A note on asynchronously automatic groups and notions of non-positive curvature
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912511215796224 |
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| author | Hughes, Sam Valiunas, Motiejus |
| author_facet | Hughes, Sam Valiunas, Motiejus |
| contents | We prove groups acting cocompactly on locally finite trees with hyperbolic vertex stabilisers are asynchronously automatic. Combining this with previous work of the authors, we obtain an example of a group satisfying several non-positive curvature properties (being a $\mathrm{CAT}(0)$ group, an injective group, a hierarchically hyperbolic group, and having quadratic Dehn function) which is asynchronously automatic but not biautomatic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01832 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on asynchronously automatic groups and notions of non-positive curvature Hughes, Sam Valiunas, Motiejus Group Theory 20F10, 20F65, 20F67, 20E08 We prove groups acting cocompactly on locally finite trees with hyperbolic vertex stabilisers are asynchronously automatic. Combining this with previous work of the authors, we obtain an example of a group satisfying several non-positive curvature properties (being a $\mathrm{CAT}(0)$ group, an injective group, a hierarchically hyperbolic group, and having quadratic Dehn function) which is asynchronously automatic but not biautomatic. |
| title | A note on asynchronously automatic groups and notions of non-positive curvature |
| topic | Group Theory 20F10, 20F65, 20F67, 20E08 |
| url | https://arxiv.org/abs/2304.01832 |