The topological complexity of pure graph braid groups is stably maximal

2022/06/13 by Knudsen, Ben · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2206.06268

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.

Cited by

• Topological persistence of configuration spaces and independence complexes for digraphs

Related

• On the stabilization of the topological complexity of graph braid groups
• Farber's conjecture and beyond
• Farber's conjecture for planar graphs
• Topological complexity of configuration spaces of fully articulated graphs and banana graphs
• Farley-Sabalka's Morse-theory model and the higher topological complexity of ordered configuration spaces on trees