Multiflypes of rectangular diagrams of links-Reference-Cited by-同舟云学术

Multiflypes of rectangular diagrams of links

Published:2021-05 Issue:06 Volume:30 Page:2150038
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Dynnikov Ivan¹²^ORCID,Sokolova Vera³

Affiliation:

1. Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Street, Moscow 119991, Russia

2. St. Petersburg State University, Line 14th (Vasilyevsky Island), 29, Saint Petersburg 199178, Russia

3. Lomonosov Moscow State University, 1 Leninskije gory, Moscow 119991, Russia

Abstract

We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and are not obtained from one another by any sequence of “simpler” moves not increasing the complexity of the diagram along the way.

Funder

Russian Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216521500383

Reference9 articles.

1. Embedding knots and links in an open book I: Basic properties

2. Arc-presentations of links: Monotonic simplification

3. Algorithms for the complete decomposition of a closed $3$-manifold

4. Algorithms for essential surfaces in 3-manifolds

5. Theorie der Normalflächen: Ein Isotopiekriterium für den Kreisknoten

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