Directional asymptotic cones of groups equipped with bi-invariant metrics

Topology and its Applications 2026 Open access

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Authors: Jarek Kędra, Assaf Libman
DOI: 10.1016/j.topol.2026.109924
Cited by: 0
References: 12

Abstract

Given a bi-invariant metric on a group, we construct a version of an asymptotic cone without using ultrafilters. The new construction, called the directional asymptotic cone, is a contractible topological group equipped with a complete bi-invariant metric and admits a canonical Lipschitz homomorphism to the standard asymptotic cone. Moreover, the directional asymptotic cone of a countable group is separable.

Fields of Study & Subjects

Advanced Operator Algebra Research Geometric and Algebraic Topology Mathematical Dynamics and Fractals

Publication details

Journal / source
Topology and its Applications
Publisher
Elsevier BV
Volume
392
Pages
109924–109924
Publication date
29 July 2026
Language
EN