Arcs Intersecting at Most Once on the 4-Punctured Sphere

TL;DR

This paper classifies the maximal collections of arcs on a 4-punctured sphere that intersect at most once, providing a comprehensive understanding of their configurations.

Contribution

It introduces a complete classification of maximal arc systems with at most one intersection on the 4-punctured sphere, a new result in geometric topology.

Findings

Complete classification of maximal arc systems

Characterization of intersection patterns

Foundational results for surface topology

Abstract

We classify maximal systems of arcs which intersect at most once on the 4-punctured sphere.