Journal of the Mathematical Society of Japan

Sheet number and quandle-colored 2-knot

Shin SATOH

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Abstract

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.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 2 (2009), 579-606.

Dates
First available in Project Euclid: 13 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1242220723

Digital Object Identifier
doi:10.2969/jmsj/06120579

Zentralblatt MATH identifier
05573651

Mathematical Reviews number (MathSciNet)
MR2532902

Subjects
Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 57Q35: Embeddings and immersions

Keywords
2-knot quandle sheet number diagram triple point

Citation

SATOH, Shin. Sheet number and quandle-colored 2-knot. J. Math. Soc. Japan 61 (2009), no. 2, 579--606. doi:10.2969/jmsj/06120579. http://projecteuclid.org/euclid.jmsj/1242220723.


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