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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 6(444), Pages 195–196 (Mi umn9860)  

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

On the equivalence of Legendrian knots

I. A. Dynnikova, V. A. Shastinb

a Steklov Mathematical Institute of Russian Academy of Sciences
b Lomonosov Moscow State University

Abstract: It is shown that the pairs of Legendrian knot types associated with two rectangular diagrams of a knot coincide if and only if the given diagrams are related by a sequence of exchange moves, provided that the knots have no orientation-preserving symmetries. It is proved that there exists an annulus embedded in the three-sphere endowed with the standard contact structure such that the annulus is tangent to the contact structure along the boundary, and the two boundary components are not Legendrian isotopic.

Keywords: Legendrian knot, contact structure, rectangular diagram of a knot.

Funding Agency Grant Number
Russian Science Foundation 16-11-10260
Ministry of Education and Science of the Russian Federation


DOI: https://doi.org/10.4213/rm9860

Full text: PDF file (341 kB)
First page: PDF file
References: PDF file   HTML file

English version:
DOI: https://doi.org/10.1070/RM9860

Document Type: Article
MSC: 57M25, 57M50, 57R17
Presented: S. K. Lando
Accepted: 23.10.2018

Citation: I. A. Dynnikov, V. A. Shastin, “On the equivalence of Legendrian knots”, Uspekhi Mat. Nauk, 73:6(444) (2018), 195–196

Citation in format AMSBIB
\Bibitem{DynSha18}
\by I.~A.~Dynnikov, V.~A.~Shastin
\paper On the equivalence of Legendrian knots
\jour Uspekhi Mat. Nauk
\yr 2018
\vol 73
\issue 6(444)
\pages 195--196
\mathnet{http://mi.mathnet.ru/umn9860}
\crossref{https://doi.org/10.4213/rm9860}
\elib{http://elibrary.ru/item.asp?id=36448102}


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