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.
@article{INTO_2021_194_a6,
author = {O. N. Biryukov},
title = {Twists on flat knot diagrams},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {71--77},
year = {2021},
volume = {194},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_194_a6/}
}
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/