Dynamical Tits alternative for groups of almost automorphisms of trees
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908445211361280 |
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| author | Vio, Martín Gilabert |
| author_facet | Vio, Martín Gilabert |
| contents | We prove a dynamical variant of the Tits alternative for the group of almost automorphisms of a locally finite tree $\mathcal{T}$: a group of almost automorphisms of $\mathcal{T}$ either contains a nonabelian free group playing ping-pong on the boundary $\partial \mathcal{T}$, or the action of the group on $\partial \mathcal{T}$ preserves a probability measure. This generalises to all groups of tree almost automorphisms a result of S. Hurtado and E. Militon for Thompson's group $V$, with a hopefully simpler proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Tits alternative for groups of almost automorphisms of trees Vio, Martín Gilabert Group Theory Dynamical Systems 20F99 (Primary) 20F65 (Secondary) We prove a dynamical variant of the Tits alternative for the group of almost automorphisms of a locally finite tree $\mathcal{T}$: a group of almost automorphisms of $\mathcal{T}$ either contains a nonabelian free group playing ping-pong on the boundary $\partial \mathcal{T}$, or the action of the group on $\partial \mathcal{T}$ preserves a probability measure. This generalises to all groups of tree almost automorphisms a result of S. Hurtado and E. Militon for Thompson's group $V$, with a hopefully simpler proof. |
| title | Dynamical Tits alternative for groups of almost automorphisms of trees |
| topic | Group Theory Dynamical Systems 20F99 (Primary) 20F65 (Secondary) |
| url | https://arxiv.org/abs/2412.08784 |