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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.20564 |
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| _version_ | 1866914615327195136 |
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| author | Hyde, James Skipper, Rachel Zaremsky, Matthew C. B. |
| author_facet | Hyde, James Skipper, Rachel Zaremsky, Matthew C. B. |
| contents | We prove a variety of results about subgroups of Thompson's group $V$. First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor space is quasi-isometric to a tree. Then we prove that for a broad class of groups of homeomorphisms of the real line, for example Thompson's group $F$, any action on the Cantor space via an embedding into Thompson's group $V$ must be semiconjugate to the standard action on the line. Finally, we use this to establish that many such groups cannot embed into $V$; in particular the Stein group $F_{2,3}$ cannot embed in $V$, answering a question of the third author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20564 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Action graphs, semiconjugacy, and non-embedding in Thompson's group $V$ Hyde, James Skipper, Rachel Zaremsky, Matthew C. B. Group Theory We prove a variety of results about subgroups of Thompson's group $V$. First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor space is quasi-isometric to a tree. Then we prove that for a broad class of groups of homeomorphisms of the real line, for example Thompson's group $F$, any action on the Cantor space via an embedding into Thompson's group $V$ must be semiconjugate to the standard action on the line. Finally, we use this to establish that many such groups cannot embed into $V$; in particular the Stein group $F_{2,3}$ cannot embed in $V$, answering a question of the third author. |
| title | Action graphs, semiconjugacy, and non-embedding in Thompson's group $V$ |
| topic | Group Theory |
| url | https://arxiv.org/abs/2605.20564 |