No quasi-isometric rigidity for proper actions on CAT(0) cube complexes

Francesco Fournier-Facio , Anthony Genevois (1)

1 I2M - Institut de Mathématiques de Marseille

We exhibit a variety of groups that act properly and even cocompactly on median graphs (a.k.a. one-skeleta of CAT(0) cube complexes), with quasi-isometric groups that do not admit any proper action on a median graph. This answers a question of Niblo, Sageev and Wise. Our examples are all quasi-isometrically trivial central extensions of certain cubulated groups.

Domaines: Mathématiques [math]

Francesco Fournier-Facio, Anthony Genevois. No quasi-isometric rigidity for proper actions on CAT(0) cube complexes. 2022. ⟨hal-03899025⟩