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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)

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