Geodesic
Characterising quasi-isometries of the free group
Goldsborough, Antoine1 ; Zbinden, Stefanie1
1 Maxwell Institute and Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom
Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 5211-5219

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.5211
Keywords: quasi-isometry, free group, geometric group theory

Goldsborough, Antoine 1 ; Zbinden, Stefanie 1

1 Maxwell Institute and Department of Mathematics, Heriot-Watt University, Edinburgh, United Kingdom 
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Goldsborough, Antoine; Zbinden, Stefanie. Characterising quasi-isometries of the free group. Algebraic and Geometric Topology, Tome 24 (2024) no. 9, pp. 5211-5219. doi: 10.2140/agt.2024.24.5211

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