ABSTRACT
I f RIII is forbidden, a knot projection will be non-trivial; this has been shown by Hagge-Yazinski [1] (Chapter 7). However, it is still unknown that which
knot projection is trivialized by a finite sequence generated by RI and RIII. By contrast, the classification of knot projections under the equivalence relation generated by RII and RIII has been completed (Chapter 3). We have also learned that the classification of knot projections under the equivalence relation generated by RI and RII is complete (Chapter 4).
