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Coding of Knots by T-Graphs

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Abstract

In this paper, knots are considered as smooth embeddings of a circle into ℝ3 defined by their flat diagrams. We propose a new method of coding knots by T-graphs describing the torsion structure on a flat diagram. For this method of coding, we introduce conceptions of a cycle and a block and describe transformations of T-graphs under the first and the third Reidemeister moves applied to the flat diagram of a knot.

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References

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    O. N. Biryukov

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  1. O. N. Biryukov
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Correspondence to O. N. Biryukov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 66, No. 4, Algebra, Geometry, and Topology, 2020.

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Biryukov, O.N. Coding of Knots by T-Graphs. J Math Sci 267, 529–540 (2022). https://doi.org/10.1007/s10958-022-06159-2

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  • DOI: https://doi.org/10.1007/s10958-022-06159-2

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