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
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.
free knot, parity, sliceness, cobordism, four-valent graph.
|Ministry of Education and Science of the Russian Federation
|Russian Foundation for Basic Research
|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).
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Sbornik: Mathematics, 2019, 210:10, 1493–1509
MSC: 57M25, 57Q45, 57Q60, 57M20
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
\by V.~O.~Manturov, D.~A.~Fedoseev
\paper A~sliceness criterion for odd free knots
\jour Mat. Sb.
\jour Sb. Math.
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