ABSTRACT
This chapter describes some series of knots and links. The number of half-turn twists for each band can be taken to be zero or one according to the Arf equivalence. Besides, the Arf equivalence allows to change the disposition of bands in 3-space, for instance, to erase knottedness. Namely, a simple observation shows that passing one band through the other is also Arf equivalence. The chapter shows how to transform any knot diagram to an unknot diagram only by switching some crossing types. A colouring of a link diagram is said to be proper if for each crossing of the diagram, the three arcs incident to it have either all three different colours: red, blue, and white. The number of proper colourings is an invariant of link isotopy types. Each proper colouring of the initial diagram uniquely corresponds to a colouring of the diagram obtained from the initial one by applying a Reidemeister move.
