Relatively geometric actions of Kähler groups on CAT(0) cube complexes

Corey Bregman, Daniel Groves, Kejia Zhu

We prove that for $n\ge 2$, a non-uniform lattice in $\text{PU}(n,1)$ does not admit a relatively geometric action on a $\mathrm{CAT}(0)$ cube complex, in the sense of Einstein an…