不可定向表面上的曲线系统

arXiv - MATH - Geometric Topology Pub Date : 2024-08-01 DOI:arxiv-2408.00369

Xiao Chen

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引用次数: 0

摘要

我们证明了在不可定向面上最大完整 1 美元循环系统的心率阶为 $\sim |/chi|^{2}$。特别是，我们确定了在有标点的投影平面上最大完整 1$-环系统的精确万有引力。为了证明这些结果，我们证明了在非定向面上最多有一次成对相交的弧的最大系统的卡的极大性为 2|\chi|(|\chi|+1)$。

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Systems of curves on non-orientable surfaces

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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arXiv - MATH - Geometric Topology

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