Crossing number of curves on surfaces

Jasmin Jörg

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arXiv · 2403.05148

Crossing number of curves on surfaces

Jasmin Jörg

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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.

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Jasmin Jörg. 2024-03-08. Crossing number of curves on surfaces. https://arxiv.org/abs/2403.05148

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