Integrable measure equivalence and rigidity of hyperbolic lattices

摘要

We study rigidity properties of lattices in (H~n)? SO_(n,1)(?), n≥3, and of surface groups in Isom(H~2)? SL_2(?) in the context of integrable measure equivalence. The results for lattices in Isom(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 Isom(H~2) allow a similar integrable measure equivalence classification.