A notion of quasiconvex subgroups in acylindrically hyperbolic groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908574195646464 |
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| author | Wan, Ping |
| author_facet | Wan, Ping |
| contents | In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off cusped spaces. We also prove that this notion of quasiconvexity is preserved under sufficiently long Dehn filling. As an application, we generalize a theorem of Groves-Manning on groups acting on $\operatorname{CAT}(0)$ cube complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A notion of quasiconvex subgroups in acylindrically hyperbolic groups Wan, Ping Group Theory 20F65, 20F67 In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off cusped spaces. We also prove that this notion of quasiconvexity is preserved under sufficiently long Dehn filling. As an application, we generalize a theorem of Groves-Manning on groups acting on $\operatorname{CAT}(0)$ cube complexes. |
| title | A notion of quasiconvex subgroups in acylindrically hyperbolic groups |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2509.20532 |