Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity
We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives the first example of an HHG which is not biautomatic, the first example of a non-biautomatic CAT(0) group of flat-rank...
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| Format: | Journal article |
| Sprog: | English |
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EMS Press
2024
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| _version_ | 1826312966241255424 |
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| author | Hughes, S Valiunas, M |
| author_facet | Hughes, S Valiunas, M |
| author_sort | Hughes, S |
| collection | OXFORD |
| description | We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives the first example of an HHG which is not biautomatic, the first example of a non-biautomatic CAT(0) group of flat-rank 2, and the first example of an HHG which is injective but not Helly. Our proofs heavily utilise the space of geodesic currents for a hyperbolic surface. |
| first_indexed | 2024-03-07T07:49:59Z |
| format | Journal article |
| id | oxford-uuid:728e94e2-10c8-403e-9b5b-3178ee9fa054 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:03:36Z |
| publishDate | 2024 |
| publisher | EMS Press |
| record_format | dspace |
| spelling | oxford-uuid:728e94e2-10c8-403e-9b5b-3178ee9fa0542024-05-13T09:30:07ZCommensurating HNN-extensions: hierarchical hyperbolicity and biautomaticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:728e94e2-10c8-403e-9b5b-3178ee9fa054EnglishSymplectic ElementsEMS Press 2024Hughes, SValiunas, MWe construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives the first example of an HHG which is not biautomatic, the first example of a non-biautomatic CAT(0) group of flat-rank 2, and the first example of an HHG which is injective but not Helly. Our proofs heavily utilise the space of geodesic currents for a hyperbolic surface. |
| spellingShingle | Hughes, S Valiunas, M Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title_full | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title_fullStr | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title_full_unstemmed | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title_short | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| title_sort | commensurating hnn extensions hierarchical hyperbolicity and biautomaticity |
| work_keys_str_mv | AT hughess commensuratinghnnextensionshierarchicalhyperbolicityandbiautomaticity AT valiunasm commensuratinghnnextensionshierarchicalhyperbolicityandbiautomaticity |