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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 476, Pages 165–186
(Mi znsl6733)
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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.
Received: 01.11.2018
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
Linking options:
https://www.mathnet.ru/eng/znsl6733 https://www.mathnet.ru/eng/znsl/v476/p165
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Statistics & downloads: |
Abstract page: | 98 | Full-text PDF : | 63 | References: | 18 |
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