一类完全非代数连接纽结与链环的构造

Construction of a class of completely non-algebraic connected knots and links

纽结与链环的分类是三维流形理论研究中的重要课题.纽结与链环对应的缠绕分解是研究纽结与链环分类的重要方法.非代数纽结与链环是纽结与链环的重要分支,从缠绕对应的平面基本多面体出发,纽结与链环可利用其投影图对应的基本多面体进行分类.利用三维流形组合拓扑的研究技巧和方法构造性的证明,对于任意的自然数n(n≥6,n≠7)均存在完全非代数连接基本多面体,进一步利用上述结果证明了完全非代数连接纽结与链环的广泛存在性.

The classification of knots and links is an important topic in the research of 3-manifold theory.Tangle decomposition of knots and links is an important method to study the classification of knots and links.Non-algebraic knots and links are important branches of knots and links,from the basic ployhedrons of tangles,knots and links can be classified by using the basic polyhedrons corresponding to their projections.Based on this result,we constructively prove the existence of a class of completely non-algebraic connected basic polyhedron for any natural number n(n≥6,n≠7)by using the research techniques and methods of three-dimensional manifold and combinatorial topology.Further,by using the above results,we prove the widespread existence of completely non-algebraic connected knots and links.