Higher topological complexity of hyperbolic groups

Author: 

Hughes, S
Li, K

Publication Date: 

11 October 2021

Last Updated: 

2021-11-12T09:54:19.163+00:00

abstract: 

We prove for non-elementary torsion-free hyperbolic groups $\Gamma$ and all
$r\ge 2$ that the higher topological complexity ${\sf{TC}}_r(\Gamma)$ is equal
to $r\cdot \mathrm{cd}(\Gamma)$. 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.

Symplectic id: 

1202996

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article