Abstract:
We consider the problem of recognizing knots as smooth embeddings of a circle into $\mathbb{R}^3$ given by their planar diagrams. The concept of a twist on a planar diagram is introduced and a method for encoding twists and nodes by T-graphs is proposed. We show that in some situations this approach allows one to recognize a trivial knot.
Keywords:knot, recognition of a trivial knot, twist, T-graph.