A note on elementarity of virtual dendro-morphisms for higher rank lattices

Savini, A.

doi:10.1090/proc/16024

A note on elementarity of virtual dendro-morphisms for higher rank lattices
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by A. Savini

Proc. Amer. Math. Soc. 150 (2022), 4995-5008

DOI: https://doi.org/10.1090/proc/16024

Published electronically: July 15, 2022

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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 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 $\operatorname {H}^2_b(\Gamma ;V)$ contains a non-zero class. As a consequence, all virtual dendro-morphisms of a higher rank lattice must be elementary.

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