Topological Complexity of Pure Graph Braid Groups

Explore the intricacies of pure graph braid groups and their topological complexity in this 56-minute lecture presented by Ben Knudsen for the Applied Algebraic Topology Network. Delve into a recent proof of Farber's conjecture, which posits that ordered configuration spaces of graphs exhibit the highest possible topological complexity in general cases. Examine key concepts such as topological robotics, the Fiokovsky theorem, and Farber's theorem. Investigate coronology classes, the planar and closed cases, and fiber bundles over sigma. Gain insights into the mathematical foundations underlying this complex topic and its implications for the field of algebraic topology.

Introduction
Topological complexity
Topological robotics
Fiokovsky theorem
Theorem of Farber
Coronology classes
The lemma
The planar case
The closed case
Fiber bundles over sigma