Geodesic
Three-Page Approach to Knot Theory. Encoding and Local Moves
Funkcionalʹnyj analiz i ego priloženiâ, Tome 33 (1999) no. 4, pp. 25-37

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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 restriction of the number of pages to three (or any other number $\ge3$) provides a convenient way to encode 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. 
@article{FAA_1999_33_4_a1,
     author = {I. A. Dynnikov},
     title = {Three-Page {Approach} to {Knot} {Theory.} {Encoding} and {Local} {Moves}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {25--37},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1999_33_4_a1/}
}
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I. A. Dynnikov. Three-Page Approach to Knot Theory. Encoding and Local Moves. Funkcionalʹnyj analiz i ego priloženiâ, Tome 33 (1999) no. 4, pp. 25-37. http://geodesic.mathdoc.fr/item/FAA_1999_33_4_a1/