Email this article A sliceness criterion for odd free knots
- Authors: Manturov V.O.1,2, Fedoseev D.A.3,4
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Affiliations:
- Bauman Moscow State Technical University
- Novosibirsk State University
- Lomonosov Moscow State University
- V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
- Issue: Vol 210, No 10 (2019)
- Pages: 161-178
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133295
- DOI: https://doi.org/10.4213/sm9144
- ID: 133295
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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.
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About the authors
Vassily Olegovich Manturov
Bauman Moscow State Technical University; Novosibirsk State University
Email: vomanturov@yandex.ru
Doctor of physico-mathematical sciences
Denis Alexandrovich Fedoseev
Lomonosov Moscow State University; V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Email: denfedex@yandex.ru
Candidate of physico-mathematical sciences, Senior Researcher
References
- В. О. Мантуров, “Четность в теории узлов”, Матем. сб., 201:5 (2010), 65–110
- В. О. Мантуров, “Четность и кобордизмы свободных узлов”, Матем. сб., 203:2 (2012), 45–76
- V. Turaev, “Topology of words”, Proc. Lond. Math. Soc. (3), 95:2 (2007), 360–412
- В. О. Мантуров, “Почти классификация свободных узлов”, Докл. РАН, 452:4 (2013), 371–374
- L. H. Kauffman, V. O. Manturov, “A graphical construction of the $operatorname{sl}(3)$ invariant for virtual knots”, Quantum Topol., 5:4 (2014), 523–539
- M. W. Chrisman, V. O. Manturov, “Fibered knots and virtual knots”, J. Knot Theory Ramifications, 22:12 (2013), 1341003, 23 pp.
- D. A. Fedoseev, V. O. Manturov, “Parities on 2-knots and 2-links”, J. Knot Theory Ramifications, 25:14 (2016), 1650079, 24 pp.
- B. K. Winter, “Virtual links in arbitrary dimensions”, J. Knot Theory Ramifications, 24:14 (2015), 1550062, 38 pp.
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