On uniqueness of coarse median structures

2025/02/19 by Elia Fioravanti, Alessandro Sisto, Fioravanti, Elia +1
Computer Science · Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2502.13865

openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any product of bushy hyperbolic spaces has a unique coarse median structure, and that having a unique coarse median structure is a property closed under relative hyperbolicity. As a consequence, in contrast with the case of mapping class groups, there are non-hyperbolic pants graphs that have unique coarse median structures.

Related

• Short hierarchically hyperbolic groups I: uncountably many coarse median structures
• Median geometry for spaces with measured walls and for groups
• A four point characterisation for coarse median spaces
• Coarse median algebras: The intrinsic geometry of coarse median spaces and their intervals
• Coarse cubical rigidity