Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929339706114048 |
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| author | Hughes, Sam Valiunas, Motiejus |
| author_facet | Hughes, Sam Valiunas, Motiejus |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_11996 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity Hughes, Sam Valiunas, Motiejus Group Theory Geometric Topology 20F65, 20F10, 57K20 (primary), 57M50, 37E30, 20F67 (secondary) 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. |
| title | Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity |
| topic | Group Theory Geometric Topology 20F65, 20F10, 57K20 (primary), 57M50, 37E30, 20F67 (secondary) |
| url | https://arxiv.org/abs/2203.11996 |