[Papers] [Alex Furman]

Integrable measure equivalence and rigidity of hyperbolic lattices

We study rigidity properties of lattices in Isom(Hn)=PO(n,1), n>2, and of surface groups in Isom(H2)=PGL(2,R) in the context of integrable Measure Equivalence. The results for lattices in Isom(Hn), n>2, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable Measure Equivalence classification. For surface groups an integrable ME rigidity is obtained via a cocycle version of Milnor-Wood inequality. The integrability condition appears in a certain (co)homological tools pertaining to L1-homology and bounded cohomology of measure equivalent groups. Some of these homological tools are developed in a companion paper Efficient subdivision in hyperbolic groups and applications.


Authors: U. Bader, A. Furman, R. Sauer
Bibliographical: Invent. Math. 194 (2013), no. 2, 313 – 379. (DOI) 10.1007/s00222-012-0445-9
Download: pdf | published-pdf | arxiv:1006.5193



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[Papers] [Alex Furman]