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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 476, Pages 165–186 (Mi znsl6733)  

Planar diagrams of surface-links

A. V. Tikhonov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
References:
Abstract: The paper discusses planar diagrams (called charts by S. Kamada) for embedded (in $\Re^{4}$) or mapped in general position (in $\Re^{3}$) surfaces and shows that the diagrams are very suitable for dealing with such surfaces and for easy construction of surface mappings with specific properties. A series of examples is constructed, including an example of a sphere immersion with two triple points and a unique double line.
Key words and phrases: surface-knot, surface-link, diagram, planar, chart, surface, embedded surface, immersed surface, Boy surface, double line, fold line, triple point, branch point, Whitney's umbrella, cusp.
Received: 01.11.2018
Document Type: Article
UDC: 515.164.634
Language: Russian
Citation: A. V. Tikhonov, “Planar diagrams of surface-links”, Geometry and topology. Part 13, Zap. Nauchn. Sem. POMI, 476, POMI, St. Petersburg, 2018, 165–186
Citation in format AMSBIB
\Bibitem{Tik18}
\by A.~V.~Tikhonov
\paper Planar diagrams of surface-links
\inbook Geometry and topology. Part~13
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 476
\pages 165--186
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6733}
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  • https://www.mathnet.ru/eng/znsl6733
  • https://www.mathnet.ru/eng/znsl/v476/p165
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