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Sbornik: Mathematics, 2019, Volume 210, Issue 10, Pages 1493–1509
DOI: https://doi.org/10.1070/SM9144 (Mi sm9144) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A sliceness criterion for odd free knots

V. O. Manturovab, D. A. Fedoseevcd

a Bauman Moscow State Technical University, Moscow, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Lomonosov Moscow State University, Moscow, Russia
d V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
English version PDF (504 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM9144
Abstract: The problem of concordance and cobordism of knots is a well-known classical problem in low-dimensional topology. The purpose of this paper is to show that for odd free knots, that is, free knots with all intersections odd, the question of whether the knot is slice (concordant to a trivial knot) can be answered effectively by analysing pairing of the chords in a knot diagram.
Bibliography: 8 titles.
Keywords: free knot, parity, sliceness, cobordism, four-valent graph.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0025
НШ-6399.2018.1
Russian Foundation for Basic Research 19-01-00775-а
The research of V. O. Manturov was supported by a grant from the Government of the Russian Federation for state support of scientific research conducted under the auspices of leading scientists (project no. 14.Y26.31.00025) at the Laboratory of Topology and Dynamics, Novosibirsk State University. The research of D. A. Fedoseev is part of the Programme of the President of the Russian Federation for State Support of Leading Scientific Schools (grant no. НШ-6399.2018.1) and was supported by the Russian Foundation for Basic Research (grant no. 19-01-00775-a).
Received: 29.06.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 10, Pages 161–178
DOI: https://doi.org/10.4213/sm9144
Bibliographic databases:
Document Type: Article
UDC: 515.162.8+515.164.24
MSC: 57M25, 57Q45, 57Q60, 57M20
Language: English
Original paper language: Russian
Citation: V. O. Manturov, D. A. Fedoseev, “A sliceness criterion for odd free knots”, Mat. Sb., 210:10 (2019), 161–178; Sb. Math., 210:10 (2019), 1493–1509
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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