Handlebody-knots and topology

车把节是嵌入在3-球体中的车把体。两个手柄节点是等价的，如果其中一个可以通过3-球面的等距变换为另一个。手体结是纽结的自然推广，它与空间图和3-流形密切相关。本文的研究结果如下：定义了归一化的Yamada多项式。我给出了利用Quandle染色不变量来检测手体结的不可约性的方法。在空间三度图的集合上引入了IH-复形，并利用不变量计算了IH-距离。

A handlebody-knot is a handlebody embedded in the 3-sphere. Two handlebody-knots are equivalent if one can be transformed into the other by an isotopy of the 3-sphere. A handlebody-knot is a natural generalization of a knot, and is closely related to a spatial graph and a 3-manifold. The results of this study are as follows : I defined a normalized Yamada polynomial. I provided methods to detect the irreducibility of a handlebody-knot by using quandle coloring invariants. I introduced the IH-complex on the set of spatial trivalent graphs, and evaluated the IH-distance by using invariants.