$\mathrm{CAT}(0)$ cube complexes are determined by their boundary cross ratio

Jonas Beyrer, Elia Fioravanti, Merlin Incerti-Medici

We introduce a $\mathbb{Z}$-valued cross ratio on Roller boundaries of $\mathrm{CAT}(0)$ cube complexes. We motivate its relevance by showing that every cross-ratio preserving bijecti…