A systematic classification of knotoids on the plane and on the sphere

Abstract

In this paper we generate and systematically classify all prime planar knotoids with up to 5 crossings. We also extend the existing list of knotoids in $S^2$ and add all knotoids with 6 crossings.

105 pages, 16 figures and 2 Appendices. The updated version corrects typos in Tables 6 and 7 and adds one missing reference