Curves on surfaces with prescribed pairwise intersection numbers
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918129038262272 |
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| author | Öztürk, Ferit |
| author_facet | Öztürk, Ferit |
| contents | Given an ordered sequence of $N$-choose-2 integers, we give necessary and sufficient conditions to have an ordered collection of $N$ simple closed curves on a torus such that the algebraic pairwise intersections of those curves are the given integers. We also present partial answers towards realizing curve systems on a surface with minimal genus, given the intersection numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curves on surfaces with prescribed pairwise intersection numbers Öztürk, Ferit Geometric Topology 57K20 Given an ordered sequence of $N$-choose-2 integers, we give necessary and sufficient conditions to have an ordered collection of $N$ simple closed curves on a torus such that the algebraic pairwise intersections of those curves are the given integers. We also present partial answers towards realizing curve systems on a surface with minimal genus, given the intersection numbers. |
| title | Curves on surfaces with prescribed pairwise intersection numbers |
| topic | Geometric Topology 57K20 |
| url | https://arxiv.org/abs/2508.16323 |