The topological complexity of pure graph braid groups is stably maximal

TL;DR

This paper proves Farber's conjecture on the stable topological complexity of graph configuration spaces, providing a significant advancement in understanding the complexity of these mathematical structures.

Contribution

It confirms Farber's conjecture and introduces a general lower bound for the topological complexity of aspherical spaces, applicable to higher topological complexity.

Findings

Confirmed Farber's conjecture on stable topological complexity

Derived a general lower bound for topological complexity

Applicable to higher topological complexity

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.