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Funktsional. Anal. i Prilozhen.:

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Funktsional. Anal. i Prilozhen., 1999, Volume 33, Issue 4, Pages 25–37 (Mi faa378)  

This article is cited in 12 scientific papers (total in 12 papers)

Three-Page Approach to Knot Theory. Encoding and Local Moves

I. A. Dynnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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 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.


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English version:
Functional Analysis and Its Applications, 1999, 33:4, 260–269

Bibliographic databases:

UDC: 515.164.63
Received: 12.05.1999

Citation: I. A. Dynnikov, “Three-Page Approach to Knot Theory. Encoding and Local Moves”, Funktsional. Anal. i Prilozhen., 33:4 (1999), 25–37; Funct. Anal. Appl., 33:4 (1999), 260–269

Citation in format AMSBIB
\by I.~A.~Dynnikov
\paper Three-Page Approach to Knot Theory. Encoding and Local Moves
\jour Funktsional. Anal. i Prilozhen.
\yr 1999
\vol 33
\issue 4
\pages 25--37
\jour Funct. Anal. Appl.
\yr 1999
\vol 33
\issue 4
\pages 260--269

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    This publication is cited in the following articles:
    1. I. A. Dynnikov, “Three-Page Approach to Knot Theory. Universal Semigroup”, Funct. Anal. Appl., 34:1 (2000), 24–32  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. I. A. Dynnikov, “Finitely Presented Groups and Semigroups in Knot Theory”, Proc. Steklov Inst. Math., 231 (2000), 220–237  mathnet  mathscinet  zmath
    3. Dynnikov, IA, “A new way to represent links. One-dimensional formalism and untangling technology”, Acta Applicandae Mathematicae, 69:3 (2001), 243  crossref  mathscinet  zmath  isi  scopus
    4. V. A. Kurlin, “Dynnikov Three-Page Diagrams of Spatial $3$-Valent Graphs”, Funct. Anal. Appl., 35:3 (2001), 230–233  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Andreeva M.V., Dynnikov I.A., Polthier K., “A mathematical webservice for recognizing the unknot”, Mathematical Software, Proceedings, 2002, 201–207  crossref  zmath  isi
    6. V. A. Kurlin, “Basic embeddings of graphs and Dynnikov's three-page embedding method”, Russian Math. Surveys, 58:2 (2003), 372–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. I. A. Dynnikov, “Recognition algorithms in knot theory”, Russian Math. Surveys, 58:6 (2003), 1093–1139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. V. V. Vershinin, V. A. Kurlin, “Three-Page Embeddings of Singular Knots”, Funct. Anal. Appl., 38:1 (2004), 14–27  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Dujmovic, V, “Stacks, queues and tracks: Layouts of graph subdivisions”, Discrete Mathematics and Theoretical Computer Science, 7:1 (2005), 155  mathscinet  zmath  isi
    10. Kurlin, V, “Three-page encoding and complexity theory for spatial graphs”, Journal of Knot Theory and Its Ramifications, 16:1 (2007), 59  crossref  mathscinet  zmath  isi  scopus
    11. Kearton, C, “All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron”, Algebraic and Geometric Topology, 8:3 (2008), 1223  crossref  mathscinet  zmath  isi  scopus
    12. Morozov A., Smirnov A., “Chern–Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix”, Nuclear Phys B, 835:3 (2010), 284–313  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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