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Three-page approach to knot theory. Encoding and local moves

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Functional Analysis and Its Applications Aims and scope

Abstract

In the present paper, we suggest a new combinatorial approach to knot theory based on embeddings of knots and links into a union of three half-planes with the same boundary. The idea to embed knots into a “book” is quite natural and was considered already in [1]. Among recent papers on embeddings of knots into a book with infinitely many pages, we mention [2] and [3] (see also references therein).

The restriction of the number of pages to three (or any other number ≥3) provides a convenient way toencode links by words in a finite alphabet. For those words, we give a finite set of local changes that realizes the equivalence of links by analogy with the Reidemeister moves for planar link diagrams.

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References

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Authors
  1. I. A. Dynnikov
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Additional information

This work is partially supported by Russian Foundation for Basic Research grant No. 99-01-00090.

Moscow State University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 4, pp. 25–37, October–December, 1999.

Translated by I. A. Dynnikov

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Dynnikov, I.A. Three-page approach to knot theory. Encoding and local moves. Funct Anal Its Appl 33, 260–269 (1999). https://doi.org/10.1007/BF02467109

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  • DOI: https://doi.org/10.1007/BF02467109

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