Geodesic
Twists on flat knot diagrams
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 71-77.

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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. 
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     title = {Twists on flat knot diagrams},
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O. N. Biryukov. Twists on flat knot diagrams. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 71-77. http://geodesic.mathdoc.fr/item/INTO_2021_194_a6/

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[2] Goeritz L., “Bemerkungen zur Knotentheorie”, Abh. Math. Sem. Univ. Hamburg., 10 (1934), 201–210 | DOI | MR