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.
| Original language | English |
|---|---|
| Pages (from-to) | 5211-5219 |
| Number of pages | 9 |
| Journal | Algebraic and Geometric Topology |
| Volume | 24 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 27 Dec 2024 |
Keywords
- free group
- geometric group theory
- quasi-isometry
ASJC Scopus subject areas
- Geometry and Topology