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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 252, Pages 114–133 (Mi tm66)  

This article is cited in 26 scientific papers (total in 26 papers)

Virtual Knots and Links

L. H. Kaufmana, V. O. Manturov

a Eastern Illinois University
References:
Abstract: This paper is an introduction to the subject of virtual knot theory and presents a discussion of some new specific theorems about virtual knots. The new results are as follows: Using a 3-dimensional topology approach, we prove that if a connected sum of two virtual knots K1 and K2 is trivial, then so are both K1 and K2. We establish an algorithm for recognizing virtual links that is based on the Haken–Matveev technique.
Received in June 2005
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 252, Pages 104–121
DOI: https://doi.org/10.1134/S0081543806010111
Bibliographic databases:
UDC: 515.1
Language: Russian
Citation: L. H. Kaufman, V. O. Manturov, “Virtual Knots and Links”, Geometric topology, discrete geometry, and set theory, Collected papers, Trudy Mat. Inst. Steklova, 252, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 114–133; Proc. Steklov Inst. Math., 252 (2006), 104–121
Citation in format AMSBIB
\Bibitem{KauMan06}
\by L.~H.~Kaufman, V.~O.~Manturov
\paper Virtual Knots and Links
\inbook Geometric topology, discrete geometry, and set theory
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 252
\pages 114--133
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm66}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2255973}
\zmath{https://zbmath.org/?q=an:1351.57012}
\elib{https://elibrary.ru/item.asp?id=14754739}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 252
\pages 104--121
\crossref{https://doi.org/10.1134/S0081543806010111}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746063170}
Linking options:
  • https://www.mathnet.ru/eng/tm66
  • https://www.mathnet.ru/eng/tm/v252/p114
  • This publication is cited in the following 26 articles:
    1. A. A. Kazakov, “The State-Sum Invariants for Virtual Knot”, Lobachevskii J Math, 44:12 (2023), 5286  crossref
    2. Chapman H., Rechnitzer A., “A Markov Chain Sampler For Plane Curves”, Exp. Math., 31:2 (2022), 552–582  crossref  isi
    3. Chrisman M., “Concordances to Prime Hyperbolic Virtual Knots”, Geod. Dedic., 212:1 (2021), 379–414  crossref  mathscinet  isi  scopus
    4. Barrett J.W., Tavares S.O.G., “Two-Dimensional State Sum Models and Spin Structures”, Commun. Math. Phys., 336:1 (2015), 63–100  crossref  mathscinet  zmath  isi  scopus
    5. Rohwer C.M., Mueller-Nedebock K.K., “Operator Formalism For Topology-Conserving Crossing Dynamics in Planar Knot Diagrams”, J. Stat. Phys., 159:1 (2015), 120–157  crossref  mathscinet  zmath  isi  elib  scopus
    6. Tubbenhauer D., “Virtual Khovanov Homology Using Cobordisms”, J. Knot Theory Ramifications, 23:9 (2014), 1450046  crossref  mathscinet  zmath  isi  elib  scopus
    7. Andreevna A.A., Matveev S.V., “Classification of Genus 1 Virtual Knots Having At Most Five Classical Crossings”, J. Knot Theory Ramifications, 23:6 (2014), 1450031  crossref  mathscinet  zmath  isi  scopus
    8. Joanna A. Ellis-Monaghan, Iain Moffatt, SpringerBriefs in Mathematics, Graphs on Surfaces, 2013, 101  crossref
    9. Joanna A. Ellis-Monaghan, Iain Moffatt, SpringerBriefs in Mathematics, Graphs on Surfaces, 2013, 23  crossref
    10. VASSILY OLEGOVICH MANTUROV, “PARITY AND PROJECTION FROM VIRTUAL KNOTS TO CLASSICAL KNOTS”, J. Knot Theory Ramifications, 22:09 (2013), 1350044  crossref
    11. S. V. Matveev, “Roots and decompositions of three-dimensional topological objects”, Russian Math. Surveys, 67:3 (2012), 459–507  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Lee S.Y., “Genera and Periodicity of Virtual Knots and Links”, J. Knot Theory Ramifications, 21:4 (2012), 1250037  crossref  mathscinet  zmath  isi  elib  scopus
    13. Manturov V.O., “Virtual Crossing Numbers for Virtual Knots”, J. Knot Theory Ramifications, 21:13, SI (2012), 1240009  crossref  mathscinet  zmath  isi  scopus
    14. Kauffman L.H., “Introduction to Virtual Knot Theory”, J. Knot Theory Ramifications, 21:13, SI (2012), 1240007  crossref  mathscinet  zmath  isi  scopus
    15. Henrich A., MacNaughton N., Narayan S., Pechenik O., Townsend J., “Classical and virtual pseudodiagram theory and new bounds on unknotting numbers and genus”, J. Knot Theory Ramifications, 20:4 (2011), 625–650  crossref  zmath  isi  elib  scopus
    16. F. G. Korablev, “Edinstvennost kornei uzlov v F×I i primarnye razlozheniya virtualnykh uzlov”, Tr. IMM UrO RAN, 17, no. 4, 2011, 160–175  mathnet  elib
    17. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov, “Parity in knot theory and graph-links”, Journal of Mathematical Sciences, 193:6 (2013), 809–965  mathnet  crossref  mathscinet
    18. Korablev F.G., Matveev S.V., “Reduction of knots in thickened surfaces and virtual knots”, Dokl. Math., 83:2 (2011), 262–264  crossref  mathscinet  zmath  isi  elib  elib  scopus
    19. Matveev S.V., “Decomposition of homologically trivial knots in F×I”, Dokl. Math., 82:1 (2010), 511–513  crossref  mathscinet  zmath  isi  elib  scopus
    20. Traldi L., “A bracket polynomial for graphs. II. Links, Euler circuits and marked graphs”, J. Knot Theory Ramifications, 19:4 (2010), 547–586  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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