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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 231–248 (Mi tm517)  

This article is cited in 4 scientific papers (total in 4 papers)

Finitely Presented Groups and Semigroups in Knot Theory

I. A. Dynnikov

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

Abstract: We construct finitely presented semigroups whose central elements are in one-to-one correspondence with the isotopy classes of non-oriented links in $\mathbb R^3$. Solving the word problem for those semigroups is equivalent to solving the classification problem for links and tangles. Also, we give a construction of finitely presented groups containing the braid group as a subgroup.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 220–237

Bibliographic databases:
UDC: 515.164.63
Received in May 2000

Citation: I. A. Dynnikov, “Finitely Presented Groups and Semigroups in Knot Theory”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 231–248; Proc. Steklov Inst. Math., 231 (2000), 220–237

Citation in format AMSBIB
\Bibitem{Dyn00}
\by I.~A.~Dynnikov
\paper Finitely Presented Groups and Semigroups in Knot Theory
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 231--248
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm517}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1841757}
\zmath{https://zbmath.org/?q=an:1032.57004}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 220--237


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. I. A. Dynnikov, “Recognition algorithms in knot theory”, Russian Math. Surveys, 58:6 (2003), 1093–1139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. Fabel P., “Completing Artin's braid group on infinitely many strands”, Journal of Knot Theory and Its Ramifications, 14:8 (2005), 979–991  crossref  mathscinet  zmath  isi  scopus  scopus
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