.svg){kind=logo}
ON ELEMENTARY MOVES OF SINGULAR LEGENDRIAN KNOTS
Keywords:
Legendrian front, Legendrian knot, contact structure, Legendrian singular knot, singular knot, plane curve.DOI:
https://doi.org/10.17654/0972415X22001Abstract
We have two results. First, we give 96 generating sets of oriented singular Reidemeister moves; it is an answer to a question by Bataineh, Elhamdadi and Hajij who give a generating set of oriented singular Reidemeister moves using their computation. Second, in the theory of plane curve and Legendrian knots introduced by V. I. Arnold, we select which moves survive as those of Legendrian singular knots and fronts diagrammatically and explicitly.
Received: January 5, 2022
Accepted: February 18, 2022
References
V. I. Arnold, Plane curves, their invariants, perestroikas and classifications, Singularities and bifurcations, with an appendix by F. Aicardi, Vol. 21 of Adv. Soviet Math., Amer. Math. Soc., Providence, RI, 1994, pp. 33-91.
Khaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij and William Youmans, Generating sets of Reidemeister moves of oriented singular links and quandles, J. Knot Theory Ramifications 27(14) (2018), 15, 1850064.
S. Chmutov and V. Goryunov, Polynomial invariants of Legendrian links and plane fronts, Topics in singularity theory, Vol. 180 of Amer. Math. Soc. Transl. Ser. 2, Amer. Math. Soc., Providence, RI, 1997, pp. 25-43.
V. Goryunov, Vassiliev type invariants in Arnold’s J+-theory of plane curves without direct self-tangencies, Topology 37(3) (1998), 603-620.
Kenta Hayano and Noboru Ito, A new aspect of the Arnold invariant from a global view-point, Indiana Univ. Math. J. 64(5) (2015), 1343-1357.
Michael Polyak, Minimal generating sets of Reidemeister moves, Quantum Topol. 1(4) (2010), 399-411.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
Publication count: 383
Google h-index: 15 
Downloads: 101100+