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<p>We construct a system of 33 essential simple closed curves that are pairwise non-homotopic and intersect at most once on the oriented, closed surface of genus 3. Moreover, we show that our construction is <i>saturated</i>, in the sense that it is not properly contained in any other such system of curves.</p>

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A saturated 1-system of curves on the surface of genus 3

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • Zhaoshen Zhai

摘要

We construct a system of 33 essential simple closed curves that are pairwise non-homotopic and intersect at most once on the oriented, closed surface of genus 3. Moreover, we show that our construction is saturated, in the sense that it is not properly contained in any other such system of curves.