Systems of curves on non-orientable surfaces

Xiao Chen

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arXiv · 2408.00369

Systems of curves on non-orientable surfaces

Xiao Chen

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Abstract

We show that the order of the cardinality of maximal complete $1$-systems of loops on non-orientable surfaces is $\sim |\chi|^{2}$. 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 $2|\chi|(|\chi|+1)$.

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Xiao Chen. 2024-08-01. Systems of curves on non-orientable surfaces. https://arxiv.org/abs/2408.00369

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