A uniform Tits alternative for endomorphisms of the projective line
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909585730699264 |
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| author | Beaumont, Alonso |
| author_facet | Beaumont, Alonso |
| contents | A recent article of J.P. Bell, K. Huang, W. Peng and T.J. Tucker establishes an analog of the Tits alternative for semigroups of endomorphisms of the projective line. The proof involves a ping-pong argument on arithmetic height functions. Extending this method, we obtain a uniform version of the same alternative. In particular, we show that semigroups of $\mathrm{End}(\mathbb{P}^{1})$ of exponential growth are of uniform exponential growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A uniform Tits alternative for endomorphisms of the projective line Beaumont, Alonso Number Theory Dynamical Systems Group Theory 20M05 (Primary) 14H37 (Secondary) A recent article of J.P. Bell, K. Huang, W. Peng and T.J. Tucker establishes an analog of the Tits alternative for semigroups of endomorphisms of the projective line. The proof involves a ping-pong argument on arithmetic height functions. Extending this method, we obtain a uniform version of the same alternative. In particular, we show that semigroups of $\mathrm{End}(\mathbb{P}^{1})$ of exponential growth are of uniform exponential growth. |
| title | A uniform Tits alternative for endomorphisms of the projective line |
| topic | Number Theory Dynamical Systems Group Theory 20M05 (Primary) 14H37 (Secondary) |
| url | https://arxiv.org/abs/2504.14263 |