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arXiv · 2310.10814

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

Zhaoshen Zhai
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Abstract

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.

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Zhaoshen Zhai. 2025-04-24. A saturated 1-system of curves on the surface of genus 3. https://doi.org/10.1007/s10711-025-01009-2

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