Hyperbolic hyperbolic-by-cyclic groups are cubulable
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915093074149376 |
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| author | Dahmani, François S, Suraj Krishna M Mutanguha, Jean Pierre |
| author_facet | Dahmani, François S, Suraj Krishna M Mutanguha, Jean Pierre |
| contents | We show that the mapping torus of a hyperbolic group by a hyperbolic automorphism is cubulable. Along the way, we (i) give an alternate proof of Hagen and Wise's theorem that hyperbolic free-by-cyclic groups are cubulable, and (ii) extend to the case with torsion Brinkmann's thesis that a torsion-free hyperbolic-by-cyclic group is hyperbolic if and only if it does not contain $\mathbb{Z}^2$-subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperbolic hyperbolic-by-cyclic groups are cubulable Dahmani, François S, Suraj Krishna M Mutanguha, Jean Pierre Group Theory 20F65, 20E36, 20E08, 20F67 We show that the mapping torus of a hyperbolic group by a hyperbolic automorphism is cubulable. Along the way, we (i) give an alternate proof of Hagen and Wise's theorem that hyperbolic free-by-cyclic groups are cubulable, and (ii) extend to the case with torsion Brinkmann's thesis that a torsion-free hyperbolic-by-cyclic group is hyperbolic if and only if it does not contain $\mathbb{Z}^2$-subgroups. |
| title | Hyperbolic hyperbolic-by-cyclic groups are cubulable |
| topic | Group Theory 20F65, 20E36, 20E08, 20F67 |
| url | https://arxiv.org/abs/2306.15054 |