Topological complexity of graph braid groups

Kasia Jankiewicz (UCSC and IAS)

Abstract: Graph braid groups are the fundamental groups of configuration spaces of particles in a graph. We study a question of whether certain sets of elements in a graph braid group generate a right-angled Artin group, and use it to compute the topological complexity of graph braid groups with sufficiently many particles. In the talk, I will discuss graph braid groups, their associated nonpositively curved cube complex, and the notion of topological complexity, and I will outline the proof of our result. This is joint work with Kevin Schreve.