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Funktsional. Anal. i Prilozhen.:

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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 1, Pages 29–40 (Mi faa280)  

This article is cited in 11 scientific papers (total in 11 papers)

Three-Page Approach to Knot Theory. Universal Semigroup

I. A. Dynnikov

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

Abstract: An explicit construction of a finitely presented semigroup whose central elements are in a one-to-one correspondence with the isotopy classes of unoriented links in the three-space is given, together with a finite presentation for the group of invertible elements of the semigroup. The group is presented by two generators and three relations. The commutator subgroup of the group is isomorphic to the braid group of infinite index. A similar construction is given for band-links. The Kauffman theorems on the existence of polynomial band-link invariants satisfying some skein-relations are stated algebraically.


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English version:
Functional Analysis and Its Applications, 2000, 34:1, 24–32

Bibliographic databases:

UDC: 515.164.63
Received: 12.10.1999

Citation: I. A. Dynnikov, “Three-Page Approach to Knot Theory. Universal Semigroup”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 29–40; Funct. Anal. Appl., 34:1 (2000), 24–32

Citation in format AMSBIB
\by I.~A.~Dynnikov
\paper Three-Page Approach to Knot Theory. Universal Semigroup
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 1
\pages 29--40
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 1
\pages 24--32

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    This publication is cited in the following articles:
    1. I. A. Dynnikov, “Finitely Presented Groups and Semigroups in Knot Theory”, Proc. Steklov Inst. Math., 231 (2000), 220–237  mathnet  mathscinet  zmath
    2. 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
    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. Andreeva M.V., Dynnikov I.A., Polthier K., “A mathematical webservice for recognizing the unknot”, Mathematical Software, Proceedings, 2002, 201–207  crossref  zmath  isi
    5. I. A. Dynnikov, “Recognition algorithms in knot theory”, Russian Math. Surveys, 58:6 (2003), 1093–1139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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. 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
    8. Dujmovic, V, “Stacks, queues and tracks: Layouts of graph subdivisions”, Discrete Mathematics and Theoretical Computer Science, 7:1 (2005), 155  mathscinet  zmath  isi
    9. 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
    10. Vernitski A., “Describing Semigroups With Defining Relations of the Form Xy = Yz and Yx = Zy and Connections With Knot Theory”, Semigr. Forum, 95:1 (2017), 66–82  crossref  mathscinet  zmath  isi  scopus
    11. Fish A., Lisitsa A., Vernitski A., “Visual Algebraic Proofs For Unknot Detection”, Diagrammatic Representation and Inference, Diagrams 2018, Lecture Notes in Artificial Intelligence, 10871, eds. Chapman P., Stapleton G., Moktefi A., PerezKriz S., Bellucci F., Springer International Publishing Ag, 2018, 89–104  crossref  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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