Georgakopoulos–Papasoglu's coarse Kuratowski conjecture

A length space is a metric space in which the distance between two points is the infimum of the lengths of paths joining them. A length space is quasi-isometric to a graph when there is a quasi-isometry between the metric space and the graph with its path metric. An asymptotic minor is the large-scale analogue of a graph minor. Georgakopoulos–Papasoglu's coarse Kuratowski conjecture. A length space is quasi-isometric to a planar graph if and only if it has no asymptotic $K_5$ or $K_{3,3}$ minor. This is proposed as a coarse analogue of Wagner's characterization of planar graphs. The source refers readers to Georgakopoulos and Papasoglu for the definition of asymptotic minors and does not state a resolution.