Crossing number of curves on surfaces

2024/03/08 by Jörg, Jasmin
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2403.05148

Abstract

We consider systems of simple closed curves on surfaces and their total number of intersection points, their so-called crossing number. For a fixed number of curves, we aim to minimise the crossing number. We determine the minimal crossing number of up to 12 curves on a surface of genus 2 and prove that minimising systems are unique up to homeomorphisms of the surface and isotopies of curves.

Related

• Crossing number inequalities for curves on surfaces
• Modular systoles are extremal for the crossing number
• On Kainen's conjectures on surface crossing numbers
• Curves on surfaces with prescribed pairwise intersection numbers
• On the crossing number of arithmetic curve systems