Higher topological complexity of hyperbolic groups

Fuente: arXiv
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Autori principali: Hughes, Sam, Li, Kevin
Natura: Preprint
Pubblicazione: 2021
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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