On the stabilization of the topological complexity of graph braid groups
Algebraic Topology
2026-02-05 v2 Geometric Topology
Abstract
We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually stabilizes at its maximal possible value, a direct analogue of a stability phenomenon in the ordered setting first conjectured by Farber. We estimate the stable range in terms of the number of trivalent vertices.
Keywords
Cite
@article{arxiv.2302.04346,
title = {On the stabilization of the topological complexity of graph braid groups},
author = {Ben Knudsen},
journal= {arXiv preprint arXiv:2302.04346},
year = {2026}
}
Comments
16 pages. To appear in the Journal of Applied and Computational Topology