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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2311.15187 |
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| _version_ | 1866913910548856832 |
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| author | Balasubramanya, Sahana Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie |
| author_facet | Balasubramanya, Sahana Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie |
| contents | In this note, we consider the notion of what we call recognizing spaces for stable subgroups of a given group. When a group $G$ is a mapping class group or right-angled Artin group, it is known that a subgroup is stable exactly when the largest acylindrical action $G \curvearrowright X$ provides a quasi-isometric embedding of the subgroup into $X$ via the orbit map. In this sense the largest acylindrical action for mapping class groups and right-angled Artin groups provides a recognizing space for all stable subgroups. In contrast, we construct an acylindrically hyperbolic group (relatively hyperbolic, in fact) whose largest acylindrical action does not recognize all stable subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15187 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | (Non-)Recognizing Spaces for Stable Subgroups Balasubramanya, Sahana Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie Group Theory 20F65, 20F67 In this note, we consider the notion of what we call recognizing spaces for stable subgroups of a given group. When a group $G$ is a mapping class group or right-angled Artin group, it is known that a subgroup is stable exactly when the largest acylindrical action $G \curvearrowright X$ provides a quasi-isometric embedding of the subgroup into $X$ via the orbit map. In this sense the largest acylindrical action for mapping class groups and right-angled Artin groups provides a recognizing space for all stable subgroups. In contrast, we construct an acylindrically hyperbolic group (relatively hyperbolic, in fact) whose largest acylindrical action does not recognize all stable subgroups. |
| title | (Non-)Recognizing Spaces for Stable Subgroups |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2311.15187 |