n,R) acting linearly on R^n, as well as acting projectively on certain flag manifolds, including the real projective space. The proof combines operator algebraic techniques with the property (T) in the sense of Zimmer for the action of SL(n,Z) on R^n, n \geq 4. We also show that the restriction of the associated orbit equivalence relation to a subset of finite Lebesgue measure, provides a II_1 equivalence relation with property (T) and yet fundamental group equal to R_+.

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