Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913634249080832 |
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| author | Kropholler, Robert Isenrich, Claudio Llosa Soroko, Ignat |
| author_facet | Kropholler, Robert Isenrich, Claudio Llosa Soroko, Ignat |
| contents | In 1999 Brady constructed the first example of a non-hyperbolic finitely presented subgroup of a hyperbolic group by fibring a non-positively curved cube complex over the circle. We show that his example has Dehn function bounded above by $n^{96}$. This provides the first explicit polynomial upper bound on the Dehn function of a finitely presented non-hyperbolic subgroup of a hyperbolic group. We also determine the precise hyperbolicity constant for the $1$-skeleton of the universal cover of the cube complex in Brady's construction with respect to the $4$-point condition for hyperbolicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups Kropholler, Robert Isenrich, Claudio Llosa Soroko, Ignat Group Theory Geometric Topology 20F67, 20F65, 20F69, 20F06 In 1999 Brady constructed the first example of a non-hyperbolic finitely presented subgroup of a hyperbolic group by fibring a non-positively curved cube complex over the circle. We show that his example has Dehn function bounded above by $n^{96}$. This provides the first explicit polynomial upper bound on the Dehn function of a finitely presented non-hyperbolic subgroup of a hyperbolic group. We also determine the precise hyperbolicity constant for the $1$-skeleton of the universal cover of the cube complex in Brady's construction with respect to the $4$-point condition for hyperbolicity. |
| title | Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups |
| topic | Group Theory Geometric Topology 20F67, 20F65, 20F69, 20F06 |
| url | https://arxiv.org/abs/2501.01688 |