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April, 2009 Sheet number and quandle-colored 2-knot
J. Math. Soc. Japan 61(2): 579-606 (April, 2009). DOI: 10.2969/jmsj/06120579


A diagram of a 2-knot consists of a finite number of compact, connected surfaces called sheets. We prove that if a 2-knot admits a non-trivial coloring by some quandle, then any diagram of the 2-knot needs at least four sheets. Moreover, if a 2-knot admits a non-trivial 5- or 7-coloring, then any diagram needs at least five or six sheets, respectively.


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Shin SATOH. "Sheet number and quandle-colored 2-knot." J. Math. Soc. Japan 61 (2) 579 - 606, April, 2009.


Published: April, 2009
First available in Project Euclid: 13 May 2009

zbMATH: 1178.57020
MathSciNet: MR2532902
Digital Object Identifier: 10.2969/jmsj/06120579

Primary: 57Q45
Secondary: 57Q35

Keywords: 2-knot , diagram , quandle , sheet number , triple point

Rights: Copyright © 2009 Mathematical Society of Japan

Vol.61 • No. 2 • April, 2009
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