Topological designs

Authors: Justin Malestein, Igor Rivin, and Louis Theran
Journal: Geometriae Dedicata, 1681221–233, 2013.
Full text: arXiv DOI

Benson Farb and Chris Leininger had asked how many pairwise non-isotopic simple closed curves can be placed on a surface of genus in such a way that any two of the curves intersect at most once. In this note we use combinatorial methods to give bounds (a lower bound of curves, and an exponential upper bound). While the bounds for the general Farb/Leininger question are (conjecturally) weak, the results presented here are of independent interest.