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arXiv · 2307.13667

Characterising quasi-isometries of the free group

Antoine Goldsborough·Stefanie Zbinden
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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.

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Antoine Goldsborough, Stefanie Zbinden. 2023-07-25. Characterising quasi-isometries of the free group. https://doi.org/10.2140/agt.2024.24.5211

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