Integrable measure equivalence and rigidity of hyperbolic lattices

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.

50 pages; final version

References in corpus (2)

• The mapping class group from the viewpoint of measure equivalence theory
• Non-ergodic actions, cocycles and superrigidity

Cited by in corpus (1)

• Invariants of orbit equivalence relations and Baumslag-Solitar groups