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Mat. Sb., 2010, Volume 201, Number 6, Pages 3–18 (Mi msb7655)  

This article is cited in 11 scientific papers (total in 11 papers)

Refining virtual knot invariants by means of parity

D. M. Afanas'ev

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

Abstract: In this work two new invariants of virtual links are constructed: the even Alexander polynomial and the even quandle. The general idea behind the construction is to split the classical crossings into two types, the even and the odd ones, and then define different operations at the crossings of different types. On the other hand, the proposed construction is a realization of the same idea using two closely related languages: the language of quandles and the language of Alexander polynomials.
Bibliography: 15 titles.

Keywords: knot, virtual knot, parity, Alexander polynomial, minimality, quandle.

DOI: https://doi.org/10.4213/sm7655

Full text: PDF file (608 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:6, 785–800

Bibliographic databases:

UDC: 515.162+519.1
MSC: 57M25, 57M27
Received: 18.11.2009

Citation: D. M. Afanas'ev, “Refining virtual knot invariants by means of parity”, Mat. Sb., 201:6 (2010), 3–18; Sb. Math., 201:6 (2010), 785–800

Citation in format AMSBIB
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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. 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
    2. V. O. Manturov, “Parity, free knots, groups, and invariants of finite type”, Trans. Moscow Math. Soc., 72 (2011), 157–169  mathnet  crossref  zmath  elib
    3. Chrisman M.W., Manturov V.O., “Parity and exotic combinatorial formulae for finite-type invariants of virtual knots”, J. Knot Theory Ramifications, 21:13 (2012), 1240001, 27 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Kaestner A.M., Kauffman L.H., “Parity, Skein polynomials and categorification”, J. Knot Theory Ramifications, 21:13 (2012), 1240011, 56 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Manturov V.O., “Virtual crossing numbers for virtual knots”, J. Knot Theory Ramifications, 21:13 (2012), 1240009, 13 pp.  crossref  mathscinet  zmath  isi  scopus  scopus
    6. M. V. Zenkina, “The parity hierarchy and new invariants of knots in thickened surfaces”, J. Knot Theory Ramifications, 22:4 (2013), 1340001, 23 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. V.O. Manturov, “Parity and projection from virtual knots to classical knots”, J. Knot Theory Ramifications, 22:9 (2013), 1350044, 20 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. M.W. Chrisman, V.O. Manturov, “Fibered knots and virtual knots”, J. Knot Theory Ramifications, 22:12 (2013), 1341003, 23 pp.  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. M. V. Zenkina, “An invariant of knots in thickened surfaces”, Journal of Mathematical Sciences, 214:5 (2016), 728–740  mathnet  crossref
    10. Kaestner A., Nelson S., Selker L., “Parity biquandle invariants of virtual knots”, Topology Appl., 209 (2016), 207–219  crossref  mathscinet  zmath  isi  scopus
    11. Fedoseev D.A., Manturov V.O., “Parities on 2-knots and 2-links”, J. Knot Theory Ramifications, 25:14 (2016), 1650079  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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