节面与空间图的推广
Generalizations of Knotoids and Spatial Graphs
摘要：
在2010年，Turaev引入了knotoids作为结的一种变体，它用带有两个端点的闭区间的嵌入代替了圆的嵌入，这里我们称之为极点。我们定义广义knotoids允许任意多个极点，区间和圆，每个极点对应于任何数量的区间端点，包括零。这个理论包含了其他各种相关的拓扑对象，并介绍了一些特别有趣的新情况。我们探讨各种类似的knotoid不变量，包括高度，指数多项式，括号多项式和双曲。我们进一步推广到knotoidal图，这是一个自然扩张的空间图，允许极点和顶点。
英文摘要：
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalized knotoids to allow arbitrarily many poles, intervals, and circles, each pole corresponding to any number of interval endpoints, including zero. This theory subsumes a variety of other related topological objects and introduces some particularly interesting new cases. We explore various analogs of knotoid invariants, including height, index polynomials, bracket polynomials and hyperbolicity. We further generalize to knotoidal graphs, which are a natural extension of spatial graphs that allow both poles and vertices.
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