Characterising quasi-isometries of the free group

Fuente: arXiv
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Main Authors: Goldsborough, Antoine, Zbinden, Stefanie
Format: Preprint
Published: 2023
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author Goldsborough, Antoine
Zbinden, Stefanie
author_facet Goldsborough, Antoine
Zbinden, Stefanie
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2307_13667
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Characterising quasi-isometries of the free group
Goldsborough, Antoine
Zbinden, Stefanie
Group Theory
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.
title Characterising quasi-isometries of the free group
topic Group Theory
url https://arxiv.org/abs/2307.13667