Systems of curves on non-orientable surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916680773402624 |
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| author | Chen, Xiao |
| author_facet | Chen, Xiao |
| contents | We show that the order of the cardinality of maximal complete $1$-systems of loops on non-orientable surfaces is $\sim |χ|^{2}$. In particular, we determine the exact cardinality of maximal complete $1$-systems of loops on punctured projective planes. To prove these results, we show that the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is $2|χ|(|χ|+1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Systems of curves on non-orientable surfaces Chen, Xiao Geometric Topology We show that the order of the cardinality of maximal complete $1$-systems of loops on non-orientable surfaces is $\sim |χ|^{2}$. In particular, we determine the exact cardinality of maximal complete $1$-systems of loops on punctured projective planes. To prove these results, we show that the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is $2|χ|(|χ|+1)$. |
| title | Systems of curves on non-orientable surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2408.00369 |