Crossing number of curves on surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909132364185600 |
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| author | Jörg, Jasmin |
| author_facet | Jörg, Jasmin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Crossing number of curves on surfaces Jörg, Jasmin Geometric Topology 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. |
| title | Crossing number of curves on surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2403.05148 |