Integrable measure equivalence and rigidity of hyperbolic lattices

Details Integrable measure equivalence and rigidity of hyperbolic lattices Integrable measure equivalence and rigidity of hyperbolic lattices

2010-06-27

arxiv.org/abs/1006.5193v1

Mathematics

Group Theory

Scientific paper

We study rigidity properties of lattices in the isometry group of hyperbolic n-space for n>2 and of surface groups in the context of integrable measure equivalence. The results for hyperbolic lattices are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. For surface groups integrable measure equivalence rigidity is obtained via a cocycle version of the Milnor-Wood inequality. The integrability condition appears in certain (co)homological tools pertaining to bounded cohomology. Some of these homological tools are developed in a companion paper.

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