Integrable measure equivalence and rigidity of hyperbolic lattices
By U. Bader, A. Furman, Roman Sauer. 2010
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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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5b867c0c929677784700b86868031d44bda1333d
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Citations in the corpus
- A Dual Interpretation of the Gromov–Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices (2012, methodology): “Furman and Sauer proved a generalization of Mostow Rigidity for cocycles in the case of real hyperbolic lattices with some integrability condition, using, among others, bounded cohomology techniques, [1]. Mostow Rigidity and Volume Rigidity for Hyperbolic Lattices 3 The aim of this paper is to give ”