Directional asymptotic cones of groups equipped with bi-invariant metrics
Group Theory
2023-08-07 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2207.12704,
title = {Directional asymptotic cones of groups equipped with bi-invariant metrics},
author = {Jarek Kędra and Assaf Libman},
journal= {arXiv preprint arXiv:2207.12704},
year = {2023}
}
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68 pages