The Tits alternative for visibility spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915528664154112 |
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| author | Ji, Ran Wu, Yunhui |
| author_facet | Ji, Ran Wu, Yunhui |
| contents | Let $Γ$ be a finitely generated group acting properly discontinuously by isometries on a visibility CAT(0) space $X$ that satisfies the bounded packing property. We prove that $Γ$ satisfies the Tits alternative: it is either almost nilpotent or contains a free nonabelian subgroup of rank $2$. In the former case, it is equivalent to that the cardinality of the limit set of $Γ$ in the geometric boundary of $X$ is no greater than $2$. As an application of the Tits alternative, we show that any finitely generated torsion group acting properly discontinuously by isometries on such a space must be a finite group and have a global fixed point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tits alternative for visibility spaces Ji, Ran Wu, Yunhui Group Theory Differential Geometry Geometric Topology Let $Γ$ be a finitely generated group acting properly discontinuously by isometries on a visibility CAT(0) space $X$ that satisfies the bounded packing property. We prove that $Γ$ satisfies the Tits alternative: it is either almost nilpotent or contains a free nonabelian subgroup of rank $2$. In the former case, it is equivalent to that the cardinality of the limit set of $Γ$ in the geometric boundary of $X$ is no greater than $2$. As an application of the Tits alternative, we show that any finitely generated torsion group acting properly discontinuously by isometries on such a space must be a finite group and have a global fixed point. |
| title | The Tits alternative for visibility spaces |
| topic | Group Theory Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2510.01008 |