Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912390237388800 |
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| author | Abbott, Carolyn Hagen, Mark Petyt, Harry Zalloum, Abdul |
| author_facet | Abbott, Carolyn Hagen, Mark Petyt, Harry Zalloum, Abdul |
| contents | We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the associated hyperbolic spaces. We then use quasimorphisms to produce examples where these latter results are sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09742 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups Abbott, Carolyn Hagen, Mark Petyt, Harry Zalloum, Abdul Geometric Topology Group Theory We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the associated hyperbolic spaces. We then use quasimorphisms to produce examples where these latter results are sharp. |
| title | Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2305.09742 |