The topological complexity of pure graph braid groups is stably maximal

Abstract

We prove Farber's conjecture on the stable topological complexity of configuration spaces of graphs. The conjecture follows from a general lower bound derived from recent insights into the topological complexity of aspherical spaces. Our arguments apply equally to higher topological complexity.

arXiv comment9 pages. Minor changes. To appear in Forum of Mathematics, Sigma. May differ slightly from published version