Farber's conjecture for planar graphs
Algebraic Topology
2021-08-03 v3 Geometric Topology
Abstract
We prove that the ordered configuration spaces of planar graphs have the highest possible topological complexity generically, as predicted by a conjecture of Farber. Our argument establishes the same generic maximality for all higher topological complexities. We include some discussion of the non-planar case, demonstrating that the standard approach to the conjecture fails at a fundamental level.
Cite
@article{arxiv.2010.13530,
title = {Farber's conjecture for planar graphs},
author = {Ben Knudsen},
journal= {arXiv preprint arXiv:2010.13530},
year = {2021}
}
Comments
11 pages, 1 figure. Accepted for publication in Selecta Mathematica. May differ slightly from published from version