Farber's conjecture and beyond
Algebraic Topology
2024-06-27 v2 Geometric Topology
Abstract
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional approach through cohomology, with its limitations, and the more modern approach through asphericity and the fundamental group, explaining how they are in fact variations on the same core ideas. We close with a list of open problems in the field.
Cite
@article{arxiv.2402.03022,
title = {Farber's conjecture and beyond},
author = {Ben Knudsen},
journal= {arXiv preprint arXiv:2402.03022},
year = {2024}
}
Comments
20 pages, 4 figures. Accepted version of invited contribution to book project "Topology and AI" (working title, ed. Michael Farber and Jes\'us Gonz\'alez)