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

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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. Kaufman^a, V. O. Manturov

^a Eastern Illinois University

Full-text PDF (279 kB) Citations (26)

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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

K_{1}

$K_1$ and

K_{2}

$K_2$ is trivial, then so are both

K_{1}

$K_1$ and

K_{2}

$K_2$ . 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

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\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.

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\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.

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\crossref{https://doi.org/10.1134/S0081543806010111}

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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:

A. A. Kazakov, “The State-Sum Invariants for Virtual Knot”, Lobachevskii J Math, 44:12 (2023), 5286
Chapman H., Rechnitzer A., “A Markov Chain Sampler For Plane Curves”, Exp. Math., 31:2 (2022), 552–582
Chrisman M., “Concordances to Prime Hyperbolic Virtual Knots”, Geod. Dedic., 212:1 (2021), 379–414
Barrett J.W., Tavares S.O.G., “Two-Dimensional State Sum Models and Spin Structures”, Commun. Math. Phys., 336:1 (2015), 63–100
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
Tubbenhauer D., “Virtual Khovanov Homology Using Cobordisms”, J. Knot Theory Ramifications, 23:9 (2014), 1450046
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
Joanna A. Ellis-Monaghan, Iain Moffatt, SpringerBriefs in Mathematics, Graphs on Surfaces, 2013, 101
Joanna A. Ellis-Monaghan, Iain Moffatt, SpringerBriefs in Mathematics, Graphs on Surfaces, 2013, 23
VASSILY OLEGOVICH MANTUROV, “PARITY AND PROJECTION FROM VIRTUAL KNOTS TO CLASSICAL KNOTS”, J. Knot Theory Ramifications, 22:09 (2013), 1350044
S. V. Matveev, “Roots and decompositions of three-dimensional topological objects”, Russian Math. Surveys, 67:3 (2012), 459–507
Lee S.Y., “Genera and Periodicity of Virtual Knots and Links”, J. Knot Theory Ramifications, 21:4 (2012), 1250037
Manturov V.O., “Virtual Crossing Numbers for Virtual Knots”, J. Knot Theory Ramifications, 21:13, SI (2012), 1240009
Kauffman L.H., “Introduction to Virtual Knot Theory”, J. Knot Theory Ramifications, 21:13, SI (2012), 1240007
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
F. G. Korablev, “Edinstvennost kornei uzlov v $F\times I$ i primarnye razlozheniya virtualnykh uzlov”, Tr. IMM UrO RAN, 17, no. 4, 2011, 160–175
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
Korablev F.G., Matveev S.V., “Reduction of knots in thickened surfaces and virtual knots”, Dokl. Math., 83:2 (2011), 262–264
Matveev S.V., “Decomposition of homologically trivial knots in $F\times I$ ”, Dokl. Math., 82:1 (2010), 511–513
Traldi L., “A bracket polynomial for graphs. II. Links, Euler circuits and marked graphs”, J. Knot Theory Ramifications, 19:4 (2010), 547–586

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

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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