Let Gamma be a discrete countable group and let (Omega, mu) be an ergodic standard Borel probability Gamma-space. Given any non-elementary virtual dendromorphism (that is a measurable cocycle in the automorphism group of a dendrite), we construct a unitary representation V with no invariant vectors such that H-b(2)(Gamma; V) contains a non-zero class. As a consequence, all virtual dendromorphisms of a higher rank lattice must be elementary.
A note on the elementarity of virtual dendro-morphisms of higher rank lattices
Savini A.
2022-01-01
Abstract
Let Gamma be a discrete countable group and let (Omega, mu) be an ergodic standard Borel probability Gamma-space. Given any non-elementary virtual dendromorphism (that is a measurable cocycle in the automorphism group of a dendrite), we construct a unitary representation V with no invariant vectors such that H-b(2)(Gamma; V) contains a non-zero class. As a consequence, all virtual dendromorphisms of a higher rank lattice must be elementary.File in questo prodotto:
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