标题： 具有最多4个交叉点的T×I中的纽结分类 显示英文标题

标题： Classification of knots in T x I with at most 4 crossings

摘要： 我们构造了在加厚环面 T x I 中具有最多 4 个交叉点的纽结表。 这些纽结是通过三步过程构建的。 首先，我们列出最多有 4 个顶点的度为 4 的正则图，然后对于每个图，枚举所有相应的纽结投影，之后构建相应的最小图。 几种已知的和新的技巧使得该过程保持在合理范围内，并提供了该表完整性的严格理论证明。 为了证明所有纽结都是不同的，我们使用了 Kauffman 多项式的广义版本。 显示英文摘要

摘要： We compose the table of knots in the thickened torus T x I having diagrams with at most 4 crossings. The knots are constructed by the three-step process. First we list regular graphs of degree 4 with at most 4 vertices, then for each graph we enumerate all corresponding knot projections, and after that we construct the corresponding minimal diagrams. Several known and new tricks made it possible to keep the process within reasonable limits and offer a rigorous theoretical proof of the completeness of the table. For proving that all knots are different we use a generalized version of the Kauffman polynomial.