Farber's topological complexity conjecture for graph configuration spaces
Farber's topological complexity conjecture for graph configuration spaces
Let be a connected graph, and let denote the set of vertices of of degree at least . Assume that and let . Farber's conjecture. The topological complexity of the ordered configuration space of points on satisfies
This conjecture predicts that, once the number of particles is sufficiently large, topological complexity is determined by the number of essential vertices of the graph. The supplied source does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Daniel Lütgehetmann and David Recio-Mitter, “Topological complexity of configuration spaces of fully articulated graphs and banana graphs”, arXiv:1806.00659 (2019).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.