Work

Median geometry for spaces with measured walls and for groups

Year: 2025

Type: article

Abstract: We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with median geometry. The result follows from an analysis of a quasification of median geometry that provides a geometric characterization of spaces at a finite Hausdorff distance from a median space. The case of complex hyperbolic metric spaces is different; we show that these spaces cannot be at finite Hausdorff distance from a median space.

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03289-1

Authors: Indira Chatterji, Cornelia Druţu

Institutions: Laboratoire Jean-Alexandre Dieudonné, University of Oxford

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Agence Nationale de la Recherche, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences