Let Γ be a discrete countable group and let (Ω, μ) be an ergodic standard Borel probability Γ-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 with no invariant vectors such that H2b(Γ; V ) contains a non-zero class. As a consequence, all virtual dendro-morphisms of a higher rank lattice must be elementary.
Savini, A. (2022). A NOTE ON ELEMENTARITY OF VIRTUAL DENDRO-MORPHISMS FOR HIGHER RANK LATTICES. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150(11), 4995-5008 [10.1090/proc/16024].
A NOTE ON ELEMENTARITY OF VIRTUAL DENDRO-MORPHISMS FOR HIGHER RANK LATTICES
Savini A.
2022
Abstract
Let Γ be a discrete countable group and let (Ω, μ) be an ergodic standard Borel probability Γ-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 with no invariant vectors such that H2b(Γ; 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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