Classification of Knots of Small Complexity in Thickened Tori

Abstract

We present a table of knots in a thickened torus T × I the diagrams of which have less than five crossing points. The knots are constructed by a three-step process: enumeration of regular graphs of degree 4, enumeration of all corresponding knot projections for each graph, and construction of minimal diagrams. The completeness of the table is proved.