# Directional asymptotic cones of groups equipped with bi-invariant metrics

Source: [Directional asymptotic cones of groups equipped with bi-invariant metrics](<https://www.sota2.com/research/paper/68fa5ab51e209131ce9c2274>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-29T05:00:01.231Z

Authors: Jarek K\\k{e}dra, Assaf Libman

Published: 2022-07-26T07:47:51.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2207.12704>)

[PDF](<https://arxiv.org/pdf/2207.12704.pdf>)