### Abstract

For a knot K in the 3-sphere, by using the linking form on the first homology group of the double branched cover of the 3-sphere, we investigate some numerical invariants, 4-genus g* (K), nonorientable 4-genus γ*(K) and 4-dimensional clasp number c* (K), defined from the four-dimensional viewpoint. T. Shibuya gave an inequality g*(K) ≤ c*(K), and asked whether the equality holds or not. From our result in this paper, we find that the equality does not hold in general.

Original language | English |
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Pages (from-to) | 3693-3699 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 12 |

Publication status | Published - 2000 Dec 1 |

### Keywords

- 4-dimensional clasp number
- 4-genus
- Linking form

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Murakami, H., & Yasuhara, A. (2000). Four-genus and four-dimensional clasp number of a knot.

*Proceedings of the American Mathematical Society*,*128*(12), 3693-3699.