论文标题
结节和空间图的概括
Generalizations of Knotoids and Spatial Graphs
论文作者
论文摘要
2010年，Turaev引入了打结，作为结的变化，将圆圈的嵌入用封闭的间隔嵌入，并用两个端点嵌入，我们称之为两极。我们定义了广义的结，以任意允许多个极线，间隔和圆圈，每个极点对应于任何数量的间隔端点，包括零。该理论涵盖了许多其他相关的拓扑对象，并引入了一些特别有趣的新案例。我们探索各种结节不变的类似物，包括高度，索引多项式，括号多项式和双曲线。我们进一步概括为结的图，这些图是允许两极和顶点的空间图的自然扩展。
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.
