Классификация нотоидов малой сложности

As the main result of the paper we present the complete classification of all prime knotoids with positive height and at most 5 crossings. We prove that there exist exactly 31 knotoids of this type. The proof is based on the complete table of knots in the thickened torus and the correspondence between knotoids in the two dimensional sphere and knots in the thickened torus.