Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911073053966336 |
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| author | Bridson, Martin R |
| author_facet | Bridson, Martin R |
| contents | We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P<G\times G$ be the fibre product associated to an epimorphism $G\twoheadrightarrow Q$. We establish inequalities that relate the conjugator length function of $P$ to the geometry of cyclic subgroups in $Q$, the Dehn function of $Q$, the {\em rel-cyclics Dehn function} of $Q$, and the distortion of $P$ in $G\times G$. These estimates provide tools for extending the library of (large) functions that are known to arise as the conjugator length functions of finitely generated and finitely presented groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups Bridson, Martin R Group Theory 20F67, 20F10, 20F65 We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P<G\times G$ be the fibre product associated to an epimorphism $G\twoheadrightarrow Q$. We establish inequalities that relate the conjugator length function of $P$ to the geometry of cyclic subgroups in $Q$, the Dehn function of $Q$, the {\em rel-cyclics Dehn function} of $Q$, and the distortion of $P$ in $G\times G$. These estimates provide tools for extending the library of (large) functions that are known to arise as the conjugator length functions of finitely generated and finitely presented groups. |
| title | Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups |
| topic | Group Theory 20F67, 20F10, 20F65 |
| url | https://arxiv.org/abs/2507.17598 |