Higher topological complexity of hyperbolic groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912186443497472 |
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| author | Hughes, Sam Li, Kevin |
| author_facet | Hughes, Sam Li, Kevin |
| contents | We prove for non-elementary torsion-free hyperbolic groups $Γ$ and all $r\ge 2$ that the higher topological complexity ${\sf{TC}}_r(Γ)$ is equal to $r\cdot \mathrm{cd}(Γ)$. In particular, hyperbolic groups satisfy the rationality conjecture on the $\sf{TC}$-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we consider certain toral relatively hyperbolic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_05114 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Higher topological complexity of hyperbolic groups Hughes, Sam Li, Kevin Algebraic Topology Group Theory 55M30, 55R35, 20F67 We prove for non-elementary torsion-free hyperbolic groups $Γ$ and all $r\ge 2$ that the higher topological complexity ${\sf{TC}}_r(Γ)$ is equal to $r\cdot \mathrm{cd}(Γ)$. In particular, hyperbolic groups satisfy the rationality conjecture on the $\sf{TC}$-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we consider certain toral relatively hyperbolic groups. |
| title | Higher topological complexity of hyperbolic groups |
| topic | Algebraic Topology Group Theory 55M30, 55R35, 20F67 |
| url | https://arxiv.org/abs/2110.05114 |