Relative cubulations and groups with a 2-sphere boundary (with E. Einstein). Preprint (2019). .pdf

Abstract We introduce a new kind of action of a relatively hyperbolic group on a CAT$(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of action on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.