Higher topological complexity of hyperbolic groups

Abstract

We prove for non-elementary torsion-free hyperbolic groups $\Gamma$ and all $r\ge 2$ that the higher topological complexity ${\mathsf{TC}}_r(\Gamma )$ is equal to $r\cdot \mathrm{cd}(\Gamma )$. In particular, hyperbolic groups satisfy the rationality conjecture on the $\mathsf{TC}$-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we consider certain toral relatively hyperbolic groups.

5 pages, comments welcome

References in corpus (2)

• Bredon cohomology and robot motion planning
• Right-angled Artin groups, polyhedral products and the TC-generating function