7-colored 2-knot diagram with six colors

Kanako Oshiro; Shin Satoh

doi:10.32917/hmj/1395061557

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Home > Journals > Hiroshima Math. J. > Volume 44 > Issue 1 > Article

March 2014 7-colored 2-knot diagram with six colors

Kanako Oshiro, Shin Satoh

Hiroshima Math. J. 44(1): 63-74 (March 2014). DOI: 10.32917/hmj/1395061557

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Abstract

It is known that any 7-colorable knot in 3-space is presented by a diagram assigned by four of the seven colors. In this paper, we prove the existence of a 7-colorable 2-knot in 4-space such that any non-trivial 7-coloring requires at least six of the seven colors.

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Kanako Oshiro. Shin Satoh. "7-colored 2-knot diagram with six colors." Hiroshima Math. J. 44 (1) 63 - 74, March 2014. https://doi.org/10.32917/hmj/1395061557