### Abstract

A 2-knot is (the isotopy class of) a 2-sphere smoothly embedded in 4-space. The apparent contour of a generic planar projection of a 2-knot divides the plane into several regions, and to each such region, we associate the number of sheets covering it. The total width of a 2-knot is defined to be the minimum of the sum of these numbers, where we take the minimum amongall generic planar projections of the given 2-knot. In this paper, we show that a 2-knot has total width eight if and only if it is an n-twist spun 2-bridge knot for some n ≠ ±1.

Original language | English |
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Pages (from-to) | 825-838 |

Number of pages | 14 |

Journal | Illinois Journal of Mathematics |

Volume | 52 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Saeki, O., & Takeda, Y. (2008). On 2-knots with total width eight.

*Illinois Journal of Mathematics*,*52*(3), 825-838. https://doi.org/10.1215/ijm/1254403717