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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. 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

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.

UDC: 515.164.634

Received: 01.11.2018



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