arXiv Open Access 2024

Systems of curves on non-orientable surfaces

Xiao Chen

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Abstrak

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 $2|χ|(|χ|+1)$.

Topik & Kata Kunci

math.GT

Penulis (1)

Xiao Chen

Format Sitasi

APA MLA BibTeX

Chen, X. (2024). Systems of curves on non-orientable surfaces. https://arxiv.org/abs/2408.00369

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓