Coarse geometry of extended admissible groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914228076544000 |
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| author | Dao, Toan Trong Nguyen, Hoang Thanh |
| author_facet | Dao, Toan Trong Nguyen, Hoang Thanh |
| contents | Extended admissible groups belong to a particular class of graphs of groups that admit a decomposition generalizing those of non-geometric 3-manifold groups and Croke-Kleiner admissible groups. In this paper, we study several coarse-geometric aspects of extended admissible groups. We show that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups. We also prove that, under mild conditions on the vertex groups, extended admissible groups exhibit large-scale nonpositive curvature, thereby answering a question posed by Nguyen-Yang.
As an application, our results enlarge the class of extended admissible groups known to admit well-defined quasi-redirecting boundaries, a notion recently introduced by Qing-Rafi. In addition, we compute the divergence of extended admissible groups, generalizing a result of Gersten from non-geometric 3-manifold groups to this broader setting. Finally, we study several aspects of subgroup structure in extended admissible groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarse geometry of extended admissible groups Dao, Toan Trong Nguyen, Hoang Thanh Group Theory 20F65, 20F67 Extended admissible groups belong to a particular class of graphs of groups that admit a decomposition generalizing those of non-geometric 3-manifold groups and Croke-Kleiner admissible groups. In this paper, we study several coarse-geometric aspects of extended admissible groups. We show that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups. We also prove that, under mild conditions on the vertex groups, extended admissible groups exhibit large-scale nonpositive curvature, thereby answering a question posed by Nguyen-Yang. As an application, our results enlarge the class of extended admissible groups known to admit well-defined quasi-redirecting boundaries, a notion recently introduced by Qing-Rafi. In addition, we compute the divergence of extended admissible groups, generalizing a result of Gersten from non-geometric 3-manifold groups to this broader setting. Finally, we study several aspects of subgroup structure in extended admissible groups. |
| title | Coarse geometry of extended admissible groups |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2512.24784 |