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Funktsional'nyi Analiz i ego Prilozheniya, 2000, Volume 34, Issue 1, Pages 29–40
DOI: https://doi.org/10.4213/faa280
(Mi faa280)
 

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

Three-Page Approach to Knot Theory. Universal Semigroup

I. A. Dynnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
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.
Received: 12.10.1999
English version:
Functional Analysis and Its Applications, 2000, Volume 34, Issue 1, Pages 24–32
DOI: https://doi.org/10.1007/BF02467064
Bibliographic databases:
Document Type: Article
UDC: 515.164.63
Language: Russian
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
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\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
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\crossref{https://doi.org/10.4213/faa280}
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\zmath{https://zbmath.org/?q=an:0958.57006}
\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 1
\pages 24--32
\crossref{https://doi.org/10.1007/BF02467064}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000087490500003}
Linking options:
  • https://www.mathnet.ru/eng/faa280
  • https://doi.org/10.4213/faa280
  • https://www.mathnet.ru/eng/faa/v34/i1/p29
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:667
    Full-text PDF :325
    References:59
    First page:3
     
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