Studies on geometric properties and realization problems of invariants for classical knots and virtual knots

在这项研究中，我们从纽结的局部运动的观点出发，得到了关于纽结的几何或代数性质的实现以及相关问题的几个结果。实际上，我们构造了任意周期p的C_n解结数为1的p-周期纽结，我们还构造了解结数为1的复合纽结。此外，我们还得到了亚历山大多项式解开第一个结点的一个实现问题的部分解答。另一方面，我们利用平凡的宫泽多项式构造了非经典的虚结点，它是Jones多项式的推广。

In this studies, we obtain several results about realizations for geometric or algebraic properties of knots and related topics from a view of local moves for knots. In fact, we construct p-periodic knots with C_n unknotting number one for any period p. We also construct composite knots with # unknotting number one. Moreover, we obtain some partial answers for a realization problem of Alexander polynomials for # unknotting number one knots. On the other hand, we construct non-classical virtual knots with the trivial Miyazawa polynomial, which is a generalization of Jones polynomial.