Inventiones mathematicae

, Volume 194, Issue 2, pp 313–379 | Cite as

Integrable measure equivalence and rigidity of hyperbolic lattices

Article

Abstract

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. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in \(\operatorname {Isom}(\mathbf {H}^{2})\) allow a similar integrable measure equivalence classification.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Department of MathematicsUniversity of ChicagoChicagoUSA
  4. 4.Department of Mathematics, Institute for Algebra and GeometryKarlsruhe Institute of TechnologyKarlsruheGermany

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