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Functional Analysis and Its Applications

, Volume 33, Issue 4, pp 260–269 | Cite as

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

  • I. A. Dynnikov
Article

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.

Keywords

Simple Move Polygonal Line Elementary Move Isotopy Class Reidemeister Move 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • I. A. Dynnikov

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