Integrable measure equivalence and rigidity of hyperbolic lattices

  title={Integrable measure equivalence and rigidity of hyperbolic lattices},
  author={Uri Bader and Alex Furman and Roman Sauer},
  journal={Inventiones mathematicae},
We study rigidity properties of lattices in $\operatorname {Isom}(\mathbf {H}^{n})\simeq \mathrm {SO}_{n,1}({\mathbb{R}})$, n≥3, and of surface groups in $\operatorname {Isom}(\mathbf {H}^{2})\simeq \mathrm {SL}_{2}({\mathbb{R}})$ in the context of integrable measure equivalence. The results for lattices in $\operatorname {Isom}(\mathbf {H}^{n})$, n≥3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification… 

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