Arcs on Punctured Disks Intersecting at Most Twice with Endpoints on the Boundary

2017/08/21 by Bar-Natan, Assaf · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1708.06402

Abstract

Let D_n be the n-punctured disk. We prove that a family of essential simple arcs starting and ending at the boundary and pairwise intersecting at most twice is of size at most \binomn+13. On the way, we also show that any nontrivial square complex homeomorphic to a disk whose hyperplanes are simple arcs intersecting at most twice must have a corner or a spur.

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