THE RESEARCH OF THE STRUCTURES AND INVARIANTS OF STABLE EQUIVALENCE CLASSES OF KNOTS IN THICKENED SURFACES

定义了加厚曲面上纽结(扭纽结)的稳定等价类的困惑，并给出了扭纽结的困惑的几何解释。我们还介绍了扭结的多元多项式不变量和指数多项式，并证明了它们对识别扭结是有用的。我们编写了计算机程序，制作了扭结图，并计算了扭结的不变量。利用这些程序，我们构造了扭结的表。

We defined the quandles of the stable equivalence classes of knots in thickened surfaces (twisted knots) and gave the geometric interpretation of the quandles of twisted knots. We also introduced the multivariable polynomial invariants and the index polynomials of twisted knots and showed that they are useful to distinguish twisted knots. We coded the computer programs to makes the list of twisted knot diagrams and to calculate the invariants of twisted knots. Using the programs, we constructed thetable of twisted knots.