Abstract
We prove for non-elementary torsion-free hyperbolic groups Gamma and all rge 2 that the higher topological complexity {textsf {TC}}_r(Gamma ) is equal to rcdot mathrm {cd}(Gamma ). In particular, hyperbolic groups satisfy the rationality conjecture on the {textsf {TC}}-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we show that the same conclusions hold for certain toral relatively hyperbolic groups.
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