Topological Designs
Geometric Topology
2013-01-04 v5 Combinatorics
Abstract
We give an exponential upper and a quadratic lower bound on the number of pairwise non-isotopic simple closed curves can be placed on a closed surface of genus g such that any two of the curves intersects at most once. Although the gap is large, both bounds are the best known for large genus. In genus one and two, we solve the problem exactly. Our methods generalize to variants in which the allowed number of pairwise intersections is odd, even, or bounded, and to surfaces with boundary components.
Cite
@article{arxiv.1008.3710,
title = {Topological Designs},
author = {Justin Malestein and Igor Rivin and Louis Theran},
journal= {arXiv preprint arXiv:1008.3710},
year = {2013}
}
Comments
14 p., 4 Figures. To appear in Geometriae Dedicata