RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (241 kB)
References: PDF file   HTML file

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

Bibliographic databases:
UDC: 515.164.63

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 

• http://mi.mathnet.ru/eng/tm517
• http://mi.mathnet.ru/eng/tm/v231/p231

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. I. A. Dynnikov, “Recognition algorithms in knot theory”, Russian Math. Surveys, 58:6 (2003), 1093–1139
3. V. V. Vershinin, V. A. Kurlin, “Three-Page Embeddings of Singular Knots”, Funct. Anal. Appl., 38:1 (2004), 14–27
4. Fabel P., “Completing Artin's braid group on infinitely many strands”, Journal of Knot Theory and Its Ramifications, 14:8 (2005), 979–991
•  Number of views: This page: 343 Full text: 118 References: 69 First page: 1