C - 复形、扣环数与三重环绕数
$C$-complexes, Clasp Number, and Triple Linking Number
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中文总结 AI 辅助
研究给定三分支链环界定的C - 复形的扣环数，通过将三重环绕数表示为平面上字曲线所围面积，进行几何和离散优化，给出扣环数新下界并构造达到界的链环。
中文摘要 AI 辅助
C - 复形是链环各分支的赛弗特曲面的并集，它们在扣环处相交。链环的扣环数是其界定的所有C - 复形中扣环的最小数量，衡量链环离边界链环的距离。本文为给定三分支链环界定的所有C - 复形的扣环数提供新下界，改进了阿蒙森 - 安德森 - D. - 盖耶的结果。还构造了达到这些界的链环。为此，将三重环绕数表示为平面上三条曲线（称为字曲线）所围面积，然后进行几何和离散优化以最小化这些曲线长度。
英文摘要
A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all C-complexes it bounds. It gives a measure of how far a link is form being a boundary link. This paper provides a new lower bound for the number of clasps of all C-complexes bounded by a given 3-component link improving results of Amundsen-Anderson-D.-Guyer. Furthermore, we construct links that achieve these bounds. In order to do so, we express the triple linking numbers as the area bounded by three curves in the plane, called word curves, and then perform the geometry and discrete optimization needed to minimize the length of these curves.
