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Abstract
Let Γ \Gamma be a discrete countable group and let ( Ω , μ ) (\Omega ,\mu ) be an ergodic standard Borel probability Γ \Gamma -space. Given any non-elementary virtual dendro-morphism (that is a measurable cocycle in the automorphism group of a dendrite), we construct a unitary representation V V with no invariant vectors such that H b 2 ( Γ ; V ) \operatorname {H}^2_b(\Gamma ;V) contains a non-zero class. As a consequence, all virtual dendro-morphisms of a higher rank lattice must be elementary.
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