ℓpᵖ metrics on cell complexes

Motivated by the observation that groups can be effectively studied using metric spaces modelled on , and geometry, we consider cell complexes equipped with an metric for arbitrary . Under weak conditions that can be checked locally, we establish non‐positive curvature properties of these complexes, such as Busemann‐convexity and strong bolicity. We also provide detailed information on the geodesics of these metrics in the special case of CAT(0) cube complexes.