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Superrigidity for homomorphisms into isometry groups of $$\text{CAT}(-1)$$ spaces. (English) Zbl 0888.22008
A $$\text{CAT}(-1)$$ space is a geodesic metric space in which the comparison maps of its geodesic triangles into the usual hyperbolic plane are distance increasing. In the paper three types of rigidity results related to $$\text{CAT}(-1)$$ spaces are proved, namely the rigidity of the actions on $$\text{CAT}(-1)$$ spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles.
Reviewer: K.Riives (Tartu)

##### MSC:
 22E40 Discrete subgroups of Lie groups 22D40 Ergodic theory on groups 53A55 Differential invariants (local theory), geometric objects
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