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arXiv · 2506.19043

Cocycle superrigidity for median spaces of finite rank

Biao Ma·Lamine Messaci
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Abstract

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank, the superrigidity of Isom(X)-valued cocycles for a product of locally compact second countable groups. In the case of actions by irreducible lattices in such product groups, this approach yields a novel proof of the superrigidity of homomorphisms.

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Biao Ma, Lamine Messaci. 2025-06-23. Cocycle superrigidity for median spaces of finite rank. https://arxiv.org/abs/2506.19043

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