Characterising quasi-isometries of the free group
Group Theory
2025-01-01 v2
Abstract
We introduce the notion of mixed subtree quasi-isometries, which are self quasi-isometries of regular trees built in a specific inductive way. We then show that any self quasi-isometry of a regular tree is at bounded distance from a mixed-subtree quasi-isometry. Since the free group is quasi-isometric to a regular tree, this provides a way to describe all self quasi-isometries of the free group. In doing this, we also give a way of constructing quasi-isometries of the free group.
Cite
@article{arxiv.2307.13667,
title = {Characterising quasi-isometries of the free group},
author = {Antoine Goldsborough and Stefanie Zbinden},
journal= {arXiv preprint arXiv:2307.13667},
year = {2025}
}
Comments
Modified the proof structure in Section 3 for better readability. Accepted in Algebraic & Geometric Topology