none 10.1070/SM9144 Steklov Mathematical Institute Steklov Mathematical Institute 2731 108236815 4170 2022013017401200 10.4213 2025-05-12T15:55:22Z 2019-07-09T18:10:12Z 1 10.4213/sm9144 Sbornik: Mathematics Sb. Math. 1064-5616 10 01 2019 210 10 V. O. Manturov D. A. Fedoseev 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. 10 01 2019 1493 1509 http://dx.doi.org/10.1088/crossmark-policy iopscience.iop.org A sliceness criterion for odd free knots Sbornik: Mathematics paper © 2019 Russian Academy of Sciences (DoM) and London Mathematical Society 2018-06-29 Russian Foundation for Basic Research http://dx.doi.org/10.13039/501100002261 19-01-00775-а Ministry of Education and Science of the Russian Federation http://dx.doi.org/10.13039/501100003443 http://dx.doi.org/10.13039/501100003443 14.Y26.31.0025 https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining English language version 10.4213/sm9144 10.1070/SM9144 https://www.mathnet.ru/eng/sm9144 https://iopscience.iop.org/article/10.1070/SM9144/pdf https://iopscience.iop.org/article/10.1070/SM9144 https://iopscience.iop.org/article/10.1070/SM9144/pdf https://iopscience.iop.org/article/10.1070/SM9144/pdf https://iopscience.iop.org/article/10.1070/SM9144/pdf https://iopscience.iop.org/article/10.1070/SM9144 https://iopscience.iop.org/article/10.1070/SM9144 https://iopscience.iop.org/article/10.1070/SM9144/pdf Mat. Sb. Manturov 10.4213/sm7574 201 65 2010 Parity in knot theory Mat. Sb. Manturov 10.4213/sm7723 203 45 2012 Parity and cobordism of free knots Proc. Lond. Math. Soc. (3) Turaev 10.1112/plms/pdm014 95 360 2007 Topology of words Dokl. Ross. Akad. Nauk Manturov 10.7868/S0869565213290057 452 371 2013 An almost classification of free knots Quantum Topol. Kauffman 10.4171/QT/57 5 523 2014 A graphical construction of the J. Knot Theory Ramifications Chrisman 10.1142/S0218216513410034 22 2013 Fibered knots and virtual knots J. Knot Theory Ramifications Fedoseev 10.1142/S0218216516500796 25 2016 Parities on 2-knots and 2-links J. Knot Theory Ramifications Winter 10.1142/S0218216515500625 24 2015 Virtual links in arbitrary dimensions