Higher topological complexity of hyperbolic groups

DOI10.1007/S41468-022-00088-4zbMATH Open1508.55001arXiv2110.05114WikidataQ115600324 ScholiaQ115600324MaRDI QIDQ6379940

Sam Hughes, Kevin Li

Publication date: 11 October 2021

Abstract: We prove for non-elementary torsion-free hyperbolic groups $Gamma$ and all $rge2$ that the higher topological complexity ${sfTC}_r(Gamma)$ is equal to $rcdotmathrmcd(Gamma)$. In particular, hyperbolic groups satisfy the rationality conjecture on the $sfTC$-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we consider certain toral relatively hyperbolic groups.

Mathematics Subject Classification ID

Lyusternik-Shnirel'man category of a space, topological complexity à la Farber, topological robotics (topological aspects) (55M30) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Hyperbolic groups and nonpositively curved groups (20F67)

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