Large Collections of Curves Pairwise Intersecting Exactly Once

Abstract

Let $\Omega =({\omega }_j{)}_{j\in I}$ be a collection of pairwise non-isotopic simple closed curves on the closed, orientable, genus $g$ surface $S_g$, such that ${\omega }_i$ and ${\omega }_j$ intersect exactly once for $i\ne j$. It was recently demonstrated by Malestein, Rivin, and Theran that the cardinality of such a collection is no more than $2g+1$. In this paper, we show that for $g\ge 3$, there exists at least two such collections with this maximum size up to the action of the mapping class group, answering a question posed by Malestein, Rivin and Theran.

References in corpus (1)

• Topological Designs