Infinite graph product of groups II: Analytic properties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915078190661632 |
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| author | Oyakawa, Koichi |
| author_facet | Oyakawa, Koichi |
| contents | We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In particular, we provide a new class of convergence groups and identify the if and only if condition for this convergence action to be geometrically finite. We also provide a new class of properly proximal groups, relatively bi-exact groups, and groups with strongly solid group von Neumann algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite graph product of groups II: Analytic properties Oyakawa, Koichi Group Theory Dynamical Systems Operator Algebras We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In particular, we provide a new class of convergence groups and identify the if and only if condition for this convergence action to be geometrically finite. We also provide a new class of properly proximal groups, relatively bi-exact groups, and groups with strongly solid group von Neumann algebras. |
| title | Infinite graph product of groups II: Analytic properties |
| topic | Group Theory Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2412.18313 |