RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



CMFD:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


CMFD, 2011, Volume 41, Pages 3–163 (Mi cmfd183)  

This article is cited in 5 scientific papers (total in 5 papers)

Parity in knot theory and graph-links

D. P. Ilyutkoa, V. O. Manturovb, I. M. Nikonova

a Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia
b Faculty of Science, Peoples' Friendship University of Russia, Moscow, Russia

Abstract: The present monograph is devoted to low-dimensional topology in the context of two thriving theories: parity theory and theory of graph-links, the latter being an important generalization of virtual knot theory constructed by means of intersection graphs. Parity theory discovered by the second-named author leads to a new perspective in virtual knot theory, the theory of cobordisms in two-dimensional surfaces, and other new domains of topology. Theory of graph-links highlights a new combinatorial approach to knot theory.

Full text: PDF file (1306 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2013, 193:6, 809–965

Bibliographic databases:

UDC: 515.16+519.17

Citation: D. P. Ilyutko, V. O. Manturov, I. M. Nikonov, “Parity in knot theory and graph-links”, Topology, CMFD, 41, PFUR, M., 2011, 3–163; Journal of Mathematical Sciences, 193:6 (2013), 809–965

Citation in format AMSBIB
\Bibitem{IlyManNik11}
\by D.~P.~Ilyutko, V.~O.~Manturov, I.~M.~Nikonov
\paper Parity in knot theory and graph-links
\inbook Topology
\serial CMFD
\yr 2011
\vol 41
\pages 3--163
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd183}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3011999}
\transl
\jour Journal of Mathematical Sciences
\yr 2013
\vol 193
\issue 6
\pages 809--965
\crossref{https://doi.org/10.1007/s10958-013-1499-y}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84882767529}


Linking options:
  • http://mi.mathnet.ru/eng/cmfd183
  • http://mi.mathnet.ru/eng/cmfd/v41/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. P. Ilyutko, V. S. Safina, “Graph-links: nonrealizability, orientation, and Jones polynomial”, Journal of Mathematical Sciences, 214:5 (2016), 632–664  mathnet  crossref
    2. I. M. Nikonov, “Weak parities and functorial maps”, Journal of Mathematical Sciences, 214:5 (2016), 699–717  mathnet  crossref
    3. V. O. Manturov, D. A. Fedoseev, “Invariants of homotopy classes of curves and graphs on $2$-surfaces”, J. Math. Sci., 206:6 (2015), 668–678  mathnet  crossref  mathscinet
    4. M. W. Chrisman, “On the combinatorics of smoothing”, Journal of Mathematical Sciences, 214:5 (2016), 609–631  mathnet  crossref
    5. D. P. Il'yutko, I. M. Nikonov, “Diagram approach in the theory of knots and its application in the graph theory”, Moscow University Mathematics Bulletin, 73:3 (2018), 124–130  mathnet  crossref  isi
  • Современная математика. Фундаментальные направления
    Number of views:
    This page:571
    Full text:202
    References:53

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020