# 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 $$g$$ 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 $$(g+1)g$$ 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.