论文标题
打结的4个规则图：多项式不变式和Pachner移动
Knotted 4-regular graphs: polynomial invariants and the Pachner moves
论文作者
论文摘要
在循环量子重力中，量子几何形状的状态由打结图的类别表示，在差异下等效。因此，值得列举和区分这些阶级是值得的。本文着眼于4个规则图的情况，该图的解释是对三维流形的三角形的对象。开发了两个不同的多项式不变式来表征这些图 - 一个是受考夫曼支架关系的启发，另一个是基于Quandles的。然后研究了后者在Pachner移动下的不变性变化，然后研究作用在图表上。
In loop quantum gravity, states of quantum geometry are represented by classes of knotted graphs, equivalent under diffeomorphisms. Thus, it is worthwhile to enumerate and distinguish these classes. This paper looks at the case of 4-regular graphs, which have an interpretation as objects dual to triangulations of three-dimensional manifolds. Two different polynomial invariants are developed to characterize these graphs -- one inspired by the Kauffman bracket relations, and the other based on quandles. How the latter invariant changes under the Pachner moves acting on the graphs is then studied.
