Characterising quasi-isometries of the free group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910767188541440 |
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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 |