Crossing number of curves on surfaces
Geometric Topology
2024-03-11 v1
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.
Cite
@article{arxiv.2403.05148,
title = {Crossing number of curves on surfaces},
author = {Jasmin Jörg},
journal= {arXiv preprint arXiv:2403.05148},
year = {2024}
}
Comments
28 pages, 4 figures