Hyperbolicity in non-metric cubical small-cancellation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917601327710208 |
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| author | Arenas, Macarena Jankiewicz, Kasia Wise, Daniel T. |
| author_facet | Arenas, Macarena Jankiewicz, Kasia Wise, Daniel T. |
| contents | Given a non-positively curved cube complex $X$, we prove that the quotient of $π_1X$ defined by a cubical presentation $\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non-metric cubical small-cancellation conditions is hyperbolic provided that $π_1X$ is hyperbolic. This generalises the fact that finitely presented classical $C(7)$ small-cancellation groups are hyperbolic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_16860 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity in non-metric cubical small-cancellation Arenas, Macarena Jankiewicz, Kasia Wise, Daniel T. Group Theory 20F06, 20F67, 20F65 Given a non-positively curved cube complex $X$, we prove that the quotient of $π_1X$ defined by a cubical presentation $\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non-metric cubical small-cancellation conditions is hyperbolic provided that $π_1X$ is hyperbolic. This generalises the fact that finitely presented classical $C(7)$ small-cancellation groups are hyperbolic. |
| title | Hyperbolicity in non-metric cubical small-cancellation |
| topic | Group Theory 20F06, 20F67, 20F65 |
| url | https://arxiv.org/abs/2309.16860 |