Integrable measure equivalence and rigidity of hyperbolic lattices

2010/06/27 by Uri Bader, Bader, Uri, Alex Furman +3 · 5 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.DS #math.GR

paper · pdf · doi:10.48550/arxiv.1006.5193

50 pages; final version

openalex publication_date 2010/06/27 · arxiv created 2012/12/12 · arxiv updated 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study rigidity properties of lattices in hyperbolic n-space with n>2 and of surface groups in the context of (integrable) measure equivalence. The results for lattices in hyperbolic n-space with n>2 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 SL(2,R) allow a similar integrable measure equivalence classification.

Citations

• Classical Descriptive Set Theory
• Non-ergodic actions, cocycles and superrigidity
• Strong rigidity ofQ-rank 1 lattices

Cited by

• Quantitative polynomial cohomology and applications to \textrm L^p-measure equivalence
• Obstructions for quantitative measure equivalence between locally compact groups
• Quantitative orbit equivalence for ℤ-odometers
• Proper cocycles, measure equivalence and L_p-Fourier multipliers
• L^p measure equivalence of nilpotent groups

Related

• On the stability of hyperbolicity under quantitative measure equivalence
• Geometric properties of partially hyperbolic measures and applications to measure rigidity
• A Dual Interpretation of the Gromov--Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices
• Rigidity, lattices and invariant measures beyond homogeneous dynamics
• Boundary amenability and measure equivalence rigidity among two-dimensional Artin groups of hyperbolic type