Spaces that can be ordered effectively: virtually free groups and hyperbolicity
Combinatorics
2023-05-22 v6 Group Theory
Metric Geometry
Abstract
We study asymptotic invariants of metric spaces, defined in terms of the travelling salesman problem, and our goal is to classify groups and spaces depending on how well they can be ordered in this context. We characterize virtually free groups as those admitting an order which has some efficiency on -point subsets. We show that all -hyperbolic spaces can be ordered extremely efficiently, for the question when the number of points of a subset tends to .
Cite
@article{arxiv.2011.01732,
title = {Spaces that can be ordered effectively: virtually free groups and hyperbolicity},
author = {Anna Erschler and Ivan Mitrofanov},
journal= {arXiv preprint arXiv:2011.01732},
year = {2023}
}
Comments
33 pages. This is the first part of the paper, which appeared on arxiv in previous versions. The paper is split in two parts, and the second one appears now as "Assouad-Nagata dimension and gap for ordered metric spaces"