ℓ^p metrics on cell complexes

2023/02/07 by Thomas Haettel, Haettel, Thomas, Nima Hoda +3
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2302.03801

Abstract

Motivated by the observation that groups can be effectively studied using metric spaces modelled on ℓ¹, ℓ², and ℓ^∞ geometry, we consider cell complexes equipped with an ℓ^p metric for arbitrary p. Under weak conditions that can be checked locally, we establish nonpositive 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.

Related

• A link condition for simplicial complexes, and CUB spaces
• Injective Metrics on Cube Complexes
• Constructing metric spaces from systems of walls
• Triangles, squares and geodesics
• Injective metrizability and the duality theory of cubings