Non-geometric property (T) of warped cones
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911083010195456 |
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| author | Deng, Jintao Toyota, Ryo |
| author_facet | Deng, Jintao Toyota, Ryo |
| contents | In this paper, we study the geometric property (T) for discretized warped cones of an action on a compact Lie group $M$ by its finitely generated subgroup. We show that if a subgroup $G$ is dense in $M$, then the associated discretized warped cone $\bigsqcup_n M\times \{t(n)\}$ does not have geometric property (T) for any sequence of positive numbers $\{t(n)\}_{n\in \mathbb{N}}$ converging to $\infty$. This result applies to certain ergodic actions of groups with property (T), for example, the action of $SO(d,\mathbb{Z}[\frac{1}{5}])$ on $SO(d)$ with $d\geq 5$.
As an application, we obtain new examples of expanders without geometric property (T), including certain superexpanders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04578 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-geometric property (T) of warped cones Deng, Jintao Toyota, Ryo Group Theory Dynamical Systems Operator Algebras 37A55 In this paper, we study the geometric property (T) for discretized warped cones of an action on a compact Lie group $M$ by its finitely generated subgroup. We show that if a subgroup $G$ is dense in $M$, then the associated discretized warped cone $\bigsqcup_n M\times \{t(n)\}$ does not have geometric property (T) for any sequence of positive numbers $\{t(n)\}_{n\in \mathbb{N}}$ converging to $\infty$. This result applies to certain ergodic actions of groups with property (T), for example, the action of $SO(d,\mathbb{Z}[\frac{1}{5}])$ on $SO(d)$ with $d\geq 5$. As an application, we obtain new examples of expanders without geometric property (T), including certain superexpanders. |
| title | Non-geometric property (T) of warped cones |
| topic | Group Theory Dynamical Systems Operator Algebras 37A55 |
| url | https://arxiv.org/abs/2503.04578 |